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Ele147

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  • 1.  ‫א‬‫א‬‫א‬ ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹] ‫א‬‫א‬‫א‬‫א‬   ‫א‬ ‫א‬١٤٧
  • 2.  ‫٧٤١ א‬ ‫א‬  ‫א‬ ‫א‬     W،،‫א‬‫א‬،‫א‬   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬ ‫א‬  ،‫א‬   ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬        ،‫א‬ ‫א‬‫א‬   ‫א‬  ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬   ‫א‬    ،   ‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬      ‫א‬  ‫א‬   ،‫א‬     K‫א‬‫א‬،‫א‬‫א‬  ?    ?  ?  ‫א‬ ? ‫א‬ ‫א‬    K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ،‫א‬،‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬  ،‫א‬‫א‬‫א‬‫א‬  K‫א‬ ‫א‬‫א‬‫א‬‫א‬       
  • 3.  ‫٧٤١ א‬ ‫א‬  ‫א‬       ،KKK‫א‬‫א‬‫א‬‫א‬ ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   K‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬،‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬  ،‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬    K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬      K‫א‬‫א‬،‫א‬،‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬،  ‫א‬،‫א‬‫א‬‫א‬‫א‬    K‫א‬‫א‬  KKKKKK،‫א‬ 
  • 4.  ‫א‬‫א‬‫א‬ ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹] ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬ ‫א‬‫א‬ ١
  • 5. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬   ‫א‬‫א‬‫א‬   W‫א‬‫א‬ K‫א‬‫א‬‫א‬ • K‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬ K‫א‬‫א‬‫א‬‫א‬‫• א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬ • -١-
  • 6. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬   Introduction١J ١   ‫א‬   (Binary Number System)‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬  K(Digital Electronic Circuits) ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬ K‫א‬(Decimal Number System)  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K(Hexadecimal Numbering System)‫א‬‫א‬‫א‬(Octal Number System)  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   W‫א‬‫א‬‫א‬‫א‬‫א‬   K‫א‬K١  K‫א‬‫א‬‫א‬K٢  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K٣  K‫א‬‫א‬‫א‬‫א‬K٤  K‫א‬‫א‬‫א‬‫א‬‫א‬K٥ (Digit)‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬(Symbol)،(Number)‫א‬ ‫א‬‫א‬‫א‬(0,1,2,3,4, ... , 8,9)،‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬ ،‫א‬(123)‫א‬‫א‬‫א‬(14)‫א‬‫א‬‫א‬،‫א‬ ‫א‬‫א‬‫א‬‫א‬(1,4)(14)‫א‬‫א‬‫א‬‫א‬  ‫א‬(6)(1,2,3)(123)  K‫א‬ -٢-
  • 7. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬   Decimal Numbering System‫א‬‫א‬‫א‬٢J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  (10)‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬  (10)10‫א‬  K0,1,2,3,4,5,6,7,8,9  (128)‫א‬‫א‬(Positional Weight)‫א‬‫א‬ ،‫א‬ E‫א‬F‫א‬‫א‬(8)‫א‬‫א‬  ‫א‬(2)‫א‬‫א‬،(8 × 1 = 8) 1‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬E‫א‬‫א‬F‫א‬  E‫א‬F‫א‬‫א‬E1F‫א‬‫א‬،(2 × 10 = 20)10  ‫א‬K(1 × 100 = 100) 100‫א‬‫א‬‫א‬  W،‫א‬‫א‬‫א‬‫א‬‫א‬  (1 × 100) + (2 × 10) + (8 × 1) = 100 + 20 + 8 = 128 ‫א‬‫א‬E10F‫א‬‫א‬‫א‬  W100 = 110 ‫א‬‫א‬‫א‬‫א‬  ........ 105 104 103 102 101 100  W128‫א‬ 1     (128)10 2 8  ‫א‬‫א‬‫א‬‫א‬ 102 1 × 102 = 100 101 100 + 2 × 101 + 8 × 100 + 20 + 8    ‫א‬10‫א‬‫א‬(128)‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬(Subscript)‫א‬ -٣-
  • 8. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W10-1‫א‬  102 101 100 • 10-1 10-2 10-3 ........  ‫א‬‫א‬ (Decimal Point)   Binary Numbering System‫א‬‫א‬‫א‬٣J ١  (2)(2) ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ .(1,0)‫א‬ ..... 2 4 ..... 16 2 8 3 2 4 2 2 2 1  W(2) 0 2 1  W‫א‬‫א‬‫א‬‫א‬  W(11001)‫א‬‫א‬  24 23 22 21 20 1 1 0 0 1 = (1 × 24) + (1 × 23) + (0 × 22) + (0 × 21) + (1 × 20) = 16 + 8 + 0 + 0 + 1 = (25)10 ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬(2)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   K(11001)2‫א‬‫א‬   W‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ (Binary Digit)‫א‬(Bit)‫א‬‫ א‬W(Bit)‫א‬‫א‬■  ‫א‬E‫א‬F‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬   ‫א‬(4-bits)(1001)2‫א‬،‫א‬‫א‬  K‫א‬(7-bits)(1101101)2 -٤-
  • 9. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  ‫א‬‫א‬ W(Number of Binary Combinations)‫א‬‫א‬■  K(bits)‫א‬‫א‬‫א‬‫א‬ N = 2n  W‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬= N W  (bits)‫א‬= n  W‫א‬‫א‬(2)‫א‬‫א‬ N = 22 = 4 N = 23 = 8 4 N = 2 = 16  W‫א‬‫א‬(3)‫א‬‫א‬  W‫א‬‫א‬(4)‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬W(Bit)‫א‬‫א‬■ ‫א‬(1)(1)20‫א‬‫א‬‫א‬‫א‬ 22‫א‬(2)21‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬(4)  ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬،‫א‬‫א‬ ‫א‬‫א‬‫א‬(LSB)‫א‬‫א‬(Least Significant Bit)   K(MSB)‫א‬‫א‬ (Most Significant Bit) ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬(Bit)‫א‬‫א‬WEByte) ‫א‬ ■  (0)‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬EF‫א‬‫א‬(1)‫א‬‫א‬  ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬  ‫א‬  K -٥-
  • 10. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  (Byte)‫א‬ ‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬K 1 byte = 8 bits Decimal-to-Binary Conversion ‫א‬‫א‬‫א‬‫א‬‫א‬٤J ١ ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ (2)‫א‬‫א‬‫א‬‫א‬(Sum of Weights Method) ‫א‬‫א‬‫א‬ (Repeated Division–by–2 Method)  K‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٤J ١ ‫א‬،214‫א‬،‫א‬(14)10‫א‬‫א‬   .(0)‫א‬2‫א‬ ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬،(MSB)‫א‬‫א‬‫א‬‫א‬(LSB)  W ‫ א‬ 14 ÷ 2 = 7 7 ÷2=3 3 ÷2=1 1 ÷2=0  0 1 1 1        1 1 1 0 (MSB) (LSB)  W (14)10 = (1110)2   K‫א‬(25)10‫א‬‫א‬WE١J ١F  W‫א‬ -٦-
  • 11. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬   ‫א‬ 25 ÷ 2 = 12 12 ÷ 2 = 6 6 ÷2=3 3 ÷2=1 1 ÷2=0 1 0 0 1 1 (LSB) (MSB)  W‫א‬ (14)10 = (1110)2  K‫א‬(87)10‫א‬‫א‬WE٢J ١F   W‫א‬ ‫א‬ 87 ÷ 2 = 43 43 ÷ 2 = 21 21 ÷ 2 = 10 10 ÷ 2 = 5 5 ÷2=2 2 ÷2=1 1 ÷2=0 1 1 1 0 1 0 1 (LSB) (MSB)  W‫א‬ (87)10 = (1010111)2  ‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٤J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ (Decimal Fractions)‫א‬‫א‬‫א‬K(2)‫א‬‫א‬  K(2)‫א‬‫א‬ 0.3125‫א‬‫א‬‫א‬‫א‬(0.3125)‫א‬‫א‬  ‫א‬‫א‬‫א‬(2)‫א‬‫א‬‫א‬،(2) (Carried Digits)‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬(0)  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬K(LSB)‫א‬‫א‬‫א‬(MSB)‫א‬‫א‬‫א‬K‫א‬  W  -٧-
  • 12. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬   ‫א‬ 0.3125 × 2 = 0.625 0 0.625 × 2 = 1.25 1 0.25 × 2 = 0.5 0 0.5  × 2 = 1.00 1 (LSB) 1 0 1 0 (MSB) ‫א‬   ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬   KEF  K‫א‬(39.25)10‫א‬‫א‬WE٣J ١F  W(2)‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬   ‫א‬ 39 ÷ 2 = 19 19 ÷ 2 = 9 9 ÷2=4 4 ÷2=2 2 ÷2=1 1 ÷2=0  1 1 1 0 0 1 (LSB) (MSB)  W‫א‬     W(2)‫א‬‫א‬‫א‬‫א‬ (39)10 = (100111) 0.25 × 2 = 0.5 0.5 × 2 = 1.00   ‫א‬ 0 1  W (0.25)10 = (0.01)2  W‫א‬‫א‬‫א‬ -٨-
  • 13. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  (39.25)10 = (100111.01)2  Binary-to-Decimal Conversion ‫א‬‫א‬‫א‬‫א‬‫א‬٥J ١ (2)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬K‫א‬16, 8, 4, 2, 1‫א‬‫א‬‫א‬‫א‬   (1)‫א‬‫א‬(Bit)‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   W‫א‬‫א‬‫א‬  K‫א‬1101001‫א‬‫א‬WE٤J ١F  ‫א‬‫א‬‫א‬‫א‬(1)W‫א‬ 26 25 24 23 22 21 20 : ‫א‬ 1 1 0 1 0  W 0 1 : ‫א‬‫א‬ = 1 × 26 + 1 × 25 + 0 × 24 + 1 × 23 + 0 × 22 + 0 × 21 + 1 × 20 = 64 + 32 + 8 + 1 = (105)10 (Bits ) ‫ﺧﺎﻧ ﺎت‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬ (Binary Point)‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(Decimal Point)‫א‬‫א‬ ……24 23 22 21 20 • 2-1 2-2 2-3 2-4…….  W  ‫א‬‫א‬   K‫א‬(0.1011)2‫א‬‫א‬‫א‬WE٥J ١F  • 2-1 0• 1 2-2 0 2-3 1  W‫א‬ 2-4 1 ∴(0.1011)2 = 1 × 2-1 + 1 × 2-3 + 1 × 2-4 = 0.5 + 0.125 + 0.0625 = (0.6875)10 -٩-
  • 14. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬   Binary Arithmetic ‫א‬‫א‬‫א‬‫א‬٦J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬  Binary Addition ‫א‬‫א‬١J ٦J ١ ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ 0 0 1 1 + + + + 0 1 0 1 = = = = 0 1 1 0 carry E‫א‬F 1 ⇒ = 10  W(Binary Digits) ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬(1)‫א‬‫א‬،(2)1 + 1 = 10  W‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬  K011, 110‫א‬‫א‬WE٦J ١F   W‫א‬‫א‬‫א‬‫א‬W‫א‬ 1 6 +3 EF 9 4 +3 EF 7 + 1 1 1 0 0  1 1 0 0 1 1  K011, 100‫א‬‫א‬‫א‬WE٧J ١F  1 0 1 0 1 1 0 1 1 W‫א‬  Binary Subtraction ‫א‬‫א‬٢J ٦J ١  W‫א‬‫א‬  K‫א‬‫א‬‫א‬J ١ K‫א‬‫א‬J ٢ -١٠-
  • 15. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  ‫א‬K‫א‬‫א‬،‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E‫א‬F‫א‬‫א‬  0–0=0 1–0=1 1–1=0 0–1=1  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ (1) ‫א‬ (1)‫א‬  W‫א‬‫א‬‫א‬  K‫א‬‫א‬ • W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬ K(0)‫א‬(1)(1)(0)(0) K(1)‫א‬(1)(0) ‫א‬F‫א‬‫א‬(0)(1)‫א‬(0)(1) K(0)(1)(1)E K‫א‬‫א‬‫א‬‫א‬‫א‬  K(011)‫א‬‫א‬(101)‫א‬‫א‬‫א‬WE٨J ١F  (0)‫א‬(1)‫א‬ ‫א‬‫א‬(1)‫א‬ (1)(10)‫א‬ 0 1  –0 0 (1)‫א‬  1 0       1 ‫א‬ 1 1 1 0 ‫א‬    W‫א‬       ‫א‬‫א‬‫א‬‫א‬‫א‬٧J ١ One's and Two's Complements of Binary Numbers ‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬(1)(0)(0)(1)‫א‬‫א‬  W‫א‬ -١١-
  • 16. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0  ‫א‬‫א‬ ‫א‬‫א‬   W‫א‬‫א‬‫א‬‫א‬    ‫א‬ (1)‫א‬K‫א‬‫א‬W‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬ 1 +‫א‬‫א‬Z‫א‬‫א‬ K10110011‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬(1)‫א‬‫א‬‫א‬ 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 + 1 0 1 0 0 1 1 1 0  ‫א‬‫א‬  ‫א‬‫א‬   ‫א‬‫א‬  (1)   ‫א‬‫א‬(LSB)‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬   ‫א‬‫א‬(0) ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬F‫א‬  ،E‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬    W‫א‬‫א‬(10101101)2‫א‬‫א‬ ‫א‬‫א‬ 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 1  ‫א‬‫א‬  ‫א‬‫א‬     Representation of Signed Numbers‫א‬‫א‬‫א‬‫א‬٨J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  (1)،‫א‬(0)‫א‬،‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬  -١٢-
  • 17. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  ‫א‬‫א‬ (Sign Bit)‫א‬‫א‬‫א‬‫א‬  .(Magnitude) ‫א‬‫א‬W ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   .(2's Complement)‫א‬‫א‬ (1's Complement) ‫א‬‫א‬(Sign-Magnitude)  (Sign-Magnitude System) ‫א‬‫א‬١J ٨J ١ ‫א‬‫א‬‫א‬(Bit)‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  (+23)‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬ 0 0 0 1 0 1 1 1 ‫א‬ (Sign Bit)    ‫א‬‫א‬     (Magnitude Bits)  W ‫)32-( ﻓﺈﻧﻨﺎ‬‫א‬‫א‬     1 0 0 1 0 0 1 1 1  K‫א‬(–23) ، (+23)‫א‬‫א‬‫א‬  (1's Complement System) ‫א‬‫א‬٢J ٨J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬  ‫א‬‫א‬‫א‬(–23) ‫א‬‫א‬K‫א‬ 00010111  1 1 1 0 1 0 0 0 (+23)‫א‬ (–23)‫א‬  W   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬  -١٣-
  • 18. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬   (2's Complement)‫א‬‫א‬٣J ٨J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬    W(+23)‫א‬‫א‬‫א‬(-23)‫א‬‫א‬ 00010111  1 1 1 0 1 0 0 1 (+23)‫א‬ (-23)‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   Arithmetic Operations with Signed Numbers‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٩J ١ ،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬KE٦J ١F‫א‬‫א‬، ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬    W‫א‬  K‫א‬‫א‬‫א‬‫א‬11111010‫א‬‫א‬00001110‫א‬‫א‬‫א‬WE٩J ١F    W‫א‬W‫א‬ 14 – (– 6) = 14 + 6 = 20  W‫א‬ 00001110 + 00000110 00010100 ‫א‬(+14) ‫א‬‫א‬(+6) ‫א‬(+20)  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬WE١٠J ١F  (00001000)2 – (00000100)2  W‫א‬W‫א‬ 8 – 4 = 8 + (-4) = 4  W   -١٤-
  • 19. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  00001000 +11111100 100000100  ‫א‬ ‫א‬(+8) ‫א‬‫א‬(-4) ‫א‬(+4)  (Discard carry)  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬WE١١J ١F  (11100111)2 – (00001001)2  W‫א‬W‫א‬ – 25 – (+9) = – 25 – 9 = -34 11100111 +11110111 111011110  ‫א‬  W ‫א‬(-25) ‫א‬‫א‬(-9) ‫)43-( א‬  (Discard carry)  The Octal Numbering System‫א‬‫א‬‫א‬١٠J ١ (8)(8)‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(0,1,2,3,4,5,6,7) ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  Octal-to-Decimal Conversion ‫א‬‫א‬‫א‬‫א‬١J ١٠J ١ (8)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬،‫א‬(……83  82 81 80) ‫א‬‫א‬‫א‬‫א‬‫א‬K،‫א‬(…... 512 64 8 1)  ‫א‬‫א‬(2275)8‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬   W ‫א‬‫א‬: 83 82 81 80 ‫א‬‫2 : א‬ 2 7 5 ∴ (2275)8 = (2 × 83) + (2 × 82) + (7 × 81) + (5 × 80) = (2 × 512) + (2 × 64) + (7 × 8) + (5 × 1) = 1024 + 128 + 56 + 5 = (1213)10 -١٥-
  • 20. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬   Decimal–to–Octal Conversion ‫א‬‫א‬‫א‬‫א‬٢J ١٠J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،(8)‫א‬  K(2)(8)  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٢J ١٠J ١ (8)150‫א‬‫א‬‫א‬(150)10‫א‬‫א‬   .(0)‫א‬(8)‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ {Most Significant Digit} ‫א‬‫א‬‫א‬‫א‬{Least Significant Digit} (LSD)  W‫א‬‫א‬(MSD)   ‫א‬ 150 ÷ 8 = 18 18 ÷ 8 = 2 2 ÷8=0 6 2 2 (LSD) (MSD)  W‫א‬ (150)10 = (226)8  K‫א‬‫א‬(624)10‫א‬‫א‬WE١٢J ١F    ‫א‬ 624 ÷ 8 = 78 78 ÷ 8 = 9 9 ÷8=1 1 ÷8=0 0 6 1 1 W‫א‬ (LSD) (MSD)  W‫א‬ (624)10 = (611)8  ‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٢J ١٠J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬(0.265)‫א‬‫א‬K(8)‫א‬‫א‬  ‫א‬‫א‬‫א‬ ،(8)0.265‫א‬‫א‬ -١٦-
  • 21. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  ‫א‬‫א‬‫א‬(0)‫א‬‫א‬‫א‬(8) K‫א‬‫א‬‫א‬‫א‬‫( א‬Carried Digits)‫א‬‫א‬K‫א‬  ‫א‬(MSD)‫א‬‫א‬(LSD)‫א‬‫א‬‫א‬    W  ‫اﻟﺤﺎﻣﻞ‬ 0.265 × 8 = 2.12 0.12 × 8 = 0.96 0.96 × 8 = 7.68 0.68 × 8 = 5.44 0.44 × 8 = 3.52 0.52 × 8 = 4.16 2 (MSD) 0 7 5 3 4 (LSD)  W‫א‬‫א‬(6)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ (0.625)10 = (0.207534)8  K‫א‬‫א‬(44.5625)10‫א‬‫א‬WE١٣J ١F   K(8)‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬   ‫א‬ 44 ÷ 8 = 5 5 ÷8=0 4 5 (LSD) (MSD)  W‫א‬ (44)10 = (54)8  W(8)‫א‬‫א‬‫א‬‫א‬  ‫اﻟﺤﺎﻣﻞ‬ 0.5625 × 8 = 4.5 0.5 × 8 = 4.00 4 4  W (0.5625)10 = (0.44)8  W‫א‬‫א‬‫א‬ (44.5625)10 = (54.44)8 -١٧-
  • 22. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬   Octal-to-Decimal Conversion ‫א‬‫א‬‫א‬‫א‬‫א‬٣J ١٠J ١ (8)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬K‫א‬4096, 512, 64, 8, 1‫א‬‫א‬‫א‬‫א‬ ‫א‬(Digit)‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬    K‫א‬‫א‬  K‫א‬‫א‬(324)8‫א‬‫א‬WE١٤J ١F   W‫א‬ ‫א‬‫א‬: 82 81 80 ‫א‬‫א‬: 3 2 4 ∴ (324)8 = (3 × 82) + (2 × 81) + (4 × 80) = (3 × 64) + (2 × 8) + (4 × 1) = 192 + 16 + 4 = (212)10 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ (Octal Point) ‫א‬‫א‬‫א‬   ……84 83 82 81  W‫א‬‫א‬‫א‬‫א‬ 80 • 8-1 8-2 8-3 8-4…….  ‫א‬‫א‬  K‫א‬‫א‬(567.14)8‫א‬‫א‬WE١٥J ١F  ‫א‬‫א‬: 82 81 80 • 8-1 8-2 ‫א‬‫א‬: 5 6 7 • 1 4 ∴ (567.14)8 = (5 × 82) + (6 × 81) + (7 × 80) + (1 × 8-1) + (4 × 8-2) = (5 × 64) + (6 × 8) + (7 × 1) + (1 × 0.125) + (4 × 0.015625) = 320 + 480 + 7 + 0.125 + 0.0625 = (375.1875)10 -١٨-  W‫א‬
  • 23. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬   Octal-to-Binary Conversion ‫א‬‫א‬‫א‬‫א‬‫א‬٤J ١٠J ١ ‫א‬‫א‬ (Digit) ‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬ ،(3-bits)   KE١J ١F‫א‬ 0  ‫א‬‫א‬ 1 2 3 4 5 6 7 000 ‫א‬‫א‬ 001 010 011 100 101 110 111  K‫א‬‫א‬‫א‬E١J ١F  ‫א‬‫א‬‫א‬  K‫א‬  K‫א‬‫א‬(357)8‫א‬‫א‬WE١٦J ١F  (357)8 = 3 011 5  W‫א‬ 7 101 111 = (011101111)2  K‫א‬(1276.543)8‫א‬‫א‬WE١٧J ١F  (1276.543)8 = 1 001 2 7 6 • 5  W‫א‬ 4 3 010 111 110 • 101 100 011 = (1010111110.101100011)2  K‫א‬‫א‬‫א‬  Binary-to-Octal Conversion ‫א‬‫א‬‫א‬‫א‬‫א‬٥J ١٠J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ J –‫א‬‫א‬K‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  -١٩-
  • 24. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  ‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬(1011001011100.00101)2‫א‬‫א‬WE١٨J ١F  001 1 011 3 001 1 011 3 100 4 • 001 010 •  W‫א‬  1 2 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ (1011001011100.00101)2 = (13134.12)8  Arithmetic Operations in Octal System  W ‫א‬‫א‬‫א‬‫א‬٦J ١٠J ١  K‫א‬‫א‬‫א‬‫א‬ Octal Addition ‫א‬‫א‬١J ٦J ١٠J ١  ‫א‬(0,9)‫א‬–‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬(10)‫א‬(9)‫א‬‫א‬‫א‬،(9)  ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬    ‫א‬‫א‬(10)‫א‬‫א‬(0,1)‫א‬‫א‬‫א‬‫א‬ ‫א‬K‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬(7)‫א‬‫א‬‫א‬‫א‬–‫א‬‫א‬‫א‬(7) (11, 12, 13, 14, 15, 16, 17)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬(10)  K‫א‬ (30, 31, ..... , 37)‫א‬‫א‬‫א‬(20,21, 22, ...... , 27) ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬E٢J ١F ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬ -٢٠-
  • 25. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •  K(7) (2)‫א‬‫א‬(7)‫א‬‫א‬‫א‬ • ‫א‬(7)‫א‬(8)‫א‬‫א‬(7)‫א‬‫א‬،‫א‬ ‫א‬‫א‬(2)‫א‬(10)‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬ KE‫א‬‫א‬‫א‬ 7 7 10 11 12 13 14 15 16 6 6 7 10 11 12 13 14 15 5 5 6 7 10 11 12 13 14 4 4 5 6 7 10 11 12 13 3 3 4 5 6 7 10 11 12 2 2 3 4 5 6 7 10 11 1 1 2 3 4 5 6 7 10 0 0 1 2 3 4 5 6 7 + 0 1 2 3 4 5 6 7  K‫א‬‫א‬‫א‬E٢J ١F    K(42)8، (38)8‫א‬‫א‬‫א‬WE١٩J ١F  34 + 42 76  W‫א‬‫א‬W‫א‬ ∴(34)8 + (42)8 = (76)8  (7)(3,4)(4,2)‫א‬‫א‬  K‫א‬ -٢١-
  • 26. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬   K(63)8،(56)8‫א‬‫א‬‫א‬WE٢٠J ١F  W‫א‬ 5 6 + 6 3 1 4 1 ‫א‬(2)(7)‫א‬‫א‬‫א‬   K‫א‬‫א‬(Carry)‫א‬ Subtraction in Octal System‫א‬‫א‬‫א‬٢J ٦J ١٠J ١  W‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬ •  ‫א‬‫א‬‫א‬–‫א‬‫א‬(1)‫א‬‫א‬‫א‬ • ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(8) K‫א‬‫א‬ (657)8 – (346)8 6 5 7 – 3 4 6 3 1 1 ‫א‬ W‫א‬‫א‬WE٢١J ١F   W‫א‬W‫א‬ ‫א‬ ∴(657)8 – (346)8 = (311)8 ‫א‬‫א‬‫א‬   K‫א‬‫א‬  (732)8 – (634)8W‫א‬‫א‬WE٢٢J ١F  W‫א‬ 6 2 1 7 3 2 – 6 3 4 0 7 6 ‫א‬ ‫א‬ ∴(732)8 – (634)8 = (76)8 -٢٢-
  • 27. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  ‫א‬‫א‬(2)(4)‫א‬‫א‬ ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(1)‫א‬  K‫א‬‫א‬(2)(3)‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬١١J ١ (16)‫א‬‫א‬‫א‬‫א‬‫א‬ Hexadecimal Numbering System ‫א‬(0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F) ‫א‬(16)    K‫א‬(10, 11, 12, 13, 14, 15)‫א‬‫א‬(A,B,C,D,E,F) Hexadecimal–to–Decimal Conversion‫א‬‫א‬‫א‬‫א‬١J ١١J ١ 16‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ (... 4096 256 16 1 )‫א‬‫א‬‫א‬‫א‬(……163 162 161 160)  W(522.39)16‫א‬‫א‬‫א‬ ‫א‬‫א‬: 162 161 160 • 16-1 16-2 ‫א‬‫א‬: 5 2 2 • 3  9 ∴ (522.39)16 = (5 × 162) + (2 × 161) + (2 × 160) + (3 × 16-1) + (9 × 16-2) = (5 × 256) + (2 × 16) + (2 × 1) + (3 × 0.0625) + (9 × 0.0039062) = 1280 + 32 + 2 + 0.1875 + 0.0351558 = (1314.222655)10 ‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   K‫א‬‫א‬(16)‫א‬‫א‬‫א‬  Decimal-to-Hexadecimal Conversion ‫א‬‫א‬‫א‬‫א‬٢J ١١J ١ (16)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  .(2)(8)(16)‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٢J ١١J ١ (16)97‫א‬‫א‬‫א‬(97)10‫א‬‫א‬  ‫א‬ (16)‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬K(0)  -٢٣-
  • 28. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬K‫א‬‫א‬  W‫א‬‫א‬(MSD)‫א‬‫א‬(LSD)   ‫א‬ 97 ÷ 16 = 6 6 ÷ 16 = 0 1 6 (LSD) (MSD)  W‫א‬ (97)10 = (61)16  K‫א‬‫א‬‫א‬(314)10‫א‬‫א‬WE٢٣J ١F   ‫א‬ 314 ÷ 16 = 19 19 ÷ 16 = 1 1 ÷ 16 = 0 A 3 1 W‫א‬ (LSD) (MSD)  W‫א‬ (314)10 = (13A)16  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٢J ١١J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ (0.78125)10‫א‬‫א‬K(16)‫א‬‫א‬‫א‬  ‫א‬‫א‬(16)‫א‬‫א‬‫א‬‫א‬‫א‬ (0)‫א‬‫א‬‫א‬‫א‬‫א‬(16)‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬ (MSD)‫א‬‫א‬‫א‬(LSD)‫א‬‫א‬‫א‬K‫א‬‫א‬   ‫اﻟﺤﺎﻣﻞ‬ 0.78125 × 16 = 12.5 0.5 × 16 = 8.00  W‫א‬ C 8  W ∴(0.78125)10 = (0.C8)16 -٢٤-
  • 29. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬   K‫א‬‫א‬(329.52)10‫א‬‫א‬WE٢٤J ١F   W16‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬   ‫א‬ 329 ÷ 16 = 20 20 ÷ 16 = 1 1 ÷ 16 = 0 9 4 1 (LSD) (MSD)  W‫א‬ ∴(329)10 = (149)16  W‫א‬‫א‬(16)‫א‬‫א‬  ‫א‬ 0.52 × 16 = 8.32 0.32 × 16 = 5.12 0.12 × 16 = 1.92 0.92 × 16 = 14.72 0.72 × 16 = 11.52 0.52 × 16 = 8.32 8 (MSD) 5 1 E B 8 (LSD)   W‫א‬(6)‫א‬‫א‬‫א‬‫א‬‫א‬ (0.52)10 = (0.851EB8)16  W‫א‬‫א‬‫א‬ (329.52)10 = (149.851EB8)16 Hexadecimal-to-Decimal Conversion ‫א‬‫א‬‫א‬‫א‬٣J ١١J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬K(16)‫א‬   W‫א‬‫א‬K‫א‬‫א‬  K‫א‬‫א‬(F9B)16‫א‬‫א‬‫א‬WE٢٥J ١F   W‫א‬ ‫א‬‫א‬: 162 161 160 ‫א‬‫א‬: F 9 B -٢٥-
  • 30. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  ∴ (F9B)16 = (F × 162) + (9 × 161) + (B × 160) = (15 × 256) + (9 × 16) + (11 × 1) = 3840 + 144 + 11 = (3995)10 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬ ……163 162 161 160 • 16-1 16-2 16-3 …….   ‫א‬‫א‬   K‫א‬(A15.C3)16‫א‬‫א‬‫א‬WE٢٦J ١F ‫א‬‫א‬: 162 161 160 • 16-1 16-2 ‫א‬‫א‬: A 1 5 • C  W‫א‬ 3 ∴ (A15.C3)16 = (A × 162) + (1 × 161) + (5 × 160) + (C × 16-1) + (3 × 16-2) = (10 × 256) + (1 × 16) + (5 × 1) + (12 × 0.0625) + (3 × 0.0039062) = 2560 + 16 + 5 + 0.75 + 0.0117186 = (2581.7617)10 Hexadecimal-to-Binary Conversion‫א‬‫א‬‫א‬‫א‬‫א‬٤J ١١J ١ (0,1,2,……,9,A,B,C,D,E,F)‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬(A,B,C,D,E,F)‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬K(10,11,12,13,14,15) (4-bits)‫א‬‫א‬‫א‬،‫א‬‫א‬  WE٣J ١F‫א‬‫א‬  K‫א‬(3A5)16‫א‬WE٢٧J ١F  (3A5)16 = 3 0011 A 5  W‫א‬ 1010 0101 = (001110100101)2  -٢٦-
  • 31. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  ‫א‬‫א‬‫א‬  ‫א‬‫א‬ 0 1 2 3 4 5 6 7 8 9 A B C D E F  ‫א‬‫א‬ 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  K‫א‬‫א‬‫א‬E٣J ١F    K‫א‬‫א‬(B35.D1)16‫א‬WE٢٨J ١F  (B35.D1)16 = B 3 5 •  W‫א‬ D 1 1011 0011 0101 • 1101 0001 = (101100110101.11010001)2 Binary-to-Hexadecimal Conversion‫א‬‫א‬‫א‬‫א‬‫א‬٥J ١١J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬ -٢٧-
  • 32. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬   K‫א‬‫א‬(110111101.101001)2‫א‬‫א‬WE٢٩J ١F   W‫א‬ 0001 1011 1101 • 1010 0100 1 B • D  A 4  K‫א‬‫א‬‫א‬ ∴(110111101.101001)2 = (1BD.A4)16  K‫א‬‫א‬‫א‬(11010010011.011001)2‫א‬‫א‬WE٣٠J ١F   W‫א‬ 0001 1010 1011 • 0110 1000 1 A  • B 6 8 ∴(11010010011.011001)2 = (1AB.68)16 Hexadecimal-to-Octal Conversion‫א‬‫א‬‫א‬‫א‬‫א‬ ٦J ١١J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬  K‫א‬‫א‬(AB3E.87D)16‫א‬WE٣١J ١F  W‫א‬‫א‬‫א‬‫א‬W‫א‬ (AB3E.87D)16 = (1010101100111110.100001111101)2 ‫א‬‫א‬‫א‬‫א‬‫א‬  W 001 010 101 001 111 110 • 100 001 111 101 1 2 5 4 7 6 •   4 1 7 5  K‫א‬‫א‬ ∴(AB3E.87D)16 = (125476.4175)8 -٢٨-
  • 33. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  Octal-to-Hexadecimal Conversion‫א‬‫א‬‫א‬‫א‬‫א‬ ٧J ١١J ١ ‫א‬‫א‬‫א‬‫א‬ ‫א‬،  ،‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬(25.342)8‫א‬‫א‬WE٣٢J ١F  ∴(25.342)8 = (010101.011100010)2  W‫א‬‫א‬W‫א‬   W‫א‬‫א‬‫א‬‫א‬‫א‬ 0001 0101 • 0111 0001 1 2 •  7 1  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ∴(25.342)8 = (12.71)16  ‫א‬‫א‬‫א‬‫א‬‫א‬٨J ١١J ١ Arithmetic Operations in Hexadecimal System  K‫א‬‫א‬‫א‬‫א‬ Hexadecimal Addition‫א‬‫א‬‫א‬‫א‬١J ٨J ١١J ١ (F)‫א‬‫א‬‫א‬‫א‬(0,F)‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(10)‫א‬‫א‬،(10) ‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ (B)16(9)16‫א‬‫א‬(A)16‫א‬(9)16‫א‬‫א‬  K(F)16‫א‬ ‫א‬‫א‬(10)16‫א‬(F)16‫א‬‫א‬ ‫א‬‫א‬‫א‬(11)16‫א‬(F)16‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬ -٢٩-
  • 34. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  ،‫א‬‫א‬‫א‬‫א‬E٤J ١F‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬ F F 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E E D C B E D C B F E D C 10 F E D 11 10 F E 12 11 10 F 13 12 11 10 14 13 12 11 15 14 13 12 16 15 14 13 17 16 15 14 18 17 16 15 19 18 17 16 1A 19 18 17 1B 1A 19 18 1C 1B 1A 19 1D 1C 1B 1A A A B C D E F 10 11 12 13 14 15 16 17 18 19 9 9 A B C D E F 10 11 12 13 14 15 16 17 18 8 8 9 A B C D E F 10 11 12 13 14 15 16 17 7 7 8 9 A B C D E F 10 11 12 13 14 15 16 6 6 7 8 9 A B C D E F 10 11 12 13 14 15 5 5 6 7 8 9 A B C D E F 10 11 12 13 14 4 4 5 6 7 8 9 A B C D E F 10 11 12 13 3 3 4 5 6 7 8 9 A B C D E F 10 11 12 2 2 3 4 5 6 7 8 9 A B C D E F 10 11 1 1 2 3 4 5 6 7 8 9 A B C D E F 10 0 0 1 2 3 4 5 6 7 8 9 A B C D E F + 0 1 2 3 4 5 6 7 8 9 A B C D E F  K‫א‬‫א‬‫א‬‫א‬E٤J ١F  W‫א‬‫א‬WE٣٣J ١F  (35AB2)16 + (1A675)16   K‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬W‫א‬ 1 3 + 1 5 1 5 A 0 1 A 6 1 B 7 2 2 5 7 ∴(35AB2)16 + (1A675)16 = (50127)16 Hexadecimal Subtraction‫א‬‫א‬‫א‬‫א‬٢J ٨J ١١J ١  W‫א‬‫א‬‫א‬‫א‬‫א‬ -٣٠-
  • 35. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •  K‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬ (1)‫א‬‫א‬‫א‬ • ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ W‫א‬‫א‬  W‫א‬‫א‬WE٣٤J ١F  (F2ABD)16 – (EF4CE)16  W‫א‬ E F – E 1 2 F 3 9 A 4 5 1A B C E 1 D E D   K‫א‬‫א‬‫א‬             -٣١-
  • 36. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬     a) 64 e) 77.0625 a) 11011 e) 10101.1101 b) 112 f) 47.875  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١ c) 257 g) 33.125  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢ b) 1110101 f) 1100001.11011 d) 1110.11 b) 1110.11 + 11.10 d) 1001.101 + 1101.11  W‫א‬‫א‬‫א‬‫א‬‫א‬ E٤ a) 1101 – 0100 c) 11010 – 10111 a) 11110110 c) 111111  W‫א‬‫א‬‫א‬‫א‬E٣ a) 100 + 111 c) 1111 + 1101 a) 00110101 d) 27.26 b) 1001 – 0111 d) 1100 – 1001 b) 11100100 b) 01011101  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٥ c) 00010101  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E٦ c) 00110011 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٧ a) +28 b) – 83  W(8-bits) ‫א‬‫א‬ c) +99 d) – 120 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٨ a) +14 b) – 63  W(8-bits) ‫א‬‫א‬ c) +107 d) – 122  -٣٢-
  • 37. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬   K‫א‬‫א‬‫א‬‫א‬E٨F‫א‬‫א‬E٩   W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٠ a) 101110001 b) 01100100 c) 10110011  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١١ a) 10011101 b) 01100110 c) 10101101  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٢ a) 10101011 b) 000111101 c) 10111011   W‫א‬‫א‬‫א‬‫א‬‫א‬E١٤ a) 00010110 – 00110011 c) 10001100 – 00111001 a) 50 e) 120.515625 a) 42 e) 96.11 a) 72 e) 122.775  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E١٥ b) 100 f) 144.5625 b) 254 f) 115.3 c) 6391 g) 915.141 d) 77.375  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٦ b) 113 f) 417.632 a) 110101.1101 d) 10001001011.1001 a) (15)8 + (17)8 c) (123)8 + (321)8 b) 01110000 – 10101111 d) 11011001 – 11100111 c) 1057 g) 14367.12 d) 37.5  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٧ c) 16.3 g) 276.621 d) 37.6  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٨ b) 11110100.110101 e) 1010111.11101 c) 110110111.10101  W‫א‬‫א‬‫א‬‫א‬E١٩ b) (44)8 + (66)8 d) (272)8 + (456)8 -٣٣-
  • 38. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬  ‫א‬   W‫א‬‫א‬‫א‬‫א‬E٢٠ a) (32)8 – (25)8 c) (315)8 – (222)8 b) (147)8 – (74)8 d) (437)8 – (340)8  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E٢١ a) 14 e) 62500 b) 80 f) 204.125 b) D52 f) B3.E a) 37 e) 1600.524 c) 67F g) 1111.1 d) ABCD h) 888.8  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢٣ b) 1C a) 1001.1111 d) 10100111.111011 a) 13A e) 78.D3 d) 3000 h) 631.25  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢٢ a) 9F e) F.4 a) 8 c) 560 g) 255.875 c) A64 d) 1F.C e) 239.4  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢٤ b) 10000.1 e) 1000000.000111 b) 25E6 f) 2659.F41 b) 725 f) 3000.6125 a) (41)16 + (36)16 c) (9B)16 + (65)16 f) (77CB5)16 + (A5F72)16 c) 110101.11001 f) 1111100.1000011  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢٥ c) 3016 d) B4.C  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢٦ c) 2476.2 d) 1117.16  W‫א‬‫א‬‫א‬‫א‬E٢٧ b) (C8)16 + (3A)16 d) (11D)16 + (2E1)16 g) (13EFD)16 + (21BB3)16  -٣٤-
  • 39.  ‫א‬‫א‬‫א‬ ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹] ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ ٢ -١-
  • 40. -١-
  • 41. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬   ‫א‬‫א‬‫א‬   W‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬‫• א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ • - ٣٥ -
  • 42. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬  Introduction ١J ٢ J ‫א‬J ‫א‬J ‫א‬‫א‬ ‫א‬     ‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬J ‫א‬    ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬  K‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬?‫א‬‫א‬?    K‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬K(INVERTER)‫א‬NOT‫א‬،OR‫א‬،AND‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬  Logic Signal Levels‫א‬‫א‬٢J ٢ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬،‫א‬‫א‬   ،، ‫א‬‫א‬‫א‬،‫א‬ ‫א‬J ‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬   (LOW)‫א‬،‫א‬(1)‫א‬(HIGH)‫א‬ ‫א‬‫א‬(1)‫א‬‫א‬،‫א‬(0)‫א‬  ‫א‬‫א‬‫א‬(0)‫א‬‫א‬،(TRUE)  K(FALSE) ‫א‬،(Positive Logic)‫א‬،‫א‬ ‫א‬(1)‫א‬‫א‬‫א‬‫א‬‫א‬ K(Negative Logic)‫א‬ (0)‫א‬‫א‬،‫א‬‫א‬،‫א‬(0)‫א‬‫א‬  K‫א‬‫א‬‫א‬(1)‫א‬‫א‬‫א‬ - ٣٦ -
  • 43. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬   AND Gate AND‫א‬٣J ٢ ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬AND‫א‬‫א‬  ‫א‬‫א‬،‫א‬AND‫א‬‫א‬K(Logic Functions) ‫א‬‫א‬‫א‬‫א‬ ،(Logical Multiplication)‫א‬ ‫א‬A, B‫א‬،E١J ٢F ‫א‬‫א‬‫א‬‫א‬ ‫א‬(0)(Two Binary Variables)‫א‬‫א‬‫א‬  K(Closed)‫א‬‫א‬(1)(Open)‫א‬  (A)    (B) (L)    Voltage Source    K‫א‬‫א‬AND‫א‬‫א‬E١J ٢F  (1)‫א‬‫א‬‫א‬"L"‫א‬ ‫א‬‫א‬K(OFF)‫א‬(0)(ON)‫א‬ ‫א‬‫א‬E١J ٢F،‫א‬، (L)‫א‬‫א‬K‫א‬(L)‫א‬   K(Truth Table)‫א‬‫א‬‫א‬‫א‬،‫א‬  A B L               KE١J ٢F ‫א‬‫א‬E١J ٢F  - ٣٧ -
  • 44. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬،AND‫א‬(Standard)‫א‬‫א‬‫א‬E٢J ٢F‫א‬ ‫א‬‫א‬E٢J ٢F‫א‬KAND‫א‬‫א‬،Y‫א‬A, B  KAND  ‫א‬ ‫א‬  A  B  Y  0  0  0  0  1  0 A  1  0  0 Y B  1 1 1  KAND‫א‬‫א‬E٢J ٢FKAND‫א‬‫א‬E٢J ٢F    ‫א‬(1)‫א‬،(bits)‫א‬ ،‫א‬‫א‬AND‫א‬،‫א‬(1)A, B‫א‬    K(1)‫א‬(1)‫א‬ ‫א‬‫א‬‫א‬J ‫א‬‫א‬  W‫א‬ N = 2n  ‫א‬‫א‬N W  K‫א‬‫א‬n  W  N = 2 2 = 4  ‫א‬‫א‬  N = 2 3 = 8 ‫א‬‫א‬  N = 2 4 = 16 ‫א‬‫א‬  WE١J ٢F   KAND‫א‬‫א‬‫• א‬  ‫؟‬AND‫א‬‫א‬ • ‫א‬E٣J ٢F،‫א‬‫א‬AND‫א‬W‫א‬  K‫א‬‫א‬ - ٣٨ -
  • 45. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬    ‫א‬ ‫א‬  A  B C Y 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0  1  0 0 0 1 0 1 0 1 1 0 0 1 1 1  1  KAND‫א‬‫א‬E٣J ٢F   W‫א‬‫א‬‫א‬• N = 2 n = 2 5 = 32  ‫א‬‫א‬‫א‬‫א‬(Boolean Algebra)‫א‬‫א‬ ‫א‬‫א‬(Boolean Expression)‫א‬‫א‬،‫א‬  W‫א‬AND‫א‬‫א‬‫א‬K Y = A•B  ‫א‬،EAND • FA AND BY‫א‬W‫א‬  W‫א‬‫א‬ Y = AB  KA AND BY‫א‬ ‫א‬‫א‬‫א‬ ‫א‬K(LOW)‫א‬(HIGH)‫א‬‫א‬(Pulses)  ‫א‬‫א‬،‫א‬‫א‬AND‫א‬  K‫א‬ ‫א‬(1)A, B‫א‬E٣J ٢F، A‫א‬،t2‫א‬‫א‬،(1)‫א‬Y‫א‬‫א‬t1‫א‬ - ٣٩ -
  • 46. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬‫א‬‫א‬،(0)Y‫א‬B‫א‬(0) ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬   A B  K(Timing Diagram) A  t1 t2 t3 t4 t5 Y B  t6 t7   Y   KAND‫א‬‫א‬‫א‬E٣J ٢F  OR Gate OR‫א‬ ٤J ٢ ‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬OR‫א‬‫א‬  ‫א‬‫א‬‫א‬،‫א‬OR ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،(Logical Addition) A, B‫א‬AND‫א‬‫א‬KE٤J ٢F   ‫א‬(1)(Open)‫א‬(0)      Voltage Source  K(Closed)  (A)      (B)    K‫א‬‫א‬OR‫א‬‫א‬E٤J ٢F ‫א‬‫א‬،‫א‬‫א‬‫א‬E٤J ٢F  K‫א‬(L)‫א‬‫א‬  - ٤٠ -
  • 47. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬  A B   L               KE٤J ٢F‫א‬‫א‬E٤J ٢F  ‫א‬A, B‫א‬،OR‫א‬‫א‬‫א‬‫א‬E٥J ٢F‫א‬  KOR‫א‬‫א‬E٥J ٢F‫א‬KY    ‫א‬ ‫א‬  A  B  Y 0  0 0 0 1 1 A Y 1 0  1 B  1 1 1  KOR‫א‬‫א‬E٥J ٢FKOR‫א‬‫א‬E٥J ٢F   ‫א‬(1)‫א‬E٥J ٢F‫א‬ ‫א‬(0)‫א‬،(1)‫א‬ Y=A+B  W‫א‬OR‫א‬‫א‬‫א‬K‫א‬(0)  K(OR+)A OR BY‫א‬W‫א‬  ،‫א‬‫א‬OR‫א‬‫א‬ ‫א‬‫א‬‫א‬AND‫א‬  K‫א‬  ‫א‬t1‫א‬‫א‬(1)A, B‫א‬E٦J ٢F A‫א‬،t2‫א‬‫א‬،(1)‫א‬Y‫א‬ ‫א‬‫א‬‫א‬‫א‬،(1)Y‫א‬B‫א‬(0)  K‫א‬ - ٤١ -
  • 48. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬  A A  B B t1 t2 t3 t4 t5 t6  Y t7   Y    KOR‫א‬‫א‬‫א‬E٦J ٢F   NOT Gate (INVERTER) E‫א‬F NOT ‫א‬٥J ٢ ‫א‬(Inversion)‫א‬NOT‫א‬‫א‬ (1)‫א‬،‫א‬‫א‬‫א‬K(Complementation)  K(1)(0)‫א‬،(0)‫א‬ E٧J ٢FK‫א‬‫א‬‫א‬NOT‫א‬‫א‬   K‫א‬‫א‬‫א‬E٦J ٢F‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬ ‫א‬  A  Y 0 1 Y A 1 0  K‫א‬NOT‫א‬‫א‬E٦J ٢FKNOT‫א‬‫א‬E٧J ٢F   ‫א‬،‫א‬‫א‬‫א‬  W‫א‬‫א‬ Y= A ‫א‬barA‫א‬not AY‫א‬W‫א‬‫א‬   KE A FA barY‫א‬،‫א‬   NAND Gate  NAND ‫א‬٦J ٢ - ٤٢ -
  • 49. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬‫א‬،AND(NOT AND)‫א‬(NAND) J ٢FAND‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬AND‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،E٨   KNAND‫א‬‫א‬E٧J ٢FK‫א‬‫א‬‫א‬‫א‬   ‫א‬ ‫א‬  A  B  Y 0  0 1 0 1 1 A 1 0 1 Y  1 1 0 B  KNAND‫א‬‫א‬E٧J ٢FKNAND‫א‬‫א‬E٨J ٢F   ‫א‬‫א‬‫א‬(0)‫א‬‫א‬ (0)‫א‬‫א‬‫א‬ (1)‫א‬،‫א‬(1) ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ NAND‫א‬‫א‬KAND‫א‬‫א‬‫א‬،‫א‬ ‫א‬‫א‬‫א‬،‫א‬ NAND‫א‬‫א‬،‫א‬‫א‬،NOT, OR, AND‫א‬  W‫א‬ Y = AB ،‫א‬‫א‬NAND‫א‬‫א‬   K(1)‫א‬(0)NAND‫א‬‫א‬ ‫א‬t1‫א‬‫א‬(1)A, B‫א‬E٩J ٢F  A‫א‬،t2‫א‬‫א‬،(0)‫א‬Y‫א‬ ‫א‬‫א‬‫א‬،(1)Y‫א‬(1)B‫א‬(0)  K‫א‬‫א‬ - ٤٣ -
  • 50. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬    A A Y B   B t1 t2 t3 t4 t5 t6  t7  Y   KNAND‫א‬‫א‬‫א‬E٩J ٢F   NOR Gate  NOR ‫א‬٧J ٢ ‫א‬‫א‬،OR(NOT OR)‫א‬(NOR) OR‫א‬‫א‬(NOT gate)‫א‬‫א‬‫א‬ NOR‫א‬‫א‬KNOR‫א‬‫א‬‫א‬‫א‬،E١٠J ٢F  KE٨J ٢F    ‫א‬ ‫א‬  A  B Y 0  0 1 0 1 0 A 1 0 0 Y B  1 1 0  KNOR‫א‬‫א‬E٨J ٢FKNOR‫א‬‫א‬E١٠J ٢F  ‫א‬‫א‬(0)(Y)‫א‬‫א‬ ‫א‬‫א‬(1)‫א‬،‫א‬ (1)‫א‬  K‫א‬(0) ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬NAND‫א‬‫א‬‫א‬NOR‫א‬‫א‬ ‫א‬K،NOT, OR, AND‫א‬،‫א‬   WNOR‫א‬‫א‬ Y= A+B - ٤٤ -
  • 51. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ،‫א‬‫א‬A, B‫א‬NOR‫א‬E١١J ٢F   K‫א‬(Y)‫א‬‫א‬NOR‫א‬‫א‬  A A Y  B B   t1 t2 t3 t4  t5 Y    KNOR‫א‬‫א‬‫א‬E١١J ٢F  Exclusive-OR Gate E‫א‬F‫ א‬OR ‫א‬٨J ٢ ،XOR-gate??‫א‬‫א‬OR‫א‬‫א‬   ‫א‬‫א‬‫א‬XOR‫א‬‫א‬K‫א‬‫א‬‫א‬E١٢J ٢F  K‫א‬   ‫א‬  A 0 0 1  1  B  0 1 0 1 ‫א‬  Y 0 1 1 0 A B Y  KXOR‫א‬‫א‬E٩J ٢FKXOR‫א‬‫א‬E١٢J ٢F (Y)‫א‬‫א‬،(9-2)XOR‫א‬‫א‬ ،‫א‬(0)‫א‬(1)،A, B‫א‬‫א‬(1)  K‫א‬(0) ‫א‬‫א‬‫א‬OR‫א‬‫א‬XOR‫א‬‫א‬ (1)XOR‫א‬‫א‬،A = B = 1   ،‫א‬‫א‬(1)(1)‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ - ٤٥ -
  • 52. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬   W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ Y = AB + AB  W‫א‬‫א‬‫א‬‫א‬ Y=A⊕B  XOR‫א‬‫א‬‫א‬‫א‬KBA⊕‫א‬ ‫א‬‫א‬E١٣J ٢F‫א‬‫א‬،AND, OR, NOT‫א‬‫א‬‫א‬‫א‬  K‫א‬XOR‫א‬‫א‬‫א‬   A B   Y    KAND, OR, NOT‫א‬XOR‫א‬‫א‬E١٣J ٢F   ‫א‬ XOR‫א‬‫א‬E١٤J ٢F ‫א‬‫א‬‫א‬،‫א‬  K‫א‬   A  A B B    t1 t2 t3 t4 t5 t6 t7 t8  Y  KXOR‫א‬‫א‬‫א‬E١٤J ٢F  - ٤٦ - Y
  • 53. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬   Exclusive-NOR Gate E‫א‬F‫ א‬NOR ‫א‬٩J ٢ ‫א‬‫א‬،XNOR-gate‫א‬NOR‫א‬‫א‬  K‫א‬‫א‬‫א‬E١٥J ٢F،XOR‫א‬‫א‬‫א‬ (Y)‫א‬‫א‬،E١٠J ٢F XNOR‫א‬‫א‬ (0)A = B = 1A = B = 0A, B‫א‬‫א‬(1)  ،‫א‬(0)‫א‬(1)‫א‬ ‫א‬‫א‬،‫א‬‫א‬(1)   K‫א‬‫א‬‫א‬‫א‬   ‫א‬ ‫א‬  A  B  Y 0  0 1 0 1 0 A 1 0 0 Y B  1 1 1  KXNOR‫א‬‫א‬E١٠J ٢FKXNOR‫א‬‫א‬E١٥J ٢F  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ Y = AB + AB  W‫א‬‫א‬‫א‬ Y=A B ‫א‬‫א‬XNOR‫א‬‫א‬‫א‬‫א‬K‫א‬ ‫א‬   ‫א‬‫א‬‫א‬E١٦J ٢F‫א‬‫א‬،AND, OR, NOT‫א‬‫א‬  K‫א‬XNOR‫א‬‫א‬   A B   Y  KAND, OR, NOT‫א‬XNOR‫א‬‫א‬E١٦J ٢F - ٤٧ - 
  • 54. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ،‫א‬A, B‫א‬XNOR‫א‬E١٧J ٢F   K(Y)‫א‬‫א‬XNOR‫א‬‫א‬  A A B   Y  B t1 t2 t3 t4 t5 t6 t7 t8  Y   KXNOR‫א‬‫א‬‫א‬E١٧J ٢F  Rules of Boolean Algebra ‫א‬‫א‬‫א‬١٠J ٢ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١١J ٢F  K‫א‬  1. 3. 5. 7. 9. A A A A A + 0 =A • 0 =0 + A=A • A=A =A 2. A + 1 = 1 4. A • 1 = A 6. A + A = 1 8. A • A = 0 10. A + AB = A  K‫א‬‫א‬‫א‬‫א‬E١١J ٢F ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   K‫א‬ ‫א‬‫א‬‫א‬A + 0 = A :(1)‫א‬  A=1‫א‬K(0)(1)‫א‬،A،‫א‬‫א‬(0)‫א‬OR‫א‬ KA(0)‫א‬A=0‫א‬KA‫א‬(1)‫א‬  K(A + 0 = A)‫א‬‫א‬‫א‬(0)OR‫א‬ ‫א‬(1)‫א‬OR‫א‬‫א‬‫א‬‫א‬A + 1 = 1:(2)‫א‬ ‫א‬OR‫א‬‫א‬(1)K(0)‫א‬(1)‫א‬،A،‫א‬ - ٤٨ -
  • 55. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬(1)    K(A + 1 = 1) (1)‫א‬‫א‬(1)OR‫א‬ (0)‫א‬AND‫א‬‫א‬‫א‬‫א‬ A • 0 = 0:(3)‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬(0)‫א‬‫א‬،A،‫א‬‫א‬    (0)‫א‬‫א‬(0)AND‫א‬   K(A • 0 = 0) (1)‫א‬AND‫א‬‫א‬‫א‬‫א‬A • 1 = A:(4)‫א‬ AND‫א‬‫א‬A=0‫א‬‫א‬،(A)‫א‬‫א‬،A،‫א‬‫א‬ ‫א‬‫א‬(1)AND‫א‬‫א‬A=1‫א‬‫א‬،(0) ‫א‬‫א‬‫א‬(1)AND‫א‬K(1)   K(A • 1 = A) ،A‫א‬OR‫א‬‫א‬‫א‬‫א‬A + A = A:(5)‫א‬   ‫א‬‫א‬،0 + 0 = 0A = 0‫א‬‫א‬K‫א‬‫א‬‫א‬  K1 + 1 = 1‫א‬A = 1 ‫א‬A‫א‬W‫א‬ A + A = 1 :(6)‫א‬  A=0‫א‬K(1)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ A ‫א‬OR   K1 + 1 = 1 + 0 = 1A = 1‫א‬K 0 + 0 = 0 + 1 = 1 ‫א‬‫א‬AND‫א‬‫א‬A‫א‬‫א‬A • A = A:(7)‫א‬ ،1 • 1 = 1‫א‬A = 1‫א‬‫א‬،0 • 0 = 0A = 0‫א‬‫א‬K‫א‬  KA‫א‬AND‫א‬‫א‬‫א‬ ‫א‬‫א‬ A ‫א‬AND‫א‬A‫א‬ A • A = 0 :(8)‫א‬   A A‫א‬‫א‬‫א‬،(0)‫א‬‫א‬‫א‬‫א‬  K(0)‫א‬‫א‬AND‫א‬(0)،‫א‬(0) ‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬ A = A :(9)‫א‬  (0)(1)‫א‬،(1)A = 0  K‫א‬‫א‬  - ٤٩ -
  • 56. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬   W(4)‫א‬(2)‫א‬‫א‬‫א‬:(10)‫א‬ A + AB = A (1 + B) = A (1) =A  The Boolean Expression for a Logic Circuit‫א‬‫א‬‫א‬١١J ٢ ‫א‬‫א‬،‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬،K‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬KE١٨J ٢F‫א‬  K AB A, B ‫א‬‫א‬AND‫א‬‫א‬‫א‬K١  K AC  A ,C ‫א‬‫א‬AND‫א‬‫א‬‫א‬K٢  K AB + AC  AB, AC ‫א‬‫א‬OR‫א‬‫א‬‫א‬K٣  W‫א‬‫א‬‫א‬ Y = AB + AC A B B A AB   C   Y AC    K‫א‬‫א‬‫א‬‫א‬E١٨J ٢F   KE١٩J ٢F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬WE٢J ٢F   W‫א‬ A B+C B  D( A + B )  Y C B+C   D   K‫א‬‫א‬‫א‬E٢J ٢F‫א‬‫א‬‫א‬E١٩J ٢F - ٥٠ - 
  • 57. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬   W‫א‬‫א‬‫א‬‫א‬‫א‬ Y = D( A + B ) + ( B + C)  ‫א‬‫א‬‫א‬‫א‬١٢J ٢ Implementation of a Logic Circuit Using a Boolean Expression ‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬  Y = AB(C D + EF)   (CD + EF) A, B‫א‬‫א‬‫א‬‫א‬‫א‬ E,F،AND‫א‬ C, D  (CD + EF) ‫א‬،AND‫א‬  KOR‫א‬AND‫א‬‫א‬،AND‫א‬  W‫א‬‫א‬ AND NOT   OR Y = A B (CD + EF)  AND     ‫( ؛‬CD + EF) ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫ ؛‬CD, EF ‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬، D   W AB(CD + EF) ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K D ‫א‬NOT‫א‬K١  K CD, EF ‫א‬AND‫א‬K٢  K (CD + EF) ‫א‬‫א‬OR‫א‬K٣  KY‫א‬‫א‬AND‫א‬K٤  KE٢٠J ٢F ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ - ٥١ -
  • 58. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬  A B  Y C D     E F   K AB(C D + EF) ‫א‬‫א‬‫א‬‫א‬E٢٠J ٢F  ‫א‬‫א‬١٣J ٢ Implementation of a Logic Circuit via a Truth Table ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬E١٢J ٢FK‫א‬  W‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬ ‫א‬‫א‬،Y = 1‫א‬‫א‬‫א‬‫א‬ K١ ،A = 0, B = 1, C = 0‫א‬Y = 1‫א‬‫א‬  ،(1)‫א‬‫א‬ ABC ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬(1)‫א‬،(0)‫א‬  K ABC ‫א‬‫א‬  ‫א‬  A 0 0 0 0  1 1 1 1  B 0 0 1 1  0 0 1 1 ‫א‬ C 0 1 0 1 0 1 0 1 Y 0 0 1 0 0 0 1 0  K‫א‬‫א‬‫א‬E١٢J ٢F   - ٥٢ -
  • 59. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬   WOR‫א‬Y = 1‫א‬‫א‬‫א‬‫א‬‫א‬ K٢  Y = ABC + ABC ‫א‬‫א‬‫א‬ ABC ‫א‬‫א‬‫א‬‫א‬‫א‬  ABC ‫א‬‫א‬‫א‬‫א‬،AND‫א‬ A, B, C OR‫א‬‫א‬‫א‬‫א‬،AND‫א‬ A, B, C ‫א‬‫א‬‫א‬  KY‫א‬‫א‬‫א‬ NOT‫א‬W ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  OR‫א‬، ABC ، ABC ‫א‬‫א‬AND‫א‬‫ ؛‬A, C ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬، ABC + ABC ‫א‬‫א‬‫א‬  KE٢١J ٢F   A B C   Y    K AB C + AB C ‫א‬‫א‬‫א‬‫א‬E٢١J ٢F  KE١٣J ٢F ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬WE٣J ٢F    ‫א‬ A 0 0 0 0  1 1 1 1  B 0 0 1 1  0 0 1 1 ‫א‬ C 0 1 0 1 0 1 0 1 Y 0 1 0 1 0 1 0 0  K‫א‬‫א‬‫א‬‫א‬‫א‬E١٣J ٢F - ٥٣ -
  • 60. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ W‫א‬  WOR‫א‬E‫א‬‫א‬FY = 1 Y = ABC + ABC + ABC    KE٢٢J ٢F ‫א‬‫א‬‫א‬  A  B C  Y       K A B C + ABC + AB C ‫א‬‫א‬‫א‬‫א‬E٢٢J ٢F  ‫א‬‫א‬‫א‬١٤J ٢ Converting a Boolean Expression to a Truth Table ‫א‬‫א‬‫א‬‫א‬‫א‬  ،(22 = 4)،‫א‬‫א‬K(1or 0)‫א‬  K‫א‬،(23 = 8)،‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬ ،‫א‬‫א‬ (Y)‫א‬(1)‫א‬‫א‬  K‫א‬‫א‬،‫א‬‫א‬(0)  W‫א‬‫א‬‫א‬WE٤J ٢F  Y = AB C + ABC + ABC + ABC    ‫א‬،‫א‬‫א‬‫א‬(A, B, C)‫א‬W‫א‬  KE١٤J ٢F ‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ AB C = 000, ABC = 010, ABC = 110, ABC = 111 - ٥٤ -
  • 61. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ،(Y)‫א‬(1)‫א‬‫א‬  K(Y)‫א‬(0)‫א‬‫א‬‫א‬   ‫א‬ ‫א‬ A  B C Y  0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 0  1  0 0 0 1 0 1 0 1 1 0 1 1 1 1 1  K Y = AB C + AB C + AB C + ABC ‫א‬‫א‬E١٤J ٢F   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١٥J ٢ Simplification of Boolean Expressions Using Boolean algebra E‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ،‫א‬،‫א‬‫א‬‫א‬  ‫א‬،‫א‬،‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬WE٥J ٢F  Y = AB + A(A + C) + B(A + C)    W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬ Y = AB + AA + AC + AB + BC   W‫א‬‫א‬E‫א‬‫א‬‫א‬7‫א‬‫א‬FAAA‫א‬ Y = AB + A + AC + AB + BC   W‫א‬‫א‬،AB + AB = AB،A + A = A5‫א‬ Y = AB + A + AC + BC - ٥٥ -
  • 62. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬    W‫א‬‫א‬‫א‬‫א‬A‫א‬  Y = A(B + 1 + C) + BC Y = A • 1 + BC Y = A + BC  W،A + 1 = 12‫א‬  W،A • 1 = A4‫א‬‫א‬ K‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬  K‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬E٢٣J ٢F  ‫א‬‫א‬‫א‬،EEF‫א‬F‫א‬‫א‬  KEEF‫א‬F‫א‬‫א‬ A B Y Y B C C  A E F EF  KE٥J ٢F‫א‬‫א‬‫א‬E٢٣J ٢F ‫א‬،‫א‬‫א‬‫א‬‫א‬   K‫א‬‫א‬‫א‬،A, B, C ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬WE٦J ٢F  K‫א‬ Y = AB C + ABC + ABC + ABC  W،‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬W‫א‬  Y = ( AB C + ABC) + ( ABC + ABC) = AB( C + C) + BC( A + A) - ٥٦ -
  • 63. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬   W6‫א‬ Y = AB • 1 + BC • 1   W‫א‬‫א‬‫א‬4‫א‬  Y = AB + BC    K‫א‬‫א‬‫א‬‫א‬E٢٤J ٢F  A B C A Y B Y C  E F EF  KE٦J ٢F‫א‬‫א‬‫א‬E٢٤J ٢F - ٥٧ -
  • 64. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬     ‫א‬،A,B‫א‬‫א‬AND‫א‬X‫א‬‫א‬‫א‬E١  A  B  K١J ‫א‬‫א‬    X    ١J   ‫א‬،A,B‫א‬‫א‬OR‫א‬X‫א‬‫א‬‫א‬E٢  K١J ‫א‬‫א‬  ‫א‬،A,B‫א‬‫א‬NAND‫א‬X‫א‬‫א‬‫א‬ E٣  K٢J ‫א‬‫א‬ A   B   X    ٢J  - ٥٨ - 
  • 65. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬‫א‬،A,B‫א‬‫א‬NOR‫א‬X‫א‬‫א‬‫א‬ E٤   K٣J ‫א‬‫א‬ A B  X  ٣J   ‫א‬‫א‬،A,B‫א‬‫א‬XOR‫א‬X‫א‬‫א‬‫א‬ E٥  K٣J ‫א‬‫א‬  ‫א‬‫א‬،A,B‫א‬‫א‬XNOR‫א‬X‫א‬‫א‬‫א‬ E٦  K٣J ‫א‬‫א‬   K٤J ‫א‬‫א‬‫א‬‫א‬‫א‬E٧ A B C      ٤J  Y     - ٥٩ -
  • 66. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬   W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٨ a) AB + AB c) AB(C + D) b) AB + AB + ABC d) A + B[C + D(B + C )]   K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٩   ‫א‬ A  0 0 0 0  1 1 1 1 B C 0 0 0 1 1 0 1 1  0 0 0 1 1  0 1 1 ‫א‬ Y 0 1 0 1 0 1 0 1  a) (A + B)C c) A(AC + AB) a) (A + B)(A + C) b) (A + A )(AB + ABC )  W‫א‬‫א‬‫א‬‫א‬‫א‬E١٠ b) (A + B)( B + C) d) A(A + AB)   W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١١ b) AB + ABC + ABCD + ABC DE d) AB + ( A + B)C + AB  - ٦٠ -
  • 67.  ‫א‬‫א‬‫א‬ ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹] ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬ ٣
  • 68. ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬   ‫א‬‫א‬‫א‬   W‫א‬‫א‬ K • KNOR‫א‬‫א‬NAND‫א‬‫א‬‫א‬‫א‬ • KNORNAND‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬ • - ٦١ - 
  • 69. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬   Introduction١J ٣ ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬    ،،‫א‬‫א‬‫א‬  ،‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬ ‫א‬‫א‬‫א‬     K‫א‬‫א‬‫א‬(10)‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬NOR‫א‬‫א‬NAND  ‫א‬‫א‬‫א‬‫א‬   K(K–map)K –‫א‬‫א‬ (Karnaugh-Map) ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬ Demorgan's Theorems٣J ٢ ‫א‬‫א‬‫א‬،‫א‬‫א‬    ‫א‬‫א‬KOR‫א‬AND‫א‬   W‫א‬‫א‬،‫ א‬‫א‬‫א‬(bars)  A+B=A•B  A • B = A + B    W‫א‬  W‫א‬   AND‫א‬OR‫א‬‫א‬ AND‫א‬‫א‬‫א‬‫א‬NOR‫א‬‫א‬E١J ٣F  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ KE١J ٣F‫א‬‫א‬‫א‬  K(negative AND)‫א‬AND‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ -٦٢-
  • 70. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬   A AB A A+B   B B  KANDOR‫א‬E١J ٣F  ‫א‬  ‫א‬ A B  A+B  A•B 0 0 1 1 0 1 0 1 1 0 0 0 1 0 0 0  K‫א‬‫א‬E١J ٣F OR‫א‬AND‫א‬‫א‬ ‫א‬OR‫א‬‫א‬‫א‬‫א‬NAND‫א‬‫א‬E٢J ٣F ‫א‬،E‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬F‫א‬ OR‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬KE٢J ٣F‫א‬‫א‬‫א‬  K(negative OR)‫א‬ A ≡ AB B  A A+B B  KORAND‫א‬E٢J ٣F  ‫א‬  ‫א‬ A B  A•B  A+B 0 0 1 1 0 1 0 1 1 0 0 0 1 0 0 0  K‫א‬‫א‬E٢J ٣F -٦٣- 
  • 71. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬  K‫א‬‫א‬‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬WE١J ٣F  Y = (A + B + C) • (A + B + C )  W‫א‬ Y = (A + B + C) • (A + B + C) = (A + B + C ) + (A + B + C ) = A BC + A BC= AB C+ A BC   W‫א‬‫א‬‫ א‬ WE٢J ٣F Y = (A + B) + CD  W‫א‬ Y = (A + B) + CD = (A + B).CD = (A.B)(C + D) = A B(C + D)  NOR , NAND‫א‬‫א‬‫א‬‫א‬٣J ٣ The Universal Property of NAND and NOR Gates ‫א‬،AND‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬NOR‫א‬NAND‫א‬‫א‬‫א‬K‫א‬‫א‬،OR ‫א‬‫א‬‫א‬K (Universal Gates)  KNOR،AND‫א‬‫א‬‫א‬NAND‫א‬ NOR‫א‬‫א‬‫א‬NOR‫א‬  KNANDOR،AND‫א‬‫א‬ -٦٤-
  • 72. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬    NAND gate as a Universal Logic Element NAND‫א‬‫א‬١J ٣J ٣ ،AND،‫א‬‫א‬‫א‬‫א‬NAND‫א‬‫א‬ NAND‫א‬‫א‬‫א‬KNOR،OR K‫א‬NAND‫א‬EF٣J ٣‫א‬‫א‬‫א‬  KEF٣J ٣NAND‫א‬‫א‬AND   NOR ‫א‬‫א‬‫א‬KEF٣J ٣NAND‫א‬ ‫א‬OR‫א‬‫א‬   KEF٣J ٣ A A  ≡ A A E F A AB AB = AB B ≡ A AB B EF A A A .B = A + B B B ≡ A A+B B EF A A A .B = A + B A+B B  B ≡ A B EF  KNAND‫א‬‫א‬‫א‬E٣J ٣F -٦٥- A+B
  • 73. ‫א‬‫א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬   ‫٧٤١ א‬  ‫א‬  NOR Gate as a Universal Logic Element NOR‫א‬‫א‬٢J ٣J ٣ ،OR،AND{‫א‬‫א‬‫א‬NOR ‫א‬‫א‬،NAND ‫א‬    ‫א‬NOR‫א‬‫א‬E٤J ٣FKNAND‫א‬  KNAND‫א‬‫א‬OR‫א‬NOT  A ≡ A A A E F A+B A A+B = A+B B ≡ A A+B B EF A A A + B = A.B ≡ B A AB B B EF A A A + B = A.B A B ≡ B EF   KNOR‫א‬‫א‬‫א‬E٤J ٣F  -٦٦- A B AB
  • 74. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬  NOR،NAND‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٤J ٣ Design of Combinational Logic Circuits using NAND and NOR Gates ‫א‬‫א‬NOR‫א‬،NAND‫א‬‫א‬‫א‬ ،(Negative-OR)‫א‬OR‫א‬‫א‬NAND‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬K(Negative - AND)‫א‬AND‫א‬‫א‬NOR‫א‬‫א‬  K‫א‬ (Logic diagram) ‫א‬‫א‬‫א‬‫א‬AND{OR‫א‬ NAND Logic NAND‫א‬‫א‬‫א‬١J ٤J ٣ ‫א‬،‫א‬OR ‫א‬NAND ‫א‬NAND‫א‬،  W‫א‬  A • B = A + B  Negative-OR NAND   KE٥J ٣F‫א‬‫א‬‫א‬‫א‬‫א‬  A   AB B  Y = AB + CD C D CD  KNAND‫א‬‫א‬‫א‬E٥J ٣F     W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(Y)‫א‬‫א‬ Y = (AB)(CD)  W‫א‬ Y = AB + CD  W(bars)‫א‬‫א‬‫א‬ Y = AB + CD AND‫א‬،AB+CD ،(Y)‫א‬ ‫א‬NAND‫א‬‫א‬(Y)‫א‬‫א‬‫א‬.OR‫א‬ -٦٧-
  • 75. ‫א‬‫א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬   ‫٧٤١ א‬  ‫א‬  KOR‫א‬‫א‬NAND‫א‬AND‫א‬E٥J ٣F NAND‫א‬‫א‬‫א‬‫א‬EF٦J ٣‫א‬(Y)‫א‬‫א‬ ‫א‬‫א‬K‫א‬OR ‫א‬‫א‬  ،EF٦J ٣‫א‬‫א‬E٥-٣F‫א‬‫א‬،EF٦J ٣‫א‬   W  (NAND-NAND-NAND)(AND-AND-OR) A A AB B Y = AB + CD C D ≡ E F CD B Y = AB + CD C EF D KE٥J ٣F‫א‬‫א‬AND-AND-OR  E٦J ٣F  ‫א‬‫א‬‫א‬NAND‫א‬‫א‬E٧J ٣F  K‫א‬J OR‫א‬‫א‬‫א‬ A AB B  C D E F  ABC  Y  DE  DE F K‫א‬J OR‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬E٧J ٣F    WE٧J ٣F‫א‬(Y)‫א‬ F = [(AB)C] • [(DE)F] = [(A + B)C] • [( D + E )F] = ( A + B )C + ( D + E ) F = ( A + B )C + ( D + E ) F -٦٨-
  • 76. ‫א‬‫א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬   ‫٧٤١ א‬  ‫א‬  ‫א‬‫א‬‫א‬ NAND‫א‬‫א‬‫א‬J OR‫א‬‫א‬  K‫א‬‫א‬‫א‬(Y)‫א‬،E٨J ٣F  A A+B  ( A + B )C B  C Y = ( A + B )C + ( D + E )F D   D+E E  ( D + E )F F  K‫א‬J OR‫א‬‫א‬ E٧J ٣F ‫א‬‫א‬‫ א‬E٨J ٣F   WNAND‫א‬‫א‬‫א‬‫א‬WE٣J ٣F (a ) Y = ABC + DE (b) Y = ABC + D + E  KE٩J ٣F‫א‬‫א‬W‫א‬  A A B ABC Y = ABC + DE C D E B DE ABC Y = ABC + D + E C D E E F EF KE٣J ٣F‫א‬‫א‬‫א‬‫ א‬E٩J ٣F  NOR Logic NOR‫א‬‫א‬‫א‬٢J ٤J ٣ ‫א‬‫א‬J AND‫א‬NOR‫א‬NOR‫א‬‫א‬  W‫א‬   A + B = A • B NOR Negative-AND    KE١٠J ٣F‫א‬‫א‬‫א‬‫א‬ -٦٩- 
  • 77. ‫א‬‫א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬   ‫٧٤١ א‬  ‫א‬    A A+B B  (A + B) (C + D)  C D  C+D  KNOR‫א‬‫א‬‫א‬E١٠J ٣F   W‫א‬‫א‬‫א‬‫א‬‫א‬ Y = (A + B) + (C + D)  W‫א‬ Y = (A + B) • (C + D)  W‫א‬‫א‬‫א‬ Y = (A + B) • (C + D)  ‫א‬،AND‫א‬OR‫א‬(A + B)(C + D)‫א‬ AND‫א‬‫א‬‫א‬‫א‬OR‫א‬‫א‬‫א‬‫א‬  K‫א‬J AND‫א‬‫א‬EF١١J ٣‫א‬‫א‬‫א‬KEF١١J ٣  A A A+B B (A + B) (C + D) C D C+D ≡ B A+B (A + B) (C + D) C D E F EF  K‫א‬J AND‫א‬‫א‬E١٠J ٣F‫א‬‫א‬‫א‬E١١J ٣F  ‫א‬‫א‬‫א‬،NOR‫א‬‫א‬E١٢J ٣F  W‫א‬(Y)‫א‬K‫א‬J AND‫א‬‫א‬ -٧٠-
  • 78. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬   Y = [(A + B) + C] + [(D + E) + F]  = [ AB + C] + [ D E + F]  = ( AB + C)( D E + F)   A A+B  ( A + B) + C B   C Y D   D+E E  ( D + E) + F  F   KNOR‫א‬‫א‬E١٢J ٣F   KE١٣J ٣F‫א‬‫א‬NOR‫א‬‫א‬‫א‬J AND‫א‬‫א‬ A AB B   AB + C  C Y = ( A B + C) (D E + F) D E F   DE DE + F  KE١٢J ٣F‫א‬‫א‬‫א‬‫א‬E١٣J ٣F -٧١-   
  • 79. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬   WNOR‫א‬‫א‬‫א‬‫א‬‫א‬WE٤J ٣F Y = AB C + ( D + E )  KE١٤J ٣F‫א‬‫א‬W‫א‬  A B A + B + C = AB C Y = A B C + ( D + E) C D  E  KNOR‫א‬‫א‬‫א‬‫א‬‫א‬E١٤J ٣F  Karnaugh Map٥J ٣ ‫א‬‫א‬،‫א‬‫א‬‫א‬K- ‫א‬‫א‬K‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫ א‬،‫א‬‫א‬‫א‬   KK‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ،‫א‬K‫א‬ ‫א‬‫א‬،(cells)‫א‬ (array) ‫א‬‫א‬‫א‬‫א‬K‫א‬  K‫א‬ ،،،‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬،‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬ (Quine - McClusky) ‫א‬‫א‬‫א‬K‫א‬ -٧٢-
  • 80. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬‫א‬K‫א‬‫א‬،   K 2 4 = 16 ‫א‬‫א‬ 2 3 = 8     Simplification using Karnaugh-map ‫א‬‫א‬‫א‬٦J ٣ KE‫א‬F‫א‬‫א‬‫א‬ ( A, B )‫א‬(A، B)‫א‬،E١٥J ٣F    K(00,01,10,11)E‫א‬F  A B Y 0 0 AB 0 1 AB 1 0 1 1 AB AB B B A AB AB A AB AB   K‫א‬E١٥J ٣F K‫א‬‫א‬‫א‬‫א‬  E١٦J ٣F‫א‬(Input Labels)‫א‬   ،‫א‬‫א‬ A ‫א‬‫א‬‫א‬،K‫א‬‫א‬  ‫א‬‫א‬ B ‫א‬‫א‬K‫א‬‫א‬A‫א‬ ‫א‬‫א‬‫א‬‫א‬،K‫א‬‫א‬‫א‬B‫א‬،‫א‬   K AB ‫א‬     -٧٣-
  • 81. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬  B  B A  A   KE22 = 4FE١٦J ٣F  ،EF‫א‬EF١٧J ٣،EF١٧J ٣   KEF‫א‬  CD CD CD AB BC BC BC BC CD      AB A  AB A   E F  AB EF   K‫א‬‫א‬E١٧J ٣F ،‫א‬ ‫א‬‫א‬،K‫א‬‫א‬‫א‬   KEF١٨J ٣‫א‬ -٧٤-
  • 82. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬  ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ OR ‫א‬‫א‬‫א‬‫א‬ (1)‫א‬‫א‬  KEF١٨J ٣ ‫א‬‫א‬KEF١٨J ٣‫א‬‫א‬‫א‬‫א‬‫א‬  KEF١٨J ٣‫א‬‫א‬‫א‬   -٧٥-
  • 83. ‫א‬‫א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬   ‫٧٤١ א‬  ‫א‬     A A B B  ‫א‬ ‫א‬ Y A B Y 0 0 0 0 1 0 1 0 1 AB 1 1 1 AB Y=AB+AB EF EF E F  B B B A 0 0 A A 1 1 A B  0 0 1   A A B B 1 Y A  EFEFEF  K‫א‬‫א‬‫א‬E١٨J ٣F  ‫א‬‫א‬   ‫א‬(1)‫א‬K‫א‬‫א‬‫א‬‫א‬ (0)‫א‬(0)‫א‬،‫א‬‫א‬ (1)    ‫א‬‫א‬(1)K‫א‬‫א‬ ‫א‬‫א‬KEABF‫א‬‫א‬‫א‬،E A B F‫א‬  K‫א‬‫א‬(0)،‫א‬(0)( AB, A B ) ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬K A + A = 1 ‫א‬،EComplements)  K‫א‬‫א‬‫א‬‫א‬‫א‬،EF١٨J ٣ -٧٦-
  • 84. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬‫א‬EF١٨J ٣‫א‬  ‫א‬‫א‬K‫א‬(adjacent cells) ‫א‬‫א‬‫א‬K‫א‬،‫א‬   ‫א‬‫א‬‫א‬EF١٨J ٣‫א‬(1)  ،‫א‬ B ، B  AB, A B ‫א‬‫א‬‫א‬K‫א‬   WA،‫א‬  Y = A B + AB E‫א‬‫א‬‫א‬F Y = A(B + B) = A •1 = A ‫א‬EF١٨J ٣‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬K(A)‫א‬(Y)‫א‬  KEF١٨J ٣ EF١٩J ٣‫א‬‫א‬‫א‬WE٥J ٣F   K‫א‬ ،‫א‬‫א‬‫א‬،‫א‬W‫א‬   KEF١٩J ٣ EF١٩J ٣‫א‬(1)‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ‫א‬‫א‬،‫א‬‫א‬‫א‬(0)KEF١٩J ٣ E‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،EF١٩J ٣   A , A ‫א‬‫א‬‫א‬K‫א‬  K A B ‫א‬ C , C ‫א‬‫א‬‫א‬، BC ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬KEF١٩J ٣،‫א‬ ‫א‬ OR ‫א‬‫א‬AND‫א‬  ‫א‬‫א‬‫א‬،١٦‫א‬‫א‬‫א‬ -٧٧-
  • 85. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬‫א‬‫א‬، OR‫א‬AND‫א‬  KEF١٩J ٣‫א‬٦‫א‬‫א‬  ‫א‬ A 0 0 0 0 1 1 1 1 A A B B B C 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1  E F ‫א‬ Y 0 0 1 0 1 1 1 0 BC CC BC A BC BC 1     Y 1 A 1 1     Y = AB + B C AB BC   EF EF  K‫א‬‫א‬E١٩J ٣F E‫א‬F‫א‬(1's)‫א‬  ،‫א‬E٢٠J ٣FK2‫א‬‫א‬،، ‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬E1'sF‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬K‫א‬  ‫א‬‫א‬F‫א‬‫א‬،‫א‬  ‫א‬،‫א‬‫א‬،   KE‫א‬‫א‬‫א‬ -٧٨-
  • 86. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬   AB  AC CD CD CD CD AB 1 1 1 1  AB 1 0 AB 1 0 0 1  AB 1 0 1 1 1 0  AB 1 0 1 1 0  AB 1 AD AB C CD AB AD CD D  + ABCD + A B C D + A B CD Y = AB C + AD + AB D + A B E F CD AB AB 1 1 1 1 1 1 1 BC Y = AC + B C + D E‫א‬F E‫א‬F  EF   B D 1 1 0 AB 1 1 1 1 CD CD 1 0 0 1 1 0 1 AB 1 1 0 1 1 1 1 1 CD AB BD     CD   AB  Y = AB C D + ABC D + ABC D + ABCD A B C D + A B C D + A B CD + A B C D + AB C D + ABCD + A B CD + ABCD + A B C D + A B C D + AB C D + A B C D CD AB 0 1 E‫א‬F 0 0 1 + A B C D + A B CD + A B C D 1 0 Y = B+D 1 AB CD AB Y= 1 + ABCD + ABC D + AB C D + ABC D E‫א‬F E‫א‬F C D CD 1 Y = A B C D + A B CD + A B C D + AB C D Y = A B C D + A B C D + A B CD + A B C D + A B C D + A BC D + AB C D + AB C D CD E‫א‬F EF + ABC D + ABC D + ABCD + AB C D + AB C D + ABCD + ABCD E‫א‬F Y = C D + AB + BD E‫א‬F EF K‫א‬‫א‬E٢٠J ٣F -٧٩-   
  • 87. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬  EF٢١J ٣‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬W٦J ٣  K‫א‬   ‫א‬ A 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 B 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 C 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 ‫א‬ D 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 Y 0 1 0 1 0 1 0 1 0 0 0 1 0 0 0 1  K‫א‬‫א‬‫א‬‫א‬EF٢١J ٣ (Y)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  KEF٢١J ٣،(1)‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬  Y = A BCD + A BCD + ABCD + ABCD + A BCD + ABCD  ،EF٢١J ٣‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬(Y)‫א‬‫א‬‫א‬   -٨٠-
  • 88. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬   AD  CD CD CD CD 0 1 1 0  0 1 1 0  AB 0 0 1 0  AB 0 0 1 0  AB  CD  K٦J ٣‫א‬EF٢١J ٣   ‫א‬EF٢١J ٣ ‫א‬‫א‬‫א‬‫א‬K(1's)‫א‬  K AD  ‫א‬ C ‫א‬، C ‫א‬ B ‫א‬ B ‫א‬   ‫א‬‫א‬‫א‬   W‫א‬‫א‬‫א‬K CD ‫א‬ A ، A ، B ، B ‫א‬‫א‬ Y = AD + CD  Binary Adders and Subtractors ‫א‬‫א‬‫א‬‫א‬٧J ٣ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ The Half-Adder Circuit ‫א‬‫א‬‫א‬١J ٧J ٣ ‫א‬‫א‬‫א‬E٣J ٣F‫א‬،‫א‬‫א‬‫א‬‫א‬   .[Carry (C)]‫א‬‫א‬‫א‬[Sum(S)]‫א‬‫א‬ A , B ‫א‬  -٨١-
  • 89. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬   ‫א‬  ‫א‬  A 0 B 0 S 0 C 0 0 + 0 = 0  0 1 1 0 0 + 1 = 1  1 0 1 0 1 + 0 = 1  1 1 0 1 1 + 1 = 102 or 210 1  0 ‫א‬  K‫א‬‫א‬‫א‬‫א‬E٣J ٣F ‫א‬‫א‬K(XOR)‫א‬‫א‬‫א‬ (S )‫א‬‫א‬ EF٢٢J ٣KAND‫א‬‫א‬(c)‫א‬   K‫א‬‫א‬‫א‬‫א‬ C, S ‫א‬‫א‬ A, B ‫א‬‫א‬‫א‬    K‫א‬‫א‬‫א‬‫א‬ A A S(sum) ‫א‬ B ≡  B  HA C(carry) ‫א‬  S C  EF EF  K‫א‬‫א‬‫א‬‫א‬E٢٢J ٣F ‫א‬EF٢٢J ٣‫א‬‫א‬‫א‬‫א‬‫א‬ S,C‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬EHalf AdderF HA  W‫א‬،‫א‬‫א‬   S = AB + A B C = AB          The Full-Adder Circuit ‫א‬‫א‬‫א‬٢J ٧J ٣ (2-bits)‫א‬‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬(carry)‫א‬‫א‬‫א‬‫א‬ -٨٢-
  • 90. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬  (bits)‫א‬‫א‬‫א‬  ‫א‬،‫א‬‫א‬‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬ ،‫א‬(bits)‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬A,B‫א‬‫א‬، ‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬EInput carryFCin  KE٤J ٣F‫א‬‫א‬‫א‬‫א‬.(Sum)‫א‬ ، (Carry) ٍ   ‫א‬ ‫א‬ A 0 B 0 Cin 0 S 0 C 0 0+0+0=0 0 0 1 1 0  0+0+1=1 0 1 0 1 0  0+1+0=1 0 1 1 0 1  1 0 0 1 0 0 + 1 + 1 = 102 or 210 1  0‫א‬ 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 1+0+0=1  1 + 0 + 1 = 102 or 210 1  0 ‫א‬ 1 + 1 + 0 = 102 or 210 1  0 ‫א‬ 1 + 1 + 1 = 112 or 310 1  1 ‫א‬  K‫א‬‫א‬‫א‬‫א‬E٤J ٣F  ‫א‬ A, B, C ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬ C, S ‫א‬‫א‬K‫א‬E 2 3 = 8 F‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬    W‫א‬ S , C ‫א‬‫א‬‫א‬‫א‬   S = A BC in + ABC in + A BC in + ABC in C = ABC in + A BC in + ABC in + ABC in  -٨٣-
  • 91. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  WS‫א‬‫א‬‫א‬‫א‬  S = A BC in + ABC in + A BC in + ABC in = (AB + A B)C in + (A B + AB)C in  XNOR   A B + AB ‫א‬‫א‬،XOR AB + A B ‫א‬‫א‬    W‫א‬‫א‬‫א‬‫א‬  S = (A ⊕ B)C in + (A ⊕ B)C in  Cin ‫א‬ (A ⊕ B) XOR‫א‬     WS‫א‬‫א‬  S = (A ⊕ B) ⊕ C in = A ⊕ B ⊕ C in   ‫א‬ A, B ‫א‬، XOR ‫א‬‫א‬ S    K Cin ‫א‬  W‫א‬‫א‬ C ‫א‬  C = ABC in + A BC in + ABC in + ABC in = (AB + A B)C in + AB(C in + C in ) = (A ⊕ B)C in + AB ⇐ ( Cin + C in = 1)  ‫א‬‫א‬‫א‬KEF٢٣J ٣‫א‬CS ‫א‬FA‫א‬EF٢٣J ٣‫א‬‫א‬  K‫א‬‫א‬ (Full Adder)  -٨٤-
  • 92. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬  A A B Cin B S(sum) ≡ Cin FA C(carry) C S E F EF  K‫א‬‫א‬‫א‬‫א‬E٢٣J ٣F ‫א‬‫א‬‫א‬EF٢٣J ٣‫א‬‫א‬  OR‫א‬2‫א‬‫א‬‫א‬‫א‬ OR‫א‬‫א‬  KE٢٤J ٣F‫א‬  S A Cin HA S A B B  C HA C C K‫א‬‫א‬‫א‬E٢٤J ٣F  S     Half Subtractor Circuit ‫א‬‫א‬‫א‬٣J ٧J ٣ ‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬ K  K ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬ (bit)،‫א‬ ،‫א‬‫א‬‫א‬K(difference)‫א‬‫א‬(bit) -٨٥-
  • 93. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬  K‫א‬‫א‬(Borrowed)(1)‫א‬   K، ‫א‬(2-bits)‫א‬‫א‬‫א‬‫א‬ ‫א‬A K‫א‬‫א‬(1)     ، A ≥ B KB, A ‫א‬(A – B)KB  ‫א‬.(Difference bit)‫א‬‫א‬0 – 0 = 0, 1 – 0 = 1, 1 – 1 = 0W‫א‬ ‫א‬‫א‬‫א‬K‫א‬‫א‬(1)‫א‬‫א‬‫א‬،0 – 1A<B  (10)‫א‬،‫א‬‫א‬،‫א‬2  K2 – 1 = 1‫א‬،(2)‫א‬K‫א‬ ‫א‬‫א‬ (D)‫א‬،‫א‬‫א‬  K(B0)‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬( B 0 )‫א‬،(D)‫א‬‫א‬KE٥J ٣F  W‫א‬ D = AB + A B B 0 = AB  ‫א‬ A 0 0 1 1  ‫א‬ B 0 1 0 1 D 0 1 1 0 B0 0 1 0 0  K‫א‬‫א‬‫א‬‫א‬E٥J ٣F ‫א‬(S)‫א‬(D)‫א‬  A ‫א‬‫א‬‫א‬(C)‫א‬( B 0 )‫א‬، XOR  ‫א‬   K B ، A ‫א‬ AND ‫א‬( B 0 )‫א‬ ‫א‬EF٢٥J ٣،‫א‬‫א‬EF٢٥J ٣  K(Half Subtractor)‫א‬ HS ‫א‬،‫א‬ -٨٦-
  • 94. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬  A A D(difference) ‫א‬ B ≡ B   HS  B0(borrow) ‫א‬ K‫א‬‫א‬‫א‬‫ א‬E٢٥J ٣F  D  B0   The Full-Subtractor Circuit ‫א‬‫א‬‫א‬٤J ٧J ٣ ‫א‬‫א‬ (2-bits)‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬K‫א‬‫א‬K‫א‬‫א‬(1)   ‫א‬K‫א‬( B i n ) ‫א‬‫א‬(B)‫א‬(A)‫א‬ A, B, B in    KE٦J ٣F‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬ D, B 0  ‫א‬ A 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 ‫א‬ Bin 0 1 0 1 0 1 0 1 D 0 1 1 0 1 0 0 1 B0 0 1 1 1 0 0 0 1  K‫א‬‫א‬‫א‬‫א‬E٦J ٣F ‫א‬ 0's,1's ‫א‬‫א‬‫א‬‫א‬‫א‬  K A − B − B in ‫א‬‫א‬‫א‬ 0's,1's K‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬ B in = 0 ‫א‬‫א‬   (2) B 0 = 1‫א‬‫א‬‫א‬(1) A = 0, B = 0, B in = 1  K D = 1 ،2 – 0 – 1 = 1،A -٨٧-
  • 95. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬‫א‬‫א‬(1) A = 0, B = 1, B in = 1   K D = 0 ،2 – 1 – 1 = 0،A = 2، B 0 = 1 K D = 0 ، B 0 = 0 ‫א‬A – B – Bin = 0، A = 1, B = 0, B in = 1  ‫א‬‫א‬‫א‬(1) A = 1, B = 1, B in = 1 ‫א‬  K D = 1 ،3 – 1 – 1 = 1،A=3، B 0 = 1  W‫א‬‫א‬‫א‬‫א‬‫א‬  D = ABB in + ABBin + AB Bin + ABBin  ‫א‬‫א‬،‫א‬‫א‬(S)  W‫א‬ D = (A ⊕ B) ⊕ Bin = A ⊕ B ⊕ Bin  W‫א‬‫א‬،(B0)‫א‬  B 0 = ABB in + ABBin + ABB in + ABBin  = B in ( AB + AB) + AB( Bin + B in )  B 0 = B in (A ⊕ B) + AB ⇐ ( Bin + B in = 1)  ‫א‬‫א‬‫א‬‫א‬،EF٢٦J ٣(B0), (D)‫א‬ (Full Subtractor)‫א‬FS‫א‬،EF٢٦J ٣‫א‬  K‫א‬‫א‬ ‫א‬‫א‬‫א‬EF٢٦J ٣‫א‬‫א‬‫א‬ ‫א‬2‫א‬‫א‬‫א‬‫א‬،OR‫א‬‫א‬  KE٢٧J ٣F‫א‬OR -٨٨-
  • 96. ‫א‬‫א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬   ‫٧٤١ א‬  ‫א‬  B A A B Bin D ≡ Bin B0 FS D B0 E F EF  K‫א‬‫א‬‫א‬‫א‬E٢٦J ٣F  D A Bin  D  HS D A HS B B0 B  B0 B0 K‫א‬‫א‬‫א‬E٢٧J ٣F            -٨٩-
  • 97. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬      W‫א‬‫א‬‫א‬E١ b) AB(CD + EF) a) AB(C + D ) c) (A + B + C + D ) + ABCD d) (A + B + C + D) (AB C D)   WNAND‫א‬‫א‬‫א‬‫א‬‫א‬E٢ a) ABCD + DE b) ABC + AB + D c) AB C + D + E d) ABC + ABC + ABC + ABC WNOR‫א‬‫א‬‫א‬‫א‬‫א‬E٣ a) (A + B + C) (A + B) b) ABC + (D + E )  d) (A + B) + ( C + D) c) (AB + C) (DE + F)   W‫א‬‫א‬‫א‬‫א‬‫א‬E٤  ‫א‬ ‫א‬ A B C Y 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 1 1  -٩٠-
  • 98. ‫א‬‫א‬   ‫٧٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬   W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٥ a) F1 = AB C D + ABCD + ABCD + ABC D + ABC D + ABCD b) F2 = ABCD + ABC D + AB C D + ABC D + ABCD + ABCD + ABCD c) F3 = ABC D + ABC D + ABC D + ABC D + AB C D     d) F4 = AB C D + + AB C D + ABC D + ABC D + ABCD + ABCD + AB C D + ABCD  (1 or 0)‫א‬‫א‬،E٢٣J ٣F‫א‬‫א‬‫א‬‫א‬E٦ a) A = 1, B = 1, Cin = 1 c) A = 0, B = 1, Cin = 0  W‫א‬‫א‬ b) A = 0, B = 1, Cin = 1 d) A = 1, B = 1, Cin = 0  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E٧ a) S = 0, Cout = 0 c) S = 1, Cout = 1 b) S = 1, Cout = 0 d) S = 0, Cout = 1 (1 or 0)‫א‬‫א‬،E٢٦J ٣F‫א‬‫א‬‫א‬‫א‬E٨ a) A = 1, B = 1, Bin = 1 c) A = 1, B = 1, Bin = 0  W‫א‬‫א‬ b) A = 1, B = 0, Bin = 1 d) A = 0, B = 1, Bin = 1    -٩١-
  • 99.  ‫א‬‫א‬‫א‬ ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹] ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ ٤
  • 100.  ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬  ‫א‬   ‫א‬‫א‬‫א‬   W‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬J ‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬ • K‫א‬555‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •               -٩٢-
  • 101.  ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬  ‫א‬    ‫א‬‫א‬  Introduction١J ٤ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬(Combinational Logic Circuits)  ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬ ‫א‬‫א‬‫א‬‫א‬ (Sequential Logic Circuits) ‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(Memory)‫א‬   K‫א‬ ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ ،(Flip-Flop Circuit)‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬(0)‫א‬‫א‬‫א‬ ‫א‬،(1)‫א‬(1)‫א‬‫א‬‫א‬‫א‬K(1) ‫א‬‫א‬‫א‬‫א‬K(0)‫א‬(0)‫א‬‫א‬  ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬.(Bistable Multivibrator)‫א‬‫א‬‫א‬‫א‬‫א‬ K(Digital Integrated Circuits)‫א‬‫א‬NOR‫א‬NAND ‫א‬‫א‬‫א‬،(Timers)‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬(Shift Registers)‫א‬‫א‬،(Counters)   K‫א‬  Latches‫א‬٢J ٤ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬  K‫א‬‫א‬ -٩٣-
  • 102.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  K(Bistable Multivibrator)‫א‬‫א‬‫א‬‫א‬‫א‬(Latch)‫א‬ S-R‫א‬‫א‬‫א‬‫א‬‫א‬E١J ٤F (Set Input)"1"‫א‬‫א‬‫א‬S  (Reset Input)"0"‫א‬‫א‬‫א‬ R  K‫א‬ Q ‫א‬Q  SET INPUT  S Q Q output RESET INPUT R Q Q output  KS-R‫א‬‫א‬‫א‬‫א‬‫א‬E١J ٤F  Q =1,  Q =0(Set Condition)‫א‬‫א‬ ‫א‬ .Q =0, Q = 1(Reset Condition) ‫א‬‫א‬(1)‫א‬S‫א‬‫א‬ ‫א‬‫א‬‫א‬،‫א‬Q‫א‬E‫א‬‫א‬FQ = 1 ‫א‬E‫א‬‫א‬F Q = 0‫א‬R‫א‬‫א‬K Q = 0  (1)‫א‬‫א‬S,R‫א‬، Q = 1‫א‬ ،(unpredictable)‫א‬‫א‬  K‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ NOR‫א‬S-R‫א‬‫א‬  KE٢J ٤F‫א‬‫א‬‫א‬‫א‬‫א‬  S Q Q R   K‫א‬‫א‬‫א‬S-R‫א‬‫א‬E٢J ٤F -٩٤-
  • 103.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬F(1)NOR‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،E‫א‬    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،E١J ٤F    K(Active High Inputs)  ‫א‬ S R ‫א‬ Q 0 0 Q0 0 1 0 1 0 1 1 1 ? ‫א‬ (Mode of Operation) E‫א‬F‫א‬ No Change ‫א‬‫א‬ Latch RESETS ‫א‬‫א‬ Latch SETS ‫א‬ Invalid condition  K‫א‬‫א‬‫א‬S-R‫א‬‫א‬‫א‬E١J ٤F   W‫א‬‫א‬‫א‬ ‫א‬‫א‬ S,R‫א‬(0)‫א‬‫א‬ -١ ‫א‬‫א‬‫א‬E‫א‬‫א‬‫א‬F(Q)‫א‬    K‫א‬ Q‫א‬‫א‬(1)(0)R‫א‬‫א‬‫א‬ -٢ ‫א‬‫א‬،‫א‬‫א‬‫א‬ E‫א‬‫א‬FQ = 0 (0) KQ = 0 ‫א‬‫א‬‫א‬(1)(0)S ‫א‬‫א‬‫א‬ -٣ ‫א‬،‫א‬‫א‬‫א‬E‫א‬‫א‬FQ = 1(1)(0)Q KQ = 1‫א‬ ‫א‬‫א‬‫א‬ S,R‫א‬(1)‫א‬‫א‬ -٤ ‫א‬‫א‬‫א‬‫א‬،NOR‫א‬‫א‬ K‫א‬ -٩٥-
  • 104.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬ -٥ ،‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬ K‫א‬ ‫א‬‫א‬‫א‬E٣J ٤FNAND‫א‬‫א‬‫א‬ E٢J ٤F‫א‬‫א‬‫א‬‫א‬‫א‬(0)NAND‫א‬    K(Active Low Inputs)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ S  Q   Q R  K‫א‬‫א‬‫א‬S-R‫א‬‫א‬E٣J ٤F   ‫א‬ S R ‫א‬ Q 0 0 ? 0 1 1 1 0 0 1 1 Q0 ‫א‬ (Mode of Operation) ‫א‬ Invalid condition ‫א‬‫א‬ Latch SETS ‫א‬‫א‬ Latch RESETS E‫א‬F‫א‬ No Change  K‫א‬‫א‬‫א‬S-R‫א‬‫א‬‫א‬E٢J ٤F  W‫א‬‫א‬‫א‬ Q‫א‬‫א‬‫א‬‫א‬‫א‬(1)‫א‬‫א‬ -١ KE‫א‬‫א‬F ‫א‬‫א‬ R = 1‫א‬، S = 0‫א‬‫א‬‫א‬ -٢ Q = 1‫א‬‫א‬،‫א‬‫א‬‫א‬ (1) K -٩٦-
  • 105.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬ R = 0‫א‬، S = 1 ‫א‬‫א‬‫א‬ -٣ Q = 0‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬،(0) K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(0)‫א‬ -٤ K‫א‬NAND ‫א‬‫א‬‫א‬‫א‬‫א‬(Logic Symbol)‫א‬‫א‬E٤J ٤F‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   S R  Q Q S Q S Q Q R Q R Q Q  EFEF  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٤J ٤F ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ، S = 0, R = 0 K(Q)‫א‬ S, R   K‫א‬‫א‬ ‫א‬KE٥J ٤F S, R ‫א‬‫א‬W١J ٤  KQ = 0‫א‬Q‫א‬‫א‬‫א‬(Q)‫א‬  W‫א‬ S R  Q  K‫א‬‫א‬‫א‬‫א‬E٥J ٤F -٩٧-
  • 106.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬   Clocked S-R Flip–Flop ‫א‬‫א‬S-R‫א‬٣J ٤ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ S − R S-R‫א‬ ‫א‬‫א‬‫א‬‫א‬(Q)‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ E‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬S-R‫א‬‫א‬،‫א‬‫א‬  K‫א‬  ‫א‬‫א‬‫א‬ ،(CK)‫א‬‫א‬(Clock Pulse)‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ S-R‫א‬‫א‬E٦J ٤F  K(CK)‫א‬‫א‬‫א‬  S Q S CK  R Q CK Q R Q  EFEF  K‫א‬‫א‬S-R‫א‬‫א‬E٦J ٤F ‫א‬‫א‬‫א‬EF٦J ٤‫א‬ ‫א‬(Positive Edge Trigger)‫א‬‫א‬S-R‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬EF٦J ٤‫א‬،(1)(0)‫א‬ ‫א‬ (Negative Edge Trigger)‫א‬‫א‬‫א‬  K(0)(1)‫א‬ ‫א‬،NAND‫א‬‫א‬‫א‬‫א‬S-R‫א‬‫א‬E٧J ٤F ‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬NAND  -٩٨-
  • 107.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬‫א‬(Q)‫א‬S,R‫א‬   K‫א‬‫א‬‫א‬  S  Q  CK  R Q  K‫א‬‫א‬S-R‫א‬‫א‬E٧J ٤F  W‫א‬‫א‬‫א‬‫א‬S-R‫א‬E٣J ٤F‫א‬ (0)‫א‬‫א‬S,R‫א‬‫א‬،‫א‬CK‫א‬‫א‬ J ١  K‫א‬‫א‬‫א‬‫א‬‫א‬ (0)‫א‬‫א‬(S = 0,R = 1)‫א‬R‫א‬‫א‬ J ٢ .(Reset)‫א‬‫א‬‫א‬(0) ‫א‬(1)  (0)‫א‬‫א‬(S = 1,R = 0)‫א‬‫א‬S‫א‬‫א‬ J ٣ .(Set)‫א‬‫א‬‫א‬Q = 1‫א‬(1) ‫א‬S = 1, R = 1‫א‬‫א‬  K‫א‬ ‫א‬ S R CK ‫א‬ (Mode of Operation) E‫א‬F‫א‬ 0 0 X Q0 No Change ‫א‬‫א‬ 0 1 0 Latch RESETS ‫א‬‫א‬ 1 0 1 Latch SETS ‫א‬ 1 1 ? Invalid condition  ↑Z(1)‫א‬(0)‫א‬   XZ ‫א‬ Q       Q0Z‫א‬‫א‬‫א‬  K‫א‬‫א‬S-R‫א‬‫א‬‫א‬E٣J ٤F -٩٩- 
  • 108.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬]‫א‬‫א‬‫א‬S-R‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬[(0)(1)  K(0)(1)‫א‬‫א‬ ‫א‬،E٦J ٤F‫א‬S-R‫א‬‫א‬ (Q)‫א‬‫א‬W٢J ٤  ‫א‬‫א‬‫א‬KE٧J ٤FS,R,CK‫א‬  K‫א‬‫א‬Q = 0  CK 1 2 3 4 5 6   S  R  Q   K‫א‬‫א‬S-R‫א‬‫א‬‫א‬‫א‬E٧J ٤F  W‫א‬  KQ = 0(Q)‫א‬،S = 0, R = 0‫א‬‫א‬‫א‬ -١ K(Reset)Q = 0‫א‬،S = 0, R = 1‫א‬‫א‬‫א‬ -٢ K(Set)Q = 1(1)Q ‫א‬،S = 1, R = 0‫א‬‫א‬‫א‬ -٣ .(Reset)Q = 0‫א‬،S = 0, R = 1‫א‬‫א‬‫א‬‫א‬ -٤ K(Set)Q =1‫א‬،S = 1, R = 0‫א‬‫א‬‫א‬ -٥ KQ = 1 (1)‫א‬،S = 1, R = 0 ‫א‬‫א‬‫א‬ -٦    -١٠٠-
  • 109.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬   D-Type Flip-FlopD ‫א‬‫א‬‫א‬٤J ٤ (Single Bit)‫א‬‫א‬‫א‬D‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬S-R‫א‬‫א‬‫א‬K(10)‫א‬  KE٨J ٤FD  S D Q CK Q R   KD‫א‬‫א‬‫א‬E٨J ٤F  ‫א‬‫א‬D‫א‬‫א‬D‫א‬‫א‬‫א‬ ‫א‬،CK‫א‬‫א‬‫א‬(1)‫א‬‫א‬D‫א‬KCK R = 0‫א‬،S = 1‫א‬‫א‬،[Set](1)‫א‬‫א‬‫א‬ ‫א‬KQ = 1‫א‬E٣J ٤F‫א‬‫א‬S-R‫א‬‫א‬‫א‬ ‫א‬‫א‬،CK‫א‬‫א‬‫א‬(0)‫א‬‫א‬D R = 1 ‫א‬،S = 0‫א‬‫א‬،[Reset](0)‫א‬‫א‬ ‫א‬(1)(Set)‫א‬‫א‬KQ = 0‫א‬E٣J ٤F  K‫א‬‫א‬(0)(0)‫א‬‫א‬،‫א‬ ‫א‬‫א‬‫א‬‫א‬D‫א‬‫א‬‫א‬‫א‬‫א‬  KE٤J ٤F‫א‬(Positive Edge Trigger) ‫א‬‫א‬  ‫א‬ D CK ‫א‬ Q ‫א‬ (Mode of Operation) 1 1 ‫א‬‫א‬(SET) 0 0 (stores a 1) ‫א‬‫א‬(RESET) (stores a 0)  ↑Z(1)‫א‬(0)‫א‬  K‫א‬‫א‬D ‫א‬‫א‬‫א‬E٣J ٤F -١٠١-
  • 110.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬K‫א‬‫א‬(D)‫א‬(Q)‫א‬‫א‬  (D)‫א‬‫א‬‫א‬D‫א‬‫א‬E٩J ٤F E١٠J ٤F‫א‬K‫א‬‫א‬‫א‬ (CK) ‫א‬‫א‬   KNAND‫א‬D‫א‬‫א‬   S D Q D Q  CK CK Q R Q     KD‫א‬‫א‬E٩J ٤FKNAND‫א‬D‫א‬‫א‬E١٠J ٤F  ‫א‬E٩J ٤F‫א‬D‫א‬‫א‬‫א‬EQF‫א‬‫א‬W٣J ٤ Q = 0 ‫א‬‫א‬‫א‬KE١١J ٤FEDF‫א‬   K‫א‬  W‫א‬ CK D Q     KD‫א‬‫א‬‫א‬‫א‬‫א‬E١١J ٤F ‫א‬(1)(0)‫א‬‫א‬‫א‬‫א‬(D)‫א‬(Q)‫א‬  K‫א‬ -١٠٢-
  • 111.  ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬  ‫א‬   J-K Flip Flop‫א‬‫א‬J-K‫א‬٥J ٤ ‫א‬‫א‬J,K‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬J-K‫א‬‫א‬   ‫א‬S-R‫א‬‫א‬‫א‬،‫א‬ ‫א‬‫א‬‫א‬S-R‫א‬J-K‫א‬K‫א‬ J-K‫א‬‫א‬.(Reset)‫א‬‫א‬(Set)‫א‬‫א‬‫א‬‫א‬  KS-R‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬J-K‫א‬‫א‬E١٢J ٤F‫א‬   ‫א‬‫א‬‫א‬S-R‫א‬‫א‬‫א‬  K‫א‬‫א‬(1)‫א‬‫א‬J,K‫א‬‫א‬‫א‬   J Q CK  Q J CK Q K K Q     K‫א‬‫א‬‫א‬‫א‬J-K‫א‬‫א‬E١٢J ٤F ‫א‬SR‫א‬‫א‬‫א‬‫א‬‫א‬E١٢J ٤F  K‫א‬ Q ،Q ‫א‬‫א‬‫א‬J-K‫א‬E٥J ٤F‫א‬ ‫א‬‫א‬‫א‬‫א‬،(0)J,K‫א‬ ‫א‬،‫א‬‫א‬J = 0, K = 1‫א‬‫א‬(0)‫א‬(Reset)‫א‬ J = 1, K = 0 ‫א‬‫א‬J-K(Set)‫א‬‫א‬‫א‬‫א‬  ،(Toggle)‫א‬J-K‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬  ‫א‬‫א‬Q‫א‬(1)‫א‬‫א‬J,K‫א‬  KCK‫א‬‫א‬‫א‬ -١٠٣-
  • 112.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬   ‫א‬ J K CK ‫א‬ Q ‫א‬ (Mode of Operation) E‫א‬F‫א‬ 0 0 Q0 No Change ‫א‬‫א‬ 0 1 0 (RESET) ‫א‬‫א‬ 1 0 1 (SET) ‫א‬ Q0 1 1 Toggle  ↓Z(0)‫א‬(1)‫א‬ Q0Z‫א‬‫א‬‫א‬  K‫א‬‫א‬J-K‫א‬E٥J ٤F ‫א‬E١٢J ٤F‫א‬J-K‫א‬‫א‬(Q)‫א‬‫א‬W٤J ٤ ‫א‬‫א‬KE١٣J ٤FCKJ-K‫א‬  K‫א‬Q = 0  W‫א‬  CK 1 3 2 4 5 J K  Q  K‫א‬‫א‬J-K‫א‬‫א‬‫א‬‫א‬E١٣J ٤F Q ‫א‬‫א‬‫א‬(1)J,K،‫א‬‫א‬‫א‬ -١ K(1)‫א‬ KJ = K = 0‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ -٢ KQ = 0(Reset)J = 0, K = 1،‫א‬‫א‬ -٣ -١٠٤-
  • 113.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  KQ = 1(Set)J = 1, K = 0،‫א‬‫א‬‫א‬ -٤ Q‫א‬J,K‫א‬‫א‬‫א‬ (Set)‫٥- א‬ K(1)‫א‬  T-Type Flip-Flop T ‫א‬‫א‬‫א‬٦J ٤ ‫א‬‫א‬J-K‫א‬‫א‬T‫א‬‫א‬‫א‬ ‫א‬‫א‬،E١٤J ٤F‫א‬J,K‫א‬ (Toggle)‫א‬T‫א‬K‫א‬‫א‬T‫א‬‫א‬T  K‫א‬‫א‬ ‫א‬‫א‬،‫א‬‫א‬CK‫א‬(1)‫א‬(T)‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬CK‫א‬‫א‬‫א‬  KE١٤J ٤FCK‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬    T J Q CK K  Q  KT‫א‬‫א‬‫א‬‫א‬‫א‬E١٤J ٤F  KE٦J ٤FT‫א‬‫א‬‫א‬‫א‬ ‫א‬ T CK ‫א‬ Q ‫א‬ (Mode of Operation) E‫א‬F‫א‬ Q0 0 No Change ‫א‬ Q0 1 Toggle  ↓Z(0)‫א‬(1)‫א‬   Q0Z‫א‬‫א‬‫א‬    KT‫א‬‫א‬E٥J ٤F -١٠٥- 
  • 114.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬E١٤J ٤F‫א‬(T)‫א‬‫א‬‫א‬Q‫א‬‫א‬W٥J ٤ ‫א‬‫א‬E١٥J ٤FCK‫א‬T‫א‬  K‫א‬Q = 0   W‫א‬  CK  T   Q  KT‫א‬‫א‬‫א‬‫א‬‫א‬E١٥J ٤F  ،‫א‬‫א‬‫א‬T = 1‫א‬Q‫א‬‫א‬ T = 1‫א‬‫א‬،Q = 0QT = 0‫א‬‫א‬‫א‬  K‫א‬(1)(0)Q‫א‬ Master-Slave Flip-Flop‫א‬–‫א‬٧J ٤ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K(Edge Triggered)‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬،(Master-Slave)‫א‬–‫א‬‫א‬(Pulse Triggered)  ‫א‬(Complete Clock Pulse)‫א‬‫א‬‫א‬  K‫א‬‫א‬ ‫א‬،‫א‬J ‫א‬‫א‬S-R‫א‬EF١٦J ٤  (Master)‫א‬‫א‬،(Slave)‫א‬(Master)‫א‬‫א‬‫א‬S-R (Slave)‫א‬‫א‬، (CK)‫א‬‫א‬‫א‬‫א‬  K( CK )‫א‬‫א‬  -١٠٦-
  • 115.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  Master S  Slave Y Q Q CK    CK Y  R   K‫א‬J ‫א‬S-R‫א‬‫א‬EF١٦J ٤   ،EF١٦J ٤CK، CK  ‫א‬‫א‬  ‫א‬‫א‬،(CK)‫א‬‫א‬‫א‬‫א‬ (Master)‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬(Slave)  K( CK )‫א‬‫א‬‫א‬  WS,R‫א‬Q، Q   (Master)‫א‬‫א‬(CK)(High)‫א‬‫א‬W‫א‬‫א‬ (Reset)‫א‬‫א‬ (Set)‫א‬‫א‬‫א‬ (Enabled)‫א‬  KS,R‫א‬‫א‬  (slave) ‫א‬‫א‬(CK)(Low)‫א‬‫א‬W‫א‬‫א‬     KY‫א‬‫א‬‫א‬‫א‬Q‫א‬(Enabled)‫א‬ S-R‫א‬‫א‬‫א‬EF١٦J ٤‫א‬‫א‬  K‫א‬‫א‬S-R‫א‬‫א‬‫א‬‫א‬K‫א‬J ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬(CK)‫א‬   K‫א‬‫א‬(Low)‫א‬(High) ،‫א‬J ‫א‬S-R‫א‬‫א‬‫א‬EF١٦J ٤  ‫א‬‫א‬‫א‬ t5t0‫א‬(CK)‫א‬‫א‬  KS,R -١٠٧-
  • 116.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬(Enabled)‫א‬ (Master)‫א‬‫א‬،t0‫א‬ • ‫א‬‫א‬ S = 1, R = 0‫א‬(CK)‫א‬‫א‬(High)‫א‬   K( Y = 0 )Y = 1‫א‬،‫א‬‫א‬(Set) • (Low)‫א‬‫א‬(Disabled)‫א‬‫א‬،t1‫א‬ ‫א‬(Enabled)‫א‬(Slave)‫א‬‫א‬،CK Q‫א‬،‫א‬‫א‬‫א‬ Y, Y K CK (High)‫א‬  ‫א‬‫א‬‫א‬‫א‬KQ = 1(Set )‫א‬‫א‬ F‫א‬‫א‬‫א‬  KE CK = 1‫א‬‫א‬ Q = 1, Q = 0 ‫א‬ Y = 1, Y = 0  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬ S R CK 0 0 0 1 ‫א‬ Q Q0 ‫א‬ (Mode of Operation) E‫א‬F‫א‬ 0 ‫א‬‫( א‬RESET) 1 0 1 ‫א‬‫(א‬SET) 1 1 ‫؟‬ ‫א‬   K‫א‬J ‫א‬S-R‫א‬‫א‬‫א‬EF١٦J ٤   -١٠٨- 
  • 117.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬  CK  R (RESET)  Master Enable Master Enable S (SET)   Master Enable Master Enable  ‫א‬ Y  t0 t1 t2 t3 t4 t5 ‫ﻜﺎل‬ ‫أﺷ‬ ‫ﻧﺒﻀﺎت اﻟﺘﺎﺑﻊ‬ (Master) Y   CK Slave Enabl Slave Enable Slave Enable   ‫أﺷﻜﺎت ﻧﺒﻀﺎت‬ ‫اﻟﻤﺘﺒﻮع‬ (Slave) Y (Slave Set) Y(Slave Re set )   Q  K‫א‬‫א‬S-R‫א‬‫א‬‫א‬‫א‬EF١٦J ٤ (High)‫א‬‫א‬،‫א‬‫א‬‫א‬،t2‫א‬  • ‫א‬‫א‬ Y = 0, Y = 1 ‫א‬S = 0, R = 1‫א‬CK  .(Reset) • ،CK (Low)‫א‬‫א‬‫א‬‫א‬،t3‫א‬   (Reset)‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬  KQ = 0‫א‬ Y‫א‬(Low)‫א‬S,R‫א‬،t4‫א‬ S‫א‬،t4‫א‬‫א‬K(Y = 0)‫א‬‫א‬‫א‬، KY = 1‫א‬‫א‬(High)‫א‬ -١٠٩- •
  • 118.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  • ،‫א‬‫א‬‫א‬‫א‬‫א‬،t5‫א‬  KQ = 1Q‫א‬Y = 1‫א‬   ‫א‬ D CK ‫א‬ Q 1 1 0 ‫א‬ (Mode of Operation)  (SET)‫א‬‫א‬ (stores a 1) (RESET)‫א‬‫א‬ (stores a 0) 0 E F D Clock in S S CK R Q CK CK R    Q E F  K‫א‬‫א‬‫א‬J ‫א‬D‫א‬‫א‬‫א‬E١٧J ٤F  EF١٧J ٤،‫–א‬‫א‬D‫א‬‫א‬EF١٧J ٤  ‫–א‬‫א‬D‫א‬‫א‬،‫–א‬‫א‬S-R‫א‬‫א‬K‫א‬‫א‬   KQ‫א‬CK‫א‬‫א‬ EF١٨J ٤‫א‬،‫–א‬‫א‬J-K‫א‬‫א‬EF١٨J ٤  ‫א‬‫א‬‫א‬EF١٨J ٤‫א‬K‫א‬‫א‬‫א‬‫א‬  (Q)‫א‬‫א‬‫–א‬‫א‬J-K    K‫–א‬‫א‬S-R‫א‬‫א‬‫א‬‫א‬‫א‬ -١١٠-
  • 119.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬   Master Slave J Y Q CK CK Q Y K   K‫א‬J ‫א‬J-K‫א‬‫א‬EF١٨J ٤  ‫א‬ ‫א‬ J K CK Q Q0 0 0 0 1 0 ‫א‬ (Mode of Operation) E‫א‬F‫א‬ ‫א‬‫( א‬RESET) 1 0 1 ‫א‬‫א‬(SET) 1 1 Q0 ‫א‬(Toggle)   K‫א‬J ‫א‬J-K‫א‬‫א‬‫א‬EF١٨J ٤ -١١١-
  • 120.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ME ME ME ME ME ME ‫א‬  ME ME ME ME CK ME = Master Enabled J K (Master) ‫أﺷﻜﺎل ﻧﺒﻀﺎت اﻟﺘﺎﺑﻊ‬ Y Y CK SE SE SE SE SE SE SE SE SE SE = Slave Enabled Y (Slave) ‫أﺷﻜﺎل ﻧﺒﻀﺎت اﻟﻤﺘﺒﻮع‬ Y Q  K‫א‬J ‫א‬J-K‫א‬‫א‬‫א‬EF١٨J ٤ ‫א‬‫א‬‫א‬‫א‬ ‫א‬ (PRE ) (PRESET)‫א‬‫א‬‫א‬K‫א‬‫א‬ ‫א‬‫א‬E١٩J ٤F‫א‬ (CLR ) (CLEAR)‫א‬‫א‬ ‫א‬‫א‬K CLR ، PRE  S-R ‫א‬  ،Q = 1(SET)‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ ‫א‬،Q = 0 (RESET)‫א‬‫א‬ (RESET)‫א‬‫א‬‫א‬K‫א‬Q‫א‬    (PRE)  ‫א‬K‫א‬‫א‬‫א‬ ‫א‬(CLEAR)‫א‬  ، PRE = 0 (1)‫א‬Q‫א‬،‫א‬ -١١٢-
  • 121.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  (0)‫א‬Q‫א‬ (CLR ) ‫א‬ S-R‫א‬‫א‬‫א‬ ‫א‬E٧J ٤FK CLR = 0  Q‫א‬EF PRE = 0 ‫א‬ CLR = 1‫א‬   PRE = 1 ‫א‬‫א‬‫א‬KCK, S, R‫א‬‫א‬،(1) ‫א‬(0)Q‫א‬‫א‬EF CLR = 0   KCK, S, R‫א‬ PRE  S Q  CK R Q  CLR   K CLR ، PRE S-R‫א‬‫א‬‫א‬‫א‬E١٩J ٤F  ‫א‬ PRE CLR CK S 0 1 X X 1 0 X X 0 0 X X R X ‫א‬ Q 1 ‫א‬ (Mode of Operation) ‫א‬‫א‬(SET) X 0 ‫א‬‫( א‬RESET) X ? ‫א‬   KS-R‫א‬‫א‬ CLR ، PRE ‫א‬E٧J ٤F -١١٣-
  • 122.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬  Timer Circuits ‫א‬‫א‬٨J ٤ ،‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬  ‫א‬K‫א‬‫א‬‫א‬‫א‬(Clock Signal)‫א‬   (Positive Edge)‫א‬‫א‬(Sharp)‫א‬‫א‬K  K‫א‬‫א‬‫א‬‫א‬(Negative Edge)‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬J-K, S-R,D-Type‫א‬   .(Set and Reset States)(bi)،(Bistable Multivibrator) ‫א‬(Astable Multivibrator)‫א‬‫א‬‫א‬،‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،   (Mono)‫א‬‫א‬‫א‬‫א‬(Monostable Multivibrator)  K(Fixed Duration)(Rectangular Pulse)(Triggered) Astable Multivibrator Circuit‫א‬‫א‬‫א‬‫א‬‫א‬١J ٨J ٤ (Free running)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬E٢٠J ٤F‫א‬‫א‬  K (Schmitt-trigger)(Inverter)‫א‬   E‫א‬FDischarge ∫ ∫ 1(0) + 0 (1) C E‫א‬F Charge +5V R     K‫א‬‫א‬‫א‬‫א‬‫א‬E٢٠J ٤F -١١٤-
  • 123.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬،‫א‬‫א‬‫א‬  .(High)(Not)‫א‬‫א‬ (Low)‫א‬‫א‬،(0) ‫א‬‫א‬‫א‬،(R)‫א‬‫א‬(C)‫א‬  (High)‫א‬‫א‬‫א‬‫א‬،R,C‫א‬‫א‬  ‫א‬،(Low)‫א‬‫א‬‫א‬K‫א‬   ‫א‬‫א‬،(Low)‫א‬‫א‬‫א‬K  K‫א‬(High) Monostable Multivibrator Circuit‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٨J ٤ ‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬EF٢١J ٤   NOR‫א‬‫א‬‫א‬،(Low)Q‫א‬‫א‬،(Low)‫א‬(Trigger) ‫א‬‫א‬‫א‬(Low)‫א‬‫א‬‫א‬(High)   K‫א‬ ‫א‬K(Low)‫א‬ NOR ‫א‬‫א‬،(High)‫א‬   ،‫א‬‫א‬‫א‬،NOR‫א‬‫א‬ (Low)(High)‫א‬ ‫א‬‫א‬Q‫א‬(High)‫א‬ ‫א‬‫א‬NOR‫א‬‫א‬‫א‬Q‫א‬‫א‬KEF٢١J ٤  K‫א‬‫א‬ (Low)‫א‬  +5V  R Input Trigger (T) C + Output Pulse (Q) E F Input Trigger (T) Output Pulse (Q)     E F  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢١J ٤F -١١٥- 
  • 124.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬NOR‫א‬‫א‬ K‫א‬‫א‬،(resistor–capacitor network)   ‫א‬‫א‬،R‫א‬C‫א‬‫א‬  KQ‫א‬(Low)‫א‬(High)‫א‬‫א‬  The 555 Timer Circuit 555‫א‬‫א‬٣J ٨J ٤ ،‫א‬‫א‬‫א‬‫א‬555‫א‬‫א‬ 555‫א‬،E٢٢J ٤F‫א‬‫א‬(IC)  K 5KΩ ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬  +VCC E‫א‬F Discharge Threshold E‫א‬F E‫א‬F 8 7  6 5 3 Control Voltage E‫א‬F 4   1 Ground E‫א‬F 2 Trigger E‫א‬F   Output E‫א‬F Reset E‫א‬‫א‬F  K555‫א‬‫א‬E٢٢J ٤F ‫א‬‫א‬، ‫א‬‫א‬(Monostable mode)‫א‬‫א‬‫א‬‫א‬‫א‬(Astable mode) ‫א‬‫א‬‫א‬(Modulator)(Frequency Divider)  K‫א‬  ‫א‬‫א‬‫א‬‫א‬555‫א‬١J ٣J ٨J ٤ 555 Timer as an Astable Multivibrator -١١٦-
  • 125.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬   ‫א‬‫א‬555‫א‬EF٢٣J ٤  ‫א‬‫א‬K(Free running)‫א‬(Astable) ،‫א‬C‫א‬‫א‬EF٢٣J ٤  K(0)E‫א‬F+Vcc‫א‬‫א‬   +5V   555 Timer 5KΩ RA 5   1/3 VCC + Comparator (A) RL - 2/3 VCC C Output Q S-R Flip-Flop 5KΩ 2 Inverting Buffer/Driver R 6 RB   - S 3 Inverter EF Comparator (B) + +  4 8 5KΩ Discharge Transistor 7 E‫א‬‫א‬F   1  K‫א‬‫א‬555‫א‬EF٢٣J ٤ -١١٧- E‫א‬F
  • 126.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ T1 ‫א‬  T2 T3 2/3 VCC Voltage Across "C" T4 T5    1/3 VCC (+VCC) Output (0)  tp tn   K‫א‬C‫א‬EF٢٣J ٤ T1‫]א‬(High)‫א‬S-R‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬(Low)‫א‬‫א‬‫א‬‫א‬‫א‬K[‫א‬  KOFF‫א‬(Discharge Transistor)‫א‬‫א‬‫א‬ ‫א‬‫א‬(C)‫א‬‫א‬،OFF‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬،T2‫א‬KRB, RA‫א‬+Vcc 1 3 2 3  VCC ‫א‬‫א‬(High) A‫א‬‫א‬، VCC  555(3)‫א‬‫א‬KQ = 0(RESET)‫א‬‫א‬‫א‬  KON‫א‬،(High)‫א‬‫א‬،(Low)‫א‬ ‫א‬KC‫א‬،ON‫א‬‫א‬‫א‬‫א‬  1 3 ‫א‬،Q = 1(SET)‫א‬S-R‫א‬‫א‬(High)‫א‬ B‫א‬، VCC ‫א‬‫א‬،T3   C،OFF‫א‬‫א‬‫א‬K‫א‬  K‫א‬ ‫א‬RB, RA‫א‬C‫א‬،EF٢٣J ٤‫א‬ 1 3 2 3  (Positive time) tp‫א‬K VCC ‫א‬RB‫א‬، VCC  W‫א‬  -١١٨-
  • 127.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  t p = 0.7(R A + R B )C  W‫א‬(Negative time) tn‫א‬  t n = 0.7 R BC  Wtn‫א‬،tp‫א‬E‫א‬‫א‬FT‫א‬  T = tp + tn  = 0.7(R A + 2R B )C f =  W‫א‬‫א‬555‫א‬  1 1 = T 0.7(R A + 2R B )C  W‫א‬‫א‬‫א‬ f =  1.43 ( R A + 2R B )C  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٣J ٨J ٤ 555 Timer as a Monostable Multivibrator ‫א‬‫א‬‫א‬‫א‬‫א‬555‫א‬EF٢٤J ٤ ‫א‬EF٢٤J ٤‫א‬‫א‬.(one-shot) ‫א‬K555‫א‬‫א‬،‫א‬،(Input - trigger)‫א‬  KRA,C‫א‬‫א‬(Pw) (RESET)S-R‫א‬‫א‬،EF٢٤J ٤T1‫א‬ ‫א‬S-R‫א‬‫א‬(Low)‫א‬‫א‬KQ = 0(Low) ‫א‬،‫א‬‫א‬(inverted and buffered)،‫א‬  K(Low)0V(3)‫א‬555 ‫א‬(High)S-R‫א‬‫א‬(Low)‫א‬  K‫א‬‫א‬‫א‬‫א‬،ON‫א‬،‫א‬ -١١٩-
  • 128.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  555‫א‬‫א‬(2)‫א‬(Trigger)‫א‬،T2‫א‬ 1 3 ، VCC  B‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬  ‫א‬KQ = 1‫א‬(SET)‫א‬S-R‫א‬‫א‬،(High)B‫א‬  ‫א‬555(3)‫א‬‫א‬‫א‬S-R‫א‬‫א‬ (High)‫א‬  KOFF‫א‬‫א‬‫א‬(High)   +5V 4 8 555 Timer 5KΩ RA 5 - 1/3 VCC + RL Comparator (A) R 6 5KΩ 2 Trigger Input S - 2/3 VCC + Inverting Buffer/Driver Q S-R Flip-Flop 3 Inverter Output Comparator (B) 5KΩ Discharge Transistor + 7 C 1  K‫א‬‫א‬‫א‬555‫א‬EF٢٤J ٤    -١٢٠-
  • 129.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ T1 T2 Trigger 1/3 VCC Input 0V 2/3 VCC ‫א‬       Voltage Across "C" Output      K‫א‬‫א‬C‫א‬‫א‬EF٢٤J ٤  +VCCRA‫א‬‫א‬C‫א‬‫א‬ ‫א‬(High)‫א‬555‫א‬KEF٢٤J ٤‫א‬ 2 3 (3)‫א‬‫א‬،(RESET)‫א‬S-R‫א‬‫א‬ ،(High)A‫א‬،(T3)‫א‬K VCC ‫א‬ C‫א‬ON‫א‬‫א‬‫א‬،(Low)‫א‬  K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K ‫א‬،‫א‬‫א‬(Leading edge)‫א‬‫א‬  ‫א‬RA‫א‬C‫א‬‫א‬(Trailing edge)‫א‬  W‫א‬‫א‬‫א‬K‫א‬  Pw = 1.1R A C    -١٢١-
  • 130.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬   Shift Registers‫א‬‫א‬٩J ٤ ،‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬(bit)‫א‬‫א‬‫א‬‫א‬ ‫א‬،‫א‬‫א‬‫א‬، ‫א‬‫א‬‫א‬ Shift )‫א‬ (Shift Left)‫א‬‫א‬‫א‬(Buffer Register)‫א‬‫א‬ ‫א‬(Parallel Data)‫א‬(Serial Data)‫א‬‫א‬‫א‬(Right  K(Shift Registers)‫א‬‫א‬  Buffer Registers‫א‬١J ٩J ٤ (Digital word)‫א‬ ‫א‬EF٢٥J ٤K(bits)‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬ D ‫א‬‫א‬‫א‬‫א‬(4-stages)  K(Positive edge-triggered)  (4-bit word to be stored)‫א‬‫א‬‫א‬‫א‬ D1 D2 Q D CLR Q D Q D4 D3 CLR Q D Q CLR Q D Q CLR Q CK CLR Q1 Q2 Q3 Q4 (parallel data outputs)‫א‬‫א‬‫א‬ E F  KD‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬EF٢٥J ٤  -١٢٢-
  • 131.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬     Clock ‫א‬ Input data  1 D1  0 D2  1 D3   0 D4  Q1 ‫א‬ Output data  Q2   Q3 Q4  E F  KEF٢٥J ٤‫א‬‫א‬‫א‬EF٢٥J ٤   ‫א‬‫א‬(4-bits)‫א‬‫א‬‫א‬ ‫א‬Q1,Q3, Q2,Q4‫א‬D1,D2,D3,D4  K(CK)‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬EF٢٥J ٤‫א‬‫א‬‫א‬ ‫א‬‫א‬Q1,Q3, Q2,Q4‫א‬  K‫א‬‫א‬K‫א‬‫א‬‫א‬ ‫א‬،‫א‬‫א‬‫א‬ ‫א‬‫א‬J ‫א‬‫א‬‫א‬،‫א‬‫א‬ ‫א‬‫א‬‫א‬(Clear-input)‫א‬K(Parallel-in, Parallel-out Registers)  KE‫א‬F‫א‬‫א‬(active-low)  -١٢٣-
  • 132.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬   Shift Registers‫א‬‫א‬٢J ٩J ٤ ‫א‬(Shift)‫א‬(move)‫א‬‫א‬‫א‬‫א‬   WKE٢٦J ٤F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K  (Serial-in, Serial-out Shift Registers)‫א‬‫א‬–‫א‬‫א‬‫א‬ -١ K(SISO)‫א‬‫א‬ (Serial-in, Parallel-out Shift Registers)‫א‬‫א‬–‫א‬‫א‬‫א‬ -٢ .(SIPO)‫א‬‫א‬ (Parallel-in, Serial-out Shift Registers) ‫א‬‫א‬–‫א‬‫א‬‫א‬J ٣  K(PISO)‫א‬‫א‬   Serial-in, serial-out (SISO) Shift Registers Shift Right Serial-In   Serial-Out Shift Left Serial-In  Rotate Right   Rotate Left E F  Serial-in, parallel-out (SIPO) Shift Registers  Serial-In Parallel-in, Serial-out Shift (PISO) Registers Parallel Data In  Serial-Out Parallel Data Out  EF  K‫א‬‫א‬EF٢٦J ٤ -١٢٤-
  • 133.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬‫א‬  W‫א‬  ‫א‬‫א‬–‫א‬‫א‬‫א‬‫א‬١J ٢J ٩J ٤ Serial-in, Serial-out (SISO) Shift registers ‫א‬‫א‬K ‫א‬‫א‬‫א‬،E٨J ٤F  1001‫א‬‫א‬‫א‬‫א‬E‫א‬‫א‬F0110‫א‬‫א‬    K‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬ ‫א‬‫א‬‫א‬ Clock Input  —  ‫א‬ Q0 Q1 Q2 Q3  — 0 1 1 0 1st 1 1 0 1 1 2nd 0 0 1 0 1 3rd 0 0 0 1 0 4th 1 1 0 0 1  K‫א‬‫א‬E٨J ٤F  ‫א‬‫א‬‫1( א‬st Clock pulse)‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ،(2nd Clock pulse)‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬(0110)‫א‬‫א‬ K‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬K(1001)‫א‬‫א‬‫א‬  ‫א‬(0110)‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ (1001)‫א‬‫א‬‫א‬،‫א‬  K -١٢٥-
  • 134.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬  Serial Data Input FF1 FF0 D Q 0 Q 1 D FF3 FF2 D Q 2 Serial Data Out D CK Clock Input SISO Shift Right E F Serial Data Input Serial Data Out Q 3 Q D D 2 CK Clock Input FF3 Q 1 CK FF1 FF2 D Q 0 CK FF0 SISO Shift Left E F SISO Rotate Left SISO Rotate Right  EF  K‫א‬‫א‬‫א‬‫א‬‫א‬ E٢٧J ٤F ‫א‬‫א‬(4-bits)‫א‬‫א‬EF٢٧J ٤ ‫א‬،(FF0)‫א‬‫א‬‫א‬D‫א‬‫א‬‫א‬‫א‬KD‫א‬‫א‬ (Q1)‫א‬‫א‬‫א‬،(FF1)‫א‬‫א‬‫א‬D‫א‬(Q0)‫א‬‫א‬ -١٢٦-
  • 135.  ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬  ‫א‬  ‫א‬‫א‬(Q2)‫א‬‫א‬‫א‬،(FF2)‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،(FF3)‫א‬‫א‬‫א‬  K‫א‬ ،‫א‬‫א‬(Clock input)‫א‬‫א‬ ،‫א‬‫א‬(1-bit)‫א‬‫א‬‫א‬ (Positive edge) ‫א‬‫א‬‫א‬‫א‬‫א‬–‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬   K‫א‬ EF٢٧J ٤‫א‬‫א‬‫א‬،  ‫א‬‫א‬–‫א‬‫א‬‫א‬‫א‬‫א‬D‫א‬‫א‬ EF٢٧J ٤‫א‬‫א‬‫א‬ .(SISO Shift-Right Shift Register)  ‫א‬–‫א‬‫א‬D‫א‬‫א‬‫א‬‫א‬   K(SISO Shift- Left Shift Register)‫א‬ EF٢٧J ٤،EF٢٧J ٤‫א‬‫א‬‫א‬،‫א‬ ‫א‬‫א‬،‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬–‫א‬‫א‬‫א‬    (SISO Rotate-Left) ‫א‬‫א‬‫א‬–‫א‬‫א‬(SISO Rotate-Right)  KEF٢٧J ٤  ‫א‬‫א‬–‫א‬‫א‬‫א‬٢J ٢J ٩J ٤ Serial-in, parallel out (SIPO) Shift registers ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢٨J ٤F‫א‬  K‫א‬‫א‬–‫א‬ (4-bits)‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ ‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬(Serial data input)‫א‬‫א‬‫א‬  KE‫א‬‫א‬ -١٢٧-
  • 136.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ Serial Data Input  FF1 FF0 D ‫א‬ Q D 0 CK CK FF2  Q 1 D  FF3 Q D 2 CK   Q 3 CK  Clock Input  Q 0   Q 1  Q Q 2 3 Parallel data outputs  K‫א‬‫א‬J ‫א‬‫א‬‫א‬‫א‬E٢٨J ٤F  ‫א‬‫א‬‫א‬‫א‬‫א‬(4-bits)   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬   K‫א‬‫א‬(4-bits)(Q3,Q2,Q1,Q0)  ‫א‬‫א‬–‫א‬‫א‬‫א‬٣J ٢J ٩J ٤ Parallel-in, Serial-out (PISO) Shift registers ‫א‬‫א‬‫א‬‫א‬E٢٩J ٤F ‫א‬‫א‬‫א‬KD‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬– ،(Low)‫א‬ SHIFT / LOAD ‫א‬K SHIFT / LOAD ‫א‬ ‫א‬(Enabled)‫א‬‫א‬AND ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬K‫א‬Inverter‫א‬   ‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬(D3,D2,D1,D0)‫א‬  .(Q3,Q2,Q1,Q0)‫א‬‫א‬‫א‬‫א‬ ،(Clock pulse)   -١٢٨-
  • 137.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  (SHIFT / LOAD) control Parallel data inputs (1 for shift , 0 for load ) D D 1 0 D FF1 FF0 D CK  Q 0 D D 2 3 FF2 Q 1 D FF3 Q 2 CK CK D Q Serial Out 3 CK Clock Input  K‫א‬‫א‬J ‫א‬‫א‬‫א‬E٢٩J ٤F AND‫א‬‫א‬،(High)‫א‬ SHIFT / LOAD ‫א‬ Q0‫א‬‫א‬‫א‬‫א‬K(Enabled)‫א‬‫א‬ ،(FF2)‫א‬‫א‬‫א‬‫א‬Q1‫א‬،(FF1)‫א‬‫א‬‫א‬D‫א‬  ‫א‬‫א‬،‫א‬‫א‬K(FF3)‫א‬‫א‬‫א‬‫א‬Q2‫א‬  (1-bit)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  .(clock inputF‫א‬‫א‬‫א‬‫א‬ Shift Register Sequencer (Ring Counter)E‫א‬F‫א‬‫א‬‫א‬٤J ٢J ٩J ٤ ‫א‬‫א‬‫א‬EF٣٠J ٤  KED0Q3‫א‬FFF0‫א‬‫א‬‫א‬(FF3)‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬Q0‫א‬Low‫א‬ SRART ‫א‬K  E CLR = 0 FLow‫א‬ Q1,Q2,Q3‫א‬،( PRE = 0 )High  KEF٣٠J ٤‫א‬ -١٢٩-
  • 138.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬   Q D PRE Q 0 Q 1 0 PRE D 1 0 CK Q Q 1 D CK FF0 Clock 2 Q 2 D 2 CK CLR CLR PRE  3 FF3 E F K‫א‬‫א‬‫א‬EF٣٠J ٤ 1 3 2 0 1 2 3 0 1 Clock START Q 1 Q 0 0 0 0 1 0 0 0 0 1 0 0 Q 1 Q 0 0 0 2 3 1 E F  K‫א‬‫א‬‫א‬EF٣٠J ٤ -١٣٠- 3 CLR FF2 START 0 Q CK CLR FF1 PRE 2 Q 3
  • 139.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ Clock Pulses 0 1 2 3 ‫א‬  ‫א‬‫א‬ Q0 1 0 0 0 Q1 0 1 0 0 Q2 Q3 0 0 1 0 0 0 0 1 Four flip-flops will have Four output states. Repeat Sequence  K‫א‬‫א‬‫א‬E٩J ٤F ‫א‬،‫א‬‫א‬‫א‬(1000)‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(1)  KE٩J ٤F  Johnson Counter‫א‬٥J ٢J ٩J ٤ ‫א‬،‫א‬‫א‬‫א‬EF٣١J ٤  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K(D0)‫א‬‫א‬‫א‬‫א‬E Q 3 F ‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬   Q3،1000،E١٠J ٤F‫א‬‫א‬EF٣١J ٤‫א‬ ‫א‬‫א‬(High)‫א‬ Q 3 ،‫א‬‫א‬(Low)‫א‬ ‫א‬ (High inputs)‫א‬‫א‬‫א‬‫א‬،D0‫א‬ K(High)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ،(Low)‫א‬ Q 3 ،E‫א‬‫א‬‫א‬F(High)‫א‬Q3  ‫א‬‫א‬‫א‬‫א‬‫א‬K(Low) D0 K(Low)‫א‬‫א‬‫א‬‫א‬(Low inputs)‫א‬ ‫א‬ Q 3 ،E‫א‬‫א‬‫א‬F(Low)‫א‬Q3  K‫א‬‫א‬‫א‬‫א‬(High)D0(High)  -١٣١-
  • 140.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ Q D PRE 0 Q ‫א‬  Q 1 0 D 1 0 CK PRE Q Q 1 D PRE 2 Q Q 2 D 2 CK CK PRE 3 Q FF0 Clock CLR FF1 3 CK Q CLR CLR 3 CLR FF2 3 FF3 E F 0 1 2 3 4 5 6 7 0 1 2 3 Clock START Q 0 Q 1 Q Q 2 3 Q 3 E F   K‫א‬‫א‬‫א‬‫א‬‫א‬E٣١J ٤F   -١٣٢-
  • 141.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ Clock Pulses ‫א‬  ‫א‬‫א‬ Q0 Q1 Q2 Q3 Q3 0 1 0 0 0 1 1 1 1 0 0 1 2 1 1 1 0 1 3 1 1 1 1 0 Four flip-flops will have 4 0 1 1 1 0 eight output states. 5 0 0 1 1 0 6 0 0 0 1 0 7 0 0 0 0 1  Repeat Sequence  K‫א‬‫א‬E١٠J ٤F  ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  F‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬KEE٩J ٤F  EF٣١J ٤‫א‬‫א‬‫א‬،‫א‬  KE١٠J ٤F(2 × 4 flip-flops = 8) -١٣٣-
  • 142.  ‫א‬‫א‬J ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬  ‫א‬ ‫א‬‫א‬  Counters‫א‬‫א‬‫א‬١٠J ٤ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ،(binary bits)‫א‬‫א‬‫א‬K‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K(clock input)‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K(Synchronous Counters ) ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(Asynchronous Counters)  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬  K(Master Clock)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  Asynchronous Binary-Up Counters ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ١٠J ٤ K‫א‬‫א‬‫א‬EF٣٢J ٤  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬J-K  K‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬،(High)‫א‬J,K‫א‬  K‫א‬‫א‬(Negative edge)(Toggle)  ‫א‬(Q)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬(4-bit word)‫א‬‫א‬Q3,Q2,Q1,Q0‫א‬KEF٣٢J ٤ ‫א‬‫א‬‫א‬0000‫א‬‫א‬ FF0‫א‬‫א‬KE١١J ٤F‫א‬‫א‬‫א‬‫א‬  K(MSB)‫א‬(Q3)FF3‫א‬‫א‬(LSB)(Q0)  - ١٣٣ -
  • 143.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ FF0 J Clock Input ‫א‬  Q Q 1 J 0 FF3 FF2 FF1 J Q CK CK CK K K J 2 K Q Q 1 0 Q 3 CK K Q Q 2 3 E F 1 Q0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0 Q1 0 Q2 0 Q3 0 E F   K‫א‬‫א‬‫א‬‫א‬E٣٢J ٤F ،(Clock input)‫א‬‫א‬‫א‬(FF0)‫א‬‫א‬ ،‫א‬‫א‬‫א‬ (Toggle)Q0‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬KEF٣٢J ٤Q0‫א‬ ‫א‬K‫א‬"0""1"‫א‬‫א‬‫א‬"1""0"Q0 Q0،FF1‫א‬‫א‬‫א‬Q0‫א‬ ‫א‬Q1K(Toggle)Q1‫א‬  KQ3‫א‬Q2،Q2  -١٣٤-
  • 144.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬  ‫א‬‫א‬ Q3 Q2 Q1 Q0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Cycle Repeats  Binary Count  K‫א‬‫א‬‫א‬‫א‬‫א‬E١١J ٤F  The Maximum Count (N) of a Counter ‫א‬• ‫א‬‫א‬‫א‬،E١١J ٤F‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬،[‫א‬‫א‬(1)‫א‬]0001‫א‬‫א‬‫א‬ ]0011‫א‬‫א‬‫א‬‫א‬‫א‬،[‫א‬‫א‬(2)‫]א‬0010‫א‬  ‫א‬‫א‬‫א‬‫א‬K‫א‬،[‫א‬‫א‬(3)    W‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬  N = 2 n − 1    W (N = maximum count before cycle repeats) ‫א‬‫א‬‫א‬ = N  (n = number of flip-flops in the counter circuit)‫א‬‫א‬‫א‬‫א‬‫א‬ = n   -١٣٥-
  • 145.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬   W‫א‬EF٣٢J ٤‫א‬‫א‬‫א‬‫א‬ N = 2n − 1 = 24 − 1 = 16 − 1 = 1510 (11112 ) The Modulus (MOD) of a counter‫א‬‫א‬‫א‬• ‫א‬(MOD)(Modulus of a counter)‫א‬‫א‬‫א‬ MODEF٣٢J ٤‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬ ‫א‬11110000(16)‫א‬‫א‬(16)  W‫א‬‫א‬‫א‬MODKE١١J ٤F n MOD = 2 MOD = modulus of the counter n = number of flip-flops in the counter circuit    W‫א‬‫א‬‫א‬‫א‬‫א‬EF٣٢J ٤‫א‬‫א‬‫א‬‫א‬  MOD = 2 n = 24 = 16 The Frequency Division of a counter ‫א‬‫א‬• EF٣٢J ٤‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬(frequency divider)‫א‬‫א‬ ‫א‬‫א‬،2‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ،‫א‬2‫א‬K2‫א‬‫א‬  ،‫א‬2‫א‬2‫א‬ 4‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬EF٣٢J ٤  ،2‫א‬‫א‬‫א‬‫א‬‫א‬،KQ1 ‫א‬  -١٣٦-
  • 146.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬  ‫א‬،8‫א‬،4‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬16  Division Factor = 2n E‫א‬F N = number of flip-flops in the counter circuit  The Propagation Delay Time (tp) of a counter‫א‬‫א‬• ‫א‬‫א‬،(Ripple counter)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬   ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬    K‫א‬‫א‬‫א‬‫א‬ E‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬،     ‫א‬‫א‬K10000111‫א‬‫א‬‫א‬‫א‬ 0111‫א‬‫א‬ (4 Flip-Flops × 10ns) 40ns 10ns (tp)‫א‬  ‫א‬‫א‬(counting speed)‫א‬K1000 ‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   W‫א‬‫א‬‫א‬ 1 × 10 9 f= n× tp f = upper clock pulse frequency limit n = number of flip-flops in the counter circuit tp= propagation delay time of each flip-flop in nanoseconds  W Asynchronous Binary Down Counters‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ١٠J ٤ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K"1" ‫א‬EF٣٣J ٤‫א‬K‫א‬"1"‫א‬  -١٣٧-
  • 147.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬   Q ‫א‬KJ-K‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬Q‫א‬‫א‬ ‫א‬KEF٣٣J ٤‫א‬‫א‬‫א‬Q‫א‬‫א‬‫א‬ Q3,Q2,Q1,Q0(RESET)‫א‬‫א‬‫א‬‫א‬    Q ‫א‬LowQ‫א‬‫א‬‫א‬‫א‬K0000 FF3,FF2,FF1‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K1111 ‫א‬High‫א‬‫א‬‫א‬J,K‫א‬‫א‬KHigh    K‫א‬‫א‬‫א‬(Toggle)  Q Q 1 0 Q Q 2 3 HIGH    FF1 FF0 Q J Clock Input CK K Q 2 CK Q 1 K 0 Q J CK K Q J 3 CK Q 2 K Q 3 E F   Q 1 J 0 FF3 FF2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Clock Input 0  Q0  Q1 0  Q2 0  Q3 0 E F  K‫א‬‫א‬‫א‬‫א‬ E٣٣J ٤F "0"Q0‫א‬،FF0‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬"0""1" Q 0 ‫א‬‫א‬،"1" -١٣٨-
  • 148.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬   Q1 ‫א‬"0""1"Q1‫א‬،FF1‫א‬‫א‬ ،FF2‫א‬"0""1" Q1 ‫א‬‫א‬K"0""1"  K‫א‬  ‫א‬  ‫א‬‫א‬ Q3 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 Q2 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 Q1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 Q0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 Binary Count Cycle Repeats   K‫א‬‫א‬‫א‬‫א‬‫א‬E١٢J ٤F (15)10 = 1111Q3,Q2,Q1,Q0‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬KE١٢J ٤F‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬   FF0‫א‬‫א‬،EF٣٣J ٤‫א‬‫א‬   ‫א‬،‫א‬Q0‫א‬،‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬Q3,Q2,Q1 -١٣٩-
  • 149.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬   ‫א‬‫א‬‫א‬L‫א‬‫א‬‫א‬‫א‬‫א‬٣J ١٠J ٤ Asynchronous Binary Up/Down Counters ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ Q‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K Q ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ L‫א‬E٣٤J ٤F  K UP / DOWN ‫א‬‫א‬AND-OR  Q HIGH FF0 Q J Clock Input 0 CK K Q 1 0 Q FF1 Q 1 J J 0 K 2 Q 1 K FF3 Q J 3 3 CK CK CK Q FF2 Q Q 2 Q 2 Q K 3 UP/DOWN control  K‫א‬‫א‬‫א‬‫א‬E٣٤J ٤F  ‫א‬AND‫א‬‫א‬،High‫א‬ UP / DOWN ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬Q،(Enabled)‫א‬ ‫א‬‫א‬،‫א‬‫א‬‫א‬،‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬،Low‫א‬ UP / DOWN (Enabled)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(Disabled)‫א‬ ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ Q    K‫א‬ -١٤٠-
  • 150.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  Asynchronous Decade (MOD-10) Counters ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٤J ١٠J ٤ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬EF٣٥J ٤  K(MOD-10)‫א‬‫א‬    HIGH FF1 FF0 J Clock Input Q Q 1 J 0 CK K FF2 J CLR Q J 2 CK CK K FF3 K CLR Q  3 CK K CLR  CLR  Q Q 1 0 Q 2 Q 3 E F 1 2 3 4 5 6 7 8 9   10  Clock Input 0  Q1 0  Q2 0 Q3 0 Q0   CLR  E F  K‫א‬‫א‬‫א‬‫א‬E٣٥J ٤F  ‫א‬E9F1001E0F0000‫א‬‫א‬‫א‬ ‫א‬‫א‬EF٣٥J ٤‫א‬‫א‬  KE١٣J ٤F -١٤١-
  • 151.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬10F1111 1010‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬E CLR F‫א‬‫א‬‫א‬‫א‬NAND ‫א‬E15  ‫א‬‫א‬KQ3‫א‬‫א‬Q1‫א‬‫א‬‫א‬K‫א‬ ،High‫א‬Q3,Q1E‫א‬‫א‬10F1010‫א‬  ‫א‬K‫א‬ (CLEAR)Low NAND‫א‬ ‫א‬(inactive) CLR ‫א‬EF٣٥J ٤‫א‬ ‫א‬KHigh‫א‬Q3,Q1‫א‬‫א‬‫א‬‫א‬K10010000 ‫א‬‫א‬‫א‬‫א‬ (CLEAR)،Q3،Q1‫א‬ E١٣J ٤F‫א‬‫א‬‫א‬‫א‬‫א‬K CLR ‫א‬‫א‬  K‫א‬9‫א‬0‫א‬‫א‬،‫א‬‫א‬  ‫א‬  ‫א‬‫א‬ Q3 0 0 0 0 0 0 0 0 1 1 Q2 0 0 0 0 1 1 1 1 0 0 Q1 0 0 1 1 0 0 1 1 0 0 Q0 0 1 0 1 0 1 0 1 0 1 0 1 2 3 4 5 6 7 8 9 Cycle Repeats Binary Count   K‫א‬‫א‬‫א‬‫א‬‫א‬E١٣J ٤F ‫א‬‫א‬(MOD-10)90‫א‬‫א‬‫א‬‫א‬ ( 1 ) Q3‫א‬،‫א‬  10  .(Clock input)‫א‬‫א‬‫א‬ -١٤٢-
  • 152.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬(Digital Voltmeter)‫א‬‫א‬ ،(Digital clocks)‫א‬‫א‬‫א‬  K(Frequency Counter)‫א‬ Synchronous Binary Counters ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٥J ١٠J ٤ AND‫א‬J-K‫א‬‫א‬EF٣٦J ٤ ‫א‬‫א‬(MOD-16) (4-bit)‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬EF‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬ (Triggered)   K‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬  Q Q 1 0 HIGH J A FF1 FF0 Q 0 Q 1 J Q Q CK  Clock Input B FF2 J CK K 2 CK K Q 2 K 3 FF3 J Q 3 CK K  K‫א‬‫א‬‫א‬E٣٦J ٤F FF0‫א‬‫א‬J,K‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬(Toggle)‫א‬،High‫א‬  Low‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬LowHighHigh ‫א‬‫א‬2‫א‬‫א‬‫א‬FF1‫א‬‫א‬J,K‫א‬ FF1‫א‬‫א‬Q1‫א‬،Low‫א‬Q0‫א‬‫א‬KFF0  Q1‫א‬،High‫א‬Q0‫א‬(No change) K(Toggle) -١٤٣-
  • 153.  ‫א‬‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬  AND(A)‫א‬‫א‬ FF2‫א‬‫א‬J,K‫א‬ ،High AND(A)‫א‬Q0 = Q1 = High‫א‬KQ0,Q1    K‫א‬‫א‬FF2‫א‬‫א‬(Enable) ‫א‬‫א‬ ‫א‬AND(B)‫א‬‫א‬ FF3‫א‬‫א‬J,K‫א‬ AND(B)‫א‬High‫א‬Q2,Q1,Q0‫א‬KQ2,Q1,Q0   K‫א‬FF3‫א‬‫א‬ ‫א‬‫א‬High  Synchronous Counters Advantages ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ٦J ١٠J ٤ (Ripple counters)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬  KEF٣٣J ٤‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬EF٣٢J ٤ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬K‫א‬  ‫א‬‫א‬K ‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬ (Propagation-delay time)   K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬F‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬KE  ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬     W‫א‬‫א‬‫א‬‫א‬‫א‬  tp = Single (flip-flop) tp + Single (AND-gate) tp -١٤٤-
  • 154.  ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬  ‫א‬                   -١٤٥-
  • 155.  ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬  ‫א‬     ‫א‬‫א‬‫א‬‫א‬S-R‫א‬‫א‬(Q)‫א‬‫א‬ E١  ‫א‬‫א‬‫א‬(negative edge trigger)‫א‬‫א‬ K‫א‬‫א‬Q=0‫א‬‫א‬‫א‬K CK S R ‫א‬‫א‬‫א‬‫א‬D‫א‬‫א‬‫א‬(Q)‫א‬‫א‬E٢ K‫א‬‫א‬‫א‬(positive edge trigger)‫א‬‫א‬ K‫א‬‫א‬Q=0‫א‬‫א‬‫א‬  CK D ‫א‬‫א‬‫א‬‫א‬JK‫א‬‫א‬(Q)‫א‬‫א‬E٣  ‫א‬K‫א‬‫א‬‫א‬(negative edge trigger)‫א‬‫א‬ K‫א‬‫א‬Q=0‫א‬‫א‬ -١٤٦- 
  • 156.  ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬  ‫א‬  CK   J    K  ‫א‬‫א‬‫א‬‫א‬T‫א‬‫א‬‫א‬(Q)‫א‬‫א‬E٤  ‫א‬‫א‬‫א‬(negative edge trigger)‫א‬‫א‬ K‫א‬‫א‬Q=0‫א‬‫א‬‫א‬K CK T ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬555‫א‬‫א‬(f)‫א‬‫א‬ E٥   KC = 0.1µf‫א‬،RB = 3kΩ‫א‬RA = 10kΩ ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬555‫א‬‫א‬ E٦ KC = 0.01µf‫א‬،ΩRA = 12kΩ‫א‬ -١٤٧-
  • 157.  ‫א‬‫א‬‫א‬ ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹] ‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬ ‫א‬‫א‬ ٥ - ١٣٣ -
  • 158. - ١٣٣ -
  • 159.  ‫א‬‫א‬ ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬  ‫א‬   ‫א‬‫א‬‫א‬   W‫א‬‫א‬ K‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬ • - ١٤٨ -
  • 160.  ‫א‬‫א‬ ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬  ‫א‬  Introduction١J ٥ ‫א‬K،‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬(fuse–programmable) ‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬(Customer)‫א‬  ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(fusible links)‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬    W‫א‬‫א‬ (The Programmable Logic Array (PLA))‫א‬‫א‬‫• א‬ (The Programmable Array Logic (PAL))‫א‬‫א‬ •  (The Programmable Logic Sequencer (PLS))‫א‬‫א‬‫• א‬ ‫א‬‫א‬‫• א‬ (Erasable Programmable Logic Device (EPLD)) ‫א‬‫א‬‫א‬‫א‬ (F) (FPLA, FPAL, ….)  K(Field Programmable Logic Devices)  Basic Programmable Logic Devices ‫א‬‫א‬‫א‬٢J ٥  PLDJ ‫א‬‫א‬‫א‬‫א‬E١J ٥F‫א‬ ‫א‬،‫א‬‫א‬‫א‬‫א‬K(2-input/4-output) (noninverting Buffer)‫א‬‫א‬‫א‬‫א‬ K(Inverting Buffer)‫א‬ A,B ‫א‬‫א‬‫א‬‫א‬‫א‬High  AND‫א‬   ‫א‬‫א‬AND‫א‬‫א‬،E١J ٥F‫א‬ ‫א‬،‫א‬،(Product Lines)  ‫א‬K‫( א‬A B, AB, AB and AB)  (fusible link)OR‫א‬‫א‬ .PLDJ ‫א‬‫א‬(×)‫א‬‫א‬،E١J ٥F  - ١٤٩ -
  • 161.  ‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬ ‫א‬   Inputs A  B   Fusible Link  A A B  B 0  × 1  2  × × × ×  3 × × × × AB × × AB × × × × × Q3 Q2 Q1 AB Q0  AB     Outputs   KPLD‫א‬‫א‬‫א‬E١J ٥F   A B High Out 0 0 AND 0 0 1 AND 1 1 0 AND 2 1 1 AND 3   KE١J ٥F‫א‬AND‫א‬‫א‬E١J ٥F  - ١٥٠ -
  • 162.  ‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬،E١J ٥F‫א‬‫א‬    ‫א‬‫א‬‫א‬‫א‬PLDs J ‫א‬K‫א‬ ‫א‬‫א‬E١J ٥F‫א‬‫א‬E٢J ٥FK‫א‬‫א‬‫א‬   K‫א‬  Inputs A  B    A A B B  0 × × × × 1 × × × × AB 2 × × × × AB 3 × × × × AB     I3 Q3 AB  Q2 Q1 Q0 Outputs  KPLD‫א‬‫א‬E٢J ٥F      ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬    AND ‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬،  ‫א‬،‫א‬‫א‬‫א‬  OR ‫א‬‫א‬‫א‬K‫א‬‫א‬   K(fusible link)‫א‬(×’s)‫א‬‫א‬ - ١٥١ -
  • 163.  ‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬ ‫א‬   ×’s‫א‬‫א‬‫א‬،OR, AND‫א‬‫א‬  K‫א‬  K‫א‬‫א‬PLD ‫א‬‫א‬‫א‬‫א‬ (Q0,Q1,Q2,Q3)A,B‫א‬E٣J ٥F  KE٢J ٥F‫א‬،PLD‫א‬    Inputs A  B   A A B   B × 0 1 × × AB  × × 2 × 3 3 2 AB  AB  AB 1 0       Q 0 = A B + AB  Q1 = AB Q 2 = AB + AB  Q 3 = AB   KPLD‫א‬‫א‬E٣J ٥F  - ١٥٢ -
  • 164.  ‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬ ‫א‬  Q3 ‫א‬،3OR ‫א‬1,3,4(blowing fuses)‫א‬‫א‬   ،2 OR ‫א‬1,3‫א‬‫א‬KAB = 01  High   2,3,4‫א‬‫א‬KAB = 11 AB = 01 High Q2 ‫א‬ ‫א‬KAB = 00HighQ1‫א‬،1OR‫א‬   High Q0‫א‬،0‫א‬2,4‫א‬‫א‬    KAB = 10AB = 00   ‫א‬ ‫א‬ A B Q3 Q2 Q1 Q0 AB 0 0 0 0 1 1 AB 0 1 1 1 0 0 AB 1 0 0 0 0 1 AB 1 1 0 1 0 0   KE٣J ٥F‫א‬‫א‬‫א‬E٢J ٥F   ‫א‬‫א‬ ‫א‬PLD ‫א‬  XOR ‫א‬(Programmable Output Polarity fuse) ‫א‬‫א‬‫א‬‫א‬،E٤J ٥F  K(blown)(Intact)‫א‬  Low XOR ‫א‬‫א‬‫א‬،‫א‬‫א‬    XOR ‫א‬‫א‬‫א‬،‫א‬‫א‬K‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬ High  KE٣J ٥F‫א‬‫א‬ - ١٥٣ -
  • 165.  ‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬ ‫א‬   × ×       Polarity Fuse   Output KPLD‫א‬‫א‬E٤J ٥F     Polarity FuseE‫א‬F XOR's Operation Intact E‫א‬F Will not invert E‫א‬F Blown E‫א‬F Will invert E‫א‬F   K‫א‬‫א‬‫א‬E٣J ٥F   The Programmable Logic Array (PLA) ‫א‬‫א‬‫א‬٣J ٥ ،‫א‬‫א‬‫א‬‫א‬  (2-bit outputs)(8-bit inputs) PLD  K (256) ‫א‬‫א‬(12) K(PLA)‫א‬‫א‬،‫א‬  PLA ‫א‬‫א‬E٥J ٥F‫א‬PLA‫א‬‫א‬‫א‬  OR  AND   K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ - ١٥٤ -
  • 166.  ‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬ I3 I 2 I1 ‫א‬  I0    × ×× × × ×× × × × × × × ×× × × ×× × × ×× × × × × × × ×× × × × × × × ×× × × × × × × ×× × × × × × × ×× × × × × × × ×× × × × × × × ×× × × × × × × ×× × × × × × × ×× × × ×× × × × × × × × × × × ×× × × × × × × ×× × × × × × × ×× × × × × × × ×× ×             × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×   O3 O2 O1   KPLA‫א‬‫א‬‫א‬E٥J ٥F  O0   The Programmable Array Logic (PAL)‫א‬‫א‬ ٤J ٥ ANDEPLAF‫א‬‫א‬‫א‬  PLA ‫א‬‫א‬K‫א‬‫א‬OR    K‫א‬‫א‬،،‫א‬‫א‬‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ OR AND،PAL ‫א‬  KE٦J ٥FE‫א‬F - ١٥٥ -
  • 167.  ‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬ ‫א‬   I3 I2 I1 I0  OR    × ×× × × ××× × ×× × × × × × × × × × × × ×× × ×× × × ××× × ×× × × × × × × ×× × × ××× × ×× × × ××× × ×× × × ×× × × ×× × × ××× × ×× × × × × × × ×× × × ××× × ×× × × ××× × ×× × × × × × × ×× × × ××× × ×× × × ××× × ×× × × ×× ×   AND O3 O2 O1 KPAL‫א‬‫א‬‫א‬E٦J ٥F O0    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬PLA‫א‬  K،‫א‬   - ١٥٦ -
  • 168.  ‫א‬‫א‬ ‫א‬‫א‬  ‫٧٤١ א‬ ‫א‬  ‫א‬   The Programmable Logic Sequencer (PLS)‫א‬‫א‬‫א‬٥J ٥ ‫א‬‫א‬‫א‬(PLS)‫א‬‫א‬‫א‬ ‫א‬،‫א‬‫א‬K‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬، (Input and output registers)  ‫א‬‫א‬‫א‬٦J ٥ Erasable Programmable Logic Device (EPLD) ‫א‬(PLDs)‫א‬‫א‬‫א‬ ،‫א‬K(blowing their internal fuses)‫א‬‫א‬‫א‬‫א‬ ‫א‬،‫א‬  ‫א‬K‫א‬‫א‬‫א‬‫א‬PLD‫א‬  K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬(erase)‫א‬  K،‫א‬‫א‬‫א‬ × - ١٥٧ -
  • 169.  ‫א‬‫א‬  ‫٧٤١ א‬  ‫א‬ ‫א‬‫א‬ ‫א‬    Q0,Q1,Q2,Q3A, B‫א‬PLD‫א‬‫א‬ E١  K‫א‬ ‫א‬ ‫א‬ A B Q3 Q2 Q1 Q0 0 0 0 1 1 1 0 1 1 1 0 0 1 0 0 1 0 1 1 1 1 0 0 0 ‫א‬Q0,Q3‫א‬‫א‬‫א‬‫א‬‫א‬ E٢  K‫א‬‫א‬   KPLA‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E٣        - ١٥٨ -
  • 170.  ‫א‬  ‫٧٤١ א‬ ‫א‬  ‫א‬   ‫א‬ ‫א‬   ‫א‬    ‫א‬‫א‬W‫א‬‫א‬  ‫א‬‫א‬‫א‬  ٢ ٣ ٤ ١J ١ ‫א‬‫א‬‫א‬٢J ١ ‫א‬‫א‬‫א‬٣J ١ ٦ ٦ ‫א‬‫א‬‫א‬‫א‬‫א‬٤J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٤J ١ ٧ ‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٤J ١ ٩ ‫א‬‫א‬‫א‬‫א‬‫א‬٥J ١ ١٠ ‫א‬‫א‬‫א‬‫א‬٦J ١ ‫א‬‫א‬١J ٦J ١ ١٠ ١٠ ١١ ١٢ ‫א‬‫א‬٢J ٦J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬٧J ١ ١٣ ‫א‬‫א‬‫א‬‫א‬٨J ١ ‫א‬‫א‬١J ٨J ١ ١٣ ‫א‬‫א‬٢J ٨J ١ ١٤ ١٤ ١٥ ١٥ ١٦ ١٦ ‫א‬‫א‬٣J ٨J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٩J ١ ‫א‬‫א‬‫א‬١٠J ١ ‫א‬‫א‬‫א‬‫א‬١J ١٠J ١ ‫א‬‫א‬‫א‬‫א‬٢J ١٠J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ٢J ١٠J ١
  • 171.  ‫א‬ ١٨ ‫א‬  ‫א‬ ١٦  ‫٧٤١ א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٢J ١٠J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬٣J ١٠J ١ ١٩ ‫א‬‫א‬‫א‬‫א‬‫א‬٤J ١٠J ١ ١٩ ‫א‬‫א‬‫א‬‫א‬‫א‬٥J ١٠J ١ ٢٠ ٢٠ ‫א‬‫א‬‫א‬‫א‬٦J ١٠J ١ ‫א‬‫א‬١J ٦J ١٠J ١ ٢٢ ‫א‬‫א‬‫א‬٢J ٦J ١٠J ١ ٢٣ ‫א‬‫א‬‫א‬‫א‬١١J ١ ‫א‬‫א‬‫א‬‫א‬١J ١١J ١ ٢٣ ٢٣ ٢٣ ٢٤ ٢٥ ‫א‬‫א‬‫א‬‫א‬٢J ١١J ١ ‫א‬‫א‬‫א‬‫א‬‫א‬١J ٢J ١١J ١ ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٢J ١١J ١ ‫א‬‫א‬‫א‬‫א‬٣J ١١J ١ ٢٦ ‫א‬‫א‬‫א‬‫א‬‫א‬٤J ١١J ١ ٢٧ ‫א‬‫א‬‫א‬‫א‬‫א‬٥J ١١J ١ ٢٨ ‫א‬‫א‬‫א‬‫א‬‫א‬ ٦J ١١J ١ ٢٩ ‫א‬‫א‬‫א‬‫א‬‫א‬٧J ١١J ١ ٢٩ ‫א‬‫א‬‫א‬‫א‬‫א‬٨J ١١J ١ ٢٩ ٣٠ ‫א‬‫א‬‫א‬‫א‬١J ٨J ١١J ١ ‫א‬‫א‬‫א‬‫א‬٢J ٨J ١١J ١
  • 172.  ‫א‬  ‫٧٤١ א‬ ‫א‬  ‫א‬  ٣١ ٣٥ ٣٦ ٣٦ ٣٧ ٤٠ ٤٢ ٤٢ ٤٤ ٤٥ ٤٧ ٤٨ ٥٠ ٥١ ٥٢ ٥٤ ٥٥ ٥٨ ٦١ ٦٢ ٦٢ ٦٤ ٦٥   ‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬  ‫א‬‫א‬‫א‬  ١J ٢  ‫א‬‫א‬٢J ٢   AND‫א‬٣J ٢   OR‫א‬ ٤J ٢   E‫א‬F NOT ‫א‬٥J ٢   NAND ‫א‬٦J ٢   NOR ‫א‬٧J ٢  E‫א‬F‫ א‬OR ‫א‬٨J ٢  E‫א‬F‫ א‬NOR ‫א‬٩J ٢  ‫א‬‫א‬‫א‬١٠J ٢  ‫א‬‫א‬‫א‬١١J ٢  ‫א‬‫א‬‫א‬‫א‬١٢J ٢  ‫א‬‫א‬١٣J ٢  ‫א‬‫א‬‫א‬١٤J ٢  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١٥J ٢    ‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬  ‫א‬‫א‬‫א‬  ١J ٣  ٣J ٢  NOR , NAND‫א‬‫א‬‫א‬‫א‬٣J ٣  NAND‫א‬‫א‬١J ٣J ٣
  • 173.  ‫א‬  ‫٧٤١ א‬ ‫א‬  ‫א‬  ٦٦  NOR‫א‬‫א‬٢J ٣J ٣ ٦٧ ،NAND‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٤J ٣    NOR  NAND‫א‬‫א‬‫א‬١J ٤J ٣ ٦٧ ٦٩ ٧٢ ٧٣ ٨١ ٨١ ٨٢ ٨٥ ٨٧ ٩٠  NOR‫א‬‫א‬‫א‬٢J ٤J ٣  ٥J ٣  ‫א‬‫א‬‫א‬٦J ٣  ‫א‬‫א‬‫א‬‫א‬٧J ٣  ‫א‬‫א‬‫א‬١J ٧J ٣  ‫א‬‫א‬‫א‬٢J ٧J ٣  ‫א‬‫א‬‫א‬٣J ٧J ٣  ‫א‬‫א‬‫א‬٤J ٧J ٣    ٩٢ ٩٣ ٩٣ ٩٨ ١٠١ ١٠٣ ١٠٥ ١٠٦ ١١٤ ١١٤ ١١٥  ‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬  ١J ٤  ‫א‬٢J ٤  ‫א‬‫א‬S-R‫א‬٣J ٤  D ‫א‬‫א‬‫א‬٤J ٤  ‫א‬‫א‬J-K‫א‬٥J ٤  T ‫א‬‫א‬‫א‬٦J ٤  ‫א‬–‫א‬٧J ٤  ‫א‬‫א‬٨J ٤  ‫א‬‫א‬‫א‬‫א‬‫א‬١J ٨J ٤  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٨J ٤
  • 174.  ‫א‬  ‫٧٤١ א‬ ‫א‬  ‫א‬  ١١٦ ١١٦  555‫א‬‫א‬٣J ٨J ٤  ‫א‬‫א‬‫א‬‫א‬555‫א‬١J ٣J ٨J ٤ ١١٩  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٣J ٨J ٤ ١٢٢  ‫א‬‫א‬٩J ٤  ‫א‬١J ٩J ٤ ١٢١ ١٢٤ ١٢٥ ١٢٧ ١٢٨ ١٢٩  ‫א‬‫א‬٢J ٩J ٤  ‫א‬‫א‬–‫א‬‫א‬‫א‬‫א‬١J ٢J ٩J ٤  ‫א‬‫א‬–‫א‬‫א‬‫א‬٢J ٢J ٩J ٤  ‫א‬‫א‬–‫א‬‫א‬‫א‬٣J ٢J ٩J ٤  E‫א‬F‫א‬‫א‬‫א‬٤J ٢J ٩J ٤ ١٣١  ‫א‬٥J ٢J ٩J ٤ ١٣٣  ‫א‬‫א‬‫א‬١٠J ٤  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ١٠J ٤ ١٣٣ ١٣٧ ١٤٠ ١٤١ ١٤٣ ١٤٤  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ١٠J ٤  ‫א‬‫א‬‫א‬L‫א‬‫א‬‫א‬‫א‬‫א‬٣J ١٠J ٤  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٤J ١٠J ٤  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٥J ١٠J ٤  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ٦J ١٠J ٤ ١٤٦    ‫א‬‫א‬W‫א‬‫א‬ ١٤٨  ‫א‬‫א‬‫א‬ ١٤٩ ١٤٩ ١٥٤ ١٥٥  ١J ٥  ‫א‬‫א‬‫א‬٢J ٥  ‫א‬‫א‬‫א‬٣J ٥  ‫א‬‫א‬ ٤J ٥
  • 175.  ‫א‬ ١٥٧ ١٥٨ ‫א‬  ‫א‬ ١٥٧  ‫٧٤١ א‬   ‫א‬‫א‬‫א‬٥J ٥  ‫א‬‫א‬‫א‬٦J ٥  
  • 176.         ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬E‫א‬F‫א‬‫א‬ GOTEVOT appreciates the financial support provided by BAE SYSTEMS

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