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Basics of digital electronics

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Basics of digital electronics

  1. 1. 1
  2. 2. 2 2 +1 =3 HOW THE COMPUTER GETS THE ANSWER
  3. 3. 3 A computer understands information composed of only zeros and ones. The decimal number system is convenient for the programmer. The computer uses binary digits for its operation. 0 1 0 1 1 0 1 1 0 0 1 0
  4. 4. BASIC NUMBER SYSTEM DECIMAL HEXA DECIMAL OCTAL BINARY 4
  5. 5. DECIMAL NUMBER SYSTEM 5 • 0,1,2,3,4,5,6,7,8,9.DIGITS • 10BASE
  6. 6. 6 8*10 9*10 5*10 4*10 DECIMAL NUMBER 4598 0 1 2 3
  7. 7. 7 BINARY NUMBER SYSTEM •0,1DIGITS •2BASE
  8. 8. 8 BINARY NUMBER 1011 1*2 1*2 0*2 1*2 0 1 2 3
  9. 9. 9 HEXADECIMAL NUMBER SYSTEM •0,1,2,3,4,5,6,7, •8,9,A,B,C,D,E,F. DIGITS •16BASE
  10. 10. 10 HEXADECIMAL NUMBER 1A5D D*16 5*16 A*16 1*16 0 1 2 3
  11. 11. 11 OCTAL NUMBER SYSTEM •0,1,2,3,4, •5,6,7,8. DIGITS •8BASE
  12. 12. 12 OCTAL NUMBER 5273 3*8 7*8 2*8 5*8 0 1 2 3
  13. 13. 13 CONVERSIONS IN BASIC NUMBER SYSTEM
  14. 14. 14 BINARY TO DECIMAL • 1 0 1 0 1 BINARY • 5 4 3 2 1 BIT POSITION • 1*2 +0*2 +1*2 +0*2 +1*2. MUL WITH BASE • 21 DECIMAL4 3 2 1 0
  15. 15. 15 HEXADECIMAL TO DECIMAL •5A9 HEX •3 2 1 BIT POSITION • 5*16 +A*16 +9*16 MUL WITH BASE •1449 DECIMAL2 1 0
  16. 16. 16 OCTAL TO DECIMAL •645 OCTAL •3 2 1 BIT POSITION •6*8 +4*8 +5*8. MUL WITH BASE •421 DECIMAL 2 1 0
  17. 17. 17 DECIMAL TO BINARY • Q=19 • R=139 • Q=9 • R=119 • Q=4 • R=19 • Q=2 • R=04 • Q=1 • R=02 • Q=0 • R=11 LSB MSB Divide through out by 2 DECIMAL = 39 BINARY = 100111
  18. 18. 18 DECIMAL TO HEX • Q=2 • R=335 • Q=0 • R=22 Divide through out by 16 LSB MSB DECIMAL = 35 HEX = 23
  19. 19. 19 DECIMAL TO OCTAL • Q=57 • R=5461 • Q=7 • R=157 • Q=0 • R=77 Divide through out by 8 LSB MSB DECIMAL = 461 OCTAL = 715
  20. 20. 20 BINARY TO HEXADECIMAL BINARY • (010111011001) 4BITS DIV • (0101)(1101)(1001) HEX • (5) (D) (9) =(5D9)2 16
  21. 21. 21 BINARY TO OCTAL BINARY • (101111100) 3BIT DIV • (101)(111)(100) OCTAL • (5) (7) (4) =(574) 2 8
  22. 22. 22 HEXADECIMAL TO BINARY HEX • (5C) EXPANSION • (0101)(1100) BINARY • (01011100)16 2
  23. 23. 23 OCTAL TO BINARY OCTAL • (436) EXPANSION • (100)(011) BINARY • (100011) 8 2
  24. 24. 24 HEXADECIMAL TO OCTAL • (4DF)HEX • (0100)(1101)(1111)EXP • (010011010000)BINARY • (010)(011)(011)(111)3BIT DIV • (2337)OCTAL 16 2 8
  25. 25. 25 OCTAL TO HEXADECIMAL • (456)OCTAL • (100)(101)(110)EXP • (100101110)BINARY • (0001)(0010)(1110)4BIT DIV • (12E)HEX 8 2 16
  26. 26. 26 REPRESENTATION OF NEGATIVE NUMBER 9’S & 10’S COMPLIMENT • DECIMAL NUMBER SYSTEM 1’S & 2’S COMPLIMENT • BINARY NUMBER SYSTEM
  27. 27. 27 BINARY ARITHMETIC 1 • BINARY ADDITION 2 • BINARY SUBTRACTION 3 • BINARY MULTIPLICATION 4 • BINARY DIVISION
  28. 28. 28 0 + 0 = 0 1 + 0 = 1 0 + 1 = 1 1 + 1 = 0 1 (Carry bit) BINARYADDITION 1 1 0 1 (13 decimal) +0 0 0 1 (+1 decimal) 1 1 1 0 (14 decimal)
  29. 29. 29 BINARY SUBTRACTION 0 ‐ 0 = 0 1 ‐ 0 = 1 0 ‐ 1 = 1 1 (Carry bit) 1 ‐ 1 = 0 1 1 0 1 (13 decimal) + 0 0 1 1 (-3 decimal) 1 0 1 0 (10 decimal) Borrow
  30. 30. 30 1 0 0 0 =810 X 0 1 1 0 =610 0 0 0 0 + 1 0 0 0 + 1 0 0 0 + 0 0 0 0 0 1 1 0 0 0 0 = 4810 BINARY MULTIPLICATION
  31. 31. 31 BINARY DIVISION 011 ) 0 1 1 0 0 1 0 ( 1 0 1 1 0 0 0 (0 0 0 0 0 0 0 (0 0 0 0 0 0 1 (0 0 0 0 0 1 0 Q=1000=1610 R=10= 210
  32. 32. 32 SIGNED ARITHMETIC OPERATION MSB bit is reserved to represent the sign of the number. When the number is negative, the sign bit is kept one. When the number is positive, the sign bit is 0. In 8-bit processor, MSB = sign bit & other 7 bits = number. In 16-bit processor, MSB = sign bit & other 15 bits = number.
  33. 33. 33 EXAMPLES 0 0 0 0 0 1 0 1 (+5 decimal) 0 0 0 0 0 1 0 0 (+4 decimal) 0 0 0 0 1 0 0 1 (+9 decimal) 0 0 0 0 0 1 0 1 (+5 decimal) 1 0 0 0 0 0 1 0 (-2 decimal) 1 1 1 1 1 1 0 1 (1’comp of -2) 1 1 1 1 1 1 1 0 (2’s comp of -2) 0 0 0 0 0 0 1 1 (+3 decimal) 1 2 1 2 1
  34. 34. 34 BCD AND GRAY CODE
  35. 35. 35 LOGIC GATES Logic gates perform basic logical functions. They are fundamental building blocks of digital integrated circuits. Most logic gates take an input of two binary values, and output a single value of a 1 or 0.  Some circuits may have only a few logic gates, while others, such as microprocessors, may have millions of them. There are seven different types of logic gates, which are outlined.
  36. 36. 36
  37. 37. 37
  38. 38. 38
  39. 39. 39
  40. 40. 40
  41. 41. 41
  42. 42. 42
  43. 43. 43 FLIP-FLOPS A flip-flop or latch is a circuit that has two stable states and can be used to store state information. Each flip-flop stores one bit of information
  44. 44. 44 THANK YOU
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