Ch 1 part-1 final

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  • 1. CH – 10 [ 8 F G L Z H }VF TV G [ ; b IF 5 â lT PART - 1 Prepared By : Amin Sir
  • 2. Introduction Sd%I}8Z V[ JLHF6] 38SM H[JF S[48=Flgh:8Z4 lZ,[4 0FIM0 JU[Z[G] AG[,] K[ H[ AWs_f VYJF RF,]s!f V[D DF+A[DFYL V[S H T[YL Sd%I}8ZGL :DlTDF 0[8F ;FRJJF _ l:YlTDF CM. XS[ K[PVG[ ! DF+ A[ H VSM WZFJTL l£VSL ;bIF5âlT (Binary NumberSystem) l£VSL 5âlTDF DF+ A[ H VSM _ VG[ ! CMI GM p5IMU SZJFDF VFJ[ K[PK[P
  • 3. Data and Information 0[8F V[ CSLST VG[ VFS0FVMGM ;D}CK[4 H[DF ;bIFVM4 XaNM VG[ lR+MGM ;DFJ[X YFI K[P j I F b I F o jIlST4 :Y/4 J:T] VYJF SM.38GF VU[GL TDFD 5|SFZGL CSLSTM4 VFS0FVMVG[ lJUTMG[ RMSS; 5|lS|IFDFYL 5FZ µTZ[,F HIFZ[ SM. c 0 [ 8 F c SC[ K[P0[8FG[ c D F l C T L c (INFORMATION) SC[ K[P
  • 4. Number Systems;bIF5âlTf j I F b I F o U6TZL SZJF DF8[4 ZSDMG;ZBFJJF DF8[4 U6TZLVM SZJF T[DH lSDTM ZH} SZJF ;bIFVM jISSZJF p5IMUDF ,[JFTL lGXFGLVMGF ;D}CG[ c ; b I F 5 â l T 5|FRLG ;DIDF XFZLlZS VUM sBF;(Number System)SZLG[ VFU/LVMf UFl6lTS SC[ K[P ;CFI TZLS[ p5IMUDF ,[JFTL CTLP
  • 5. Number Systems;bIF5âlTf gI}HLGLJFGL ;:SlT D]HA tIFGF ,MSM ;bIFVZH} SZJF XZLZGF p5ZGF EFU[ VFJ[,F 27 H[8,F VUMGM p5IMSZTFP
  • 6. Number Systems;bIF5âlTf
  • 7. Decimal Number System ZMlHNF HLJGDF U6TZL DF8[ ;J";FDFgIZLT[ NXFX ;bIF5âlTGM p5IMU SZJFDF VFJ[TZLS[ VM/BFTF _4! NXFX ;bIF5âlT VS K[P4Z4#4$454&4*4( pNFP)#Z!4 $Z54 Z55_ JU[Z[P VCL HD6L VG[ V[ NX VHM0 lRíGM p5IMU SZ[ K[PAFH]GF K[<,F VSGL lSDT ;F{YL VMKL K[ VG[ 0FAL AFH] V[S5KL V[S VFU/ VFJTF VS µRL :YFGlSDT WZFJ[ K[P
  • 8. Decimal Number System SM. 56 ;bIFGF 0FAL AFH]GF 5C[,FVSG[ JW] DCtJGM VS SM. 56 ;bIFGF HD6L Digit) SC[ K[P (MSD – Most SignificantAFH]GF 5C[,FVSG[ VMKF DCtJGM VS (LSD – Leat Significant Digit) SC[ K[P
  • 9. Binary To Decimal 27 26 25 24 23 22 21 20128 64 32 16 8 4 2 1
  • 10. Binary To Decimal (1011)2 = (…………)10
  • 11. Binary To Decimal (1011)2 = (…………)10 1 1x20
  • 12. Binary To Decimal (1011)2 = (…………)10 1 1 1x21 + 1x20
  • 13. Binary To Decimal (1011)2 = (…………)10 0 1 1 0x22 + 1x21 + 1x20
  • 14. Binary To Decimal (1011)2 = (…………)10 1 0 1 1 1x23 + 0x22 + 1x21 + 1x20
  • 15. Binary To Decimal (1011)2 = (…………)10 1 0 1 1 1x23 + 0x22 + 1x21 + 1x20= 1x8 + 0x4 + 1x2 + 1x1
  • 16. Binary To Decimal (1011)2 = (…………)10 1 0 1 1 1x23 + 0x22 + 1x21 + 1x20= 1x8 + 0x4 + 1x2 + 1x1= 8 + 0 + 2 + 1
  • 17. Binary To Decimal (1011)2 = (…………)10 1 0 1 1 1x23 + 0x22 + 1x21 + 1x20= 1x8 + 0x4 + 1x2 + 1x1= 8 + 0 + 2 + 1= (11)10
  • 18. Binary To Decimal (101101)2 = (…………)10
  • 19. Binary To Decimal (101101)2 = (…………)10 1 1x20
  • 20. Binary To Decimal (101101)2 = (…………)10 0 1 0x21 + 1x20
  • 21. Binary To Decimal (101101)2 = (…………)10 1 0 1 1x22 + 0x21 + 1x20
  • 22. Binary To Decimal (101101)2 = (…………)10 1 1 0 1 1x23 + 1x22 + 0x21 + 1x20
  • 23. Binary To Decimal (101101)2 = (…………)10 0 1 1 0 1 0x24 + 1x23 + 1x22 + 0x21 + 1x20
  • 24. Binary To Decimal  (101101)2 = (…………)10 1 0 1 1 0 11x25 + 0x24 + 1x23 + 1x22 + 0x21 + 1x20
  • 25. Binary To Decimal  (101101)2 = (…………)10 1 0 1 1 0 11x25 + 0x248++1x23 0 + 1 2 + 0x21 + 1x20= 32 + 0 + 4 + + 1x2
  • 26. Binary To Decimal  (101101)2 = (…………)10 1 0 1 1 0 11x25 + 0x248++1x23 0 + 1 2 + 0x21 + 1x20= 32 + 0 + 4 + + 1x2= (45)10
  • 27. Binary To Decimal (11001011)2 = (…………)10
  • 28. Binary To Decimal (11001011)2 = (…………)10 (DO IT YOUR SELF) 1 1 0 0 1 0 1 1=128+ 1x26 + 0x25+ 8 + 0 + 1x231+ 0x22 + 1x21 + 1x201x27 + 64 + 0 + 0 + 0x24 + 2 += (203)10
  • 29. Binary To Decimal Do It Your Self (11101)2 = (…………)10 (1010101)2 = (…………)10 (1110011)2 = (…………)10
  • 30. Binary To Decimal (1010.11)2 = (…………)10
  • 31. Binary To Decimal  (1010.11)2 = (…………)10 11x2-2
  • 32. Binary To Decimal (1010.11)2 = (…………)10 1 1 1x2-1 + 1x2-2
  • 33. Binary To Decimal (1010.11)2 = (…………)10 0 1 1 0x20 + 1x2-1 + 1x2-2
  • 34. Binary To Decimal (1010.11)2 = (…………)10 1 0 1 1 1x21 + 0x20 + 1x2-1 + 1x2-2
  • 35. Binary To Decimal (1010.11)2 = (…………)10 0 1 0 1 1 0x22 + 1x21 + 0x20 + 1x2-1 + 1x2-2
  • 36. Binary To Decimal (1010.11)2 = (…………)10 1 0 1 0 1 1 1x23 + 0x22 + 1x21 + 0x20 + 1x2-1 + 1x2-2
  • 37. Binary To Decimal (1010.11)2 = (…………)10 1 0 1 0 1 1 1x23 + 0x22 + 1x21 + 0x20 + 1x2-1 + 1x2-2= 1x8 + 0 + 2 + 0 +½ + ¼
  • 38. Binary To Decimal (1010.11)2 = (…………)10 1 0 1 0 1 1 1x23 + 0x22 + 1x21 + 0x20 + 1x2-1 + 1x2-2= 1x8 + 0 + 2 + 0 +½ + ¼= 8 + 0 + 2 + 0 + 0.5 + 0.25
  • 39. Binary To Decimal (1010.11)2 = (…………)10 1 0 1 0 1 1 1x23 + 0x22 + 1x21 + 0x20 + 1x2-1 + 1x2-2= 1x8 + 0 + 2 + 0 +½ + ¼= 8 + 0 + 2 + 0 + 0.5 + 0.25= 10 + 0.75
  • 40. Binary To Decimal (1010.11)2 = (…………)10 1 0 1 0 1 1 1x23 + 0x22 + 1x21 + 0x20 + 1x2-1 + 1x2-2= 1x8 + 0 + 2 + 0 +½ + ¼= 8 + 0 + 2 + 0 + 0.5 + 0.25= 10 + 0.75= (10.75)10
  • 41. Binary To Decimal (1101.101)2 = (…………)10
  • 42. Binary To Decimal (1101.101)2 = (…………)10 1 1x2-3
  • 43. Binary To Decimal (1101.101)2 = (…………)10 0 1 0x2-2 + 1x2-3
  • 44. Binary To Decimal (1101.101)2 = (…………)10 1 0 1 1x2-1 + 0x2-2 + 1x2-3
  • 45. Binary To Decimal (1101.101)2 = (…………)10 1 1 0 1 1x20 + 1x2-1 + 0x2-2 + 1x2-3
  • 46. Binary To Decimal (1101.101)2 = (…………)10 0 1 1 0 1 0x21 + 1x20 + 1x2-1 + 0x2-2 + 1x2-3
  • 47. Binary To Decimal (1101.101)2 = (…………)10 1 0 1 1 0 1 1x22 + 0x21 + 1x20 + 1x2-1 + 0x2-2 + 1x2-3
  • 48. Binary To Decimal (1101.101)2 = (…………)10 1 1 0 1 1 0 11x23 + 1x22 + 0x21 + 1x20 + 1x2-1 + 0x2-2 + 1x2-3
  • 49. Binary To Decimal  (1101.101)2 = (…………)10 1 1 0 1 1 0 1 1x23 + 1x22 + 0x21 + 1x20 + 1x2-1 + 0x2-2 + 1x2-3= 1x8 + 1x4 + 0x2 + 1x1 + ½ + 0 + 1/8
  • 50. Binary To Decimal  (1101.101)2 = (…………)10 1 1 0 1 1 0 1 1x23 + 1x22 + 0x21 + 1x20 + 1x2-1 + 0x2-2 + 1x2-3= 1x8 + 1x4 + 0x2 + 1x1 + ½ + 0 + 1/8= 8 + 4 + 0 + 1 + 0.5 + 0 + 0.125
  • 51. Binary To Decimal  (1101.101)2 = (…………)10 1 1 0 1 1 0 1 1x23 + 1x22 + 0x21 + 1x20 + 1x2-1 + 0x2-2 + 1x2-3= 1x8 + 1x4 + 0x2 + 1x1 + ½ + 0 + 1/8= 8 + 4 + 0 + 1 + 0.5 + 0 + 0.125= 13 + 0.625
  • 52. Binary To Decimal  (1101.101)2 = (…………)10 1 1 0 1 1 0 1 1x23 + 1x22 + 0x21 + 1x20 + 1x2-1 + 0x2-2 + 1x2-3= 1x8 + 1x4 + 0x2 + 1x1 + ½ + 0 + 1/8= 8 + 4 + 0 + 1 + 0.5 + 0 + 0.125= 13 + 0.625= (13.625)10
  • 53. Decimal To Binary (153)10 = (…………)2
  • 54. Decimal To Binary (153)10 = (…………)2 153 2 76 1 76 2 153 14 013 012 001
  • 55. Decimal To Binary (153)10 = (…………)2 153 2 76 1 2 38 0 38 76 2 76 2 153 6 14 16 013 16 012 000 001
  • 56. Decimal To Binary (153)10 = (…………)2 153 2 76 1 2 38 0 2 19 0
  • 57. Decimal To Binary (153)10 = (…………)2 153 2 76 1 2 38 0 2 19 0 2 9 1
  • 58. Decimal To Binary (153)10 = (…………)2 153 2 76 1 2 38 0 2 19 0 2 9 1 2 4 1
  • 59. Decimal To Binary (153)10 = (…………)2 153 2 76 1 2 38 0 2 19 0 2 9 1 2 4 1 2 2 0
  • 60. Decimal To Binary (153)10 = (…………)2 153 2 76 1 2 38 0 2 19 0 2 9 1 2 4 1 2 2 0 2 1 0
  • 61. Decimal To Binary (153)10 = (…………)2 153 2 76 1 2 38 0 2 19 0 2 9 1 2 4 1 2 2 0 2 1 0 0 1
  • 62. Decimal To Binary (153)10 = (…………)2 (153)10 = (10011001)2
  • 63. Decimal To Binary (573)10 = (…………)2 573 2 286 1
  • 64. Decimal To Binary (573)10 = (…………)2 573 2 286 1 2 143 0
  • 65. Decimal To Binary (573)10 = (…………)2 573 2 286 1 2 143 0 2 71 1
  • 66. Decimal To Binary (573)10 = (…………)2 573 2 286 1 2 143 0 2 71 1 2 35 1
  • 67. Decimal To Binary (573)10 = (…………)2 573 2 286 1 2 143 0 2 71 1 2 35 1 2 17 1
  • 68. Decimal To Binary (573)10 = (…………)2 573 2 286 1 2 143 0 2 71 1 2 35 1 2 17 1 2 8 1
  • 69. Decimal To Binary (573)10 = (…………)2 573 2 286 1 2 143 0 2 71 1 2 35 1 2 17 1 2 8 1 2 4 0
  • 70. Decimal To Binary (573)10 = (…………)2 573 2 286 1 2 143 0 2 71 1 2 35 1 2 17 1 2 8 1 2 4 0 2 2 0
  • 71. Decimal To Binary (573)10 = (…………)2 573 2 286 1 2 143 0 2 71 1 2 35 1 2 17 1 2 8 1 2 4 0 2 2 0 2 1 0
  • 72. Decimal To Binary (573)10 = (…………)2 573 2 286 1 2 143 0 2 71 1 2 35 1 2 17 1 2 8 1 2 4 0 2 2 0 2 1 0 0 1
  • 73. Decimal To Binary (573)10 = (…………)2 (573)10 = (1000111101)2
  • 74. Decimal To Binary (1021)10 = (…………)2 1021 2 510 1
  • 75. Decimal To Binary (1021)10 = (…………)2 1021 2 510 1 2 255 0
  • 76. Decimal To Binary (1021)10 = (…………)2 1021 2 510 1 2 255 0 2 127 1
  • 77. Decimal To Binary (1021)10 = (…………)2 1021 2 510 1 2 255 0 2 127 1 2 63 1
  • 78. Decimal To Binary (1021)10 = (…………)2 1021 2 510 1 2 255 0 2 127 1 2 63 1 2 31 1
  • 79. Decimal To Binary (1021)10 = (…………)2 1021 2 510 1 2 255 0 2 127 1 2 63 1 2 31 1 2 15 1
  • 80. Decimal To Binary (1021)10 = (…………)2 1021 2 510 1 2 255 0 2 127 1 2 63 1 2 31 1 2 15 1 2 7 1
  • 81. Decimal To Binary (1021)10 = (…………)2 1021 2 510 1 2 255 0 2 127 1 2 63 1 2 31 1 2 15 1 2 7 1 2 3 1
  • 82. Decimal To Binary (1021)10 = (…………)2 1021 2 510 1 2 255 0 2 127 1 2 63 1 2 31 1 2 15 1 2 7 1 2 3 1 2 1 1 0 1
  • 83. Decimal To Binary (1021)10 = (…………)2 (1021)10 = (1111111101)2
  • 84. Decimal To Binary (1703)10 = (…………)2 (DO IT YOUR SELF)
  • 85. Decimal To Binary (1703)10 = (…………)2 (DO IT YOUR SELF) 1703 2 851 1 2 425 1 2 212 1 2 106 0 2 53 0 2 26 1 2 13 0 2 6 1 2 3 0 2 1 1 0 1
  • 86. Decimal To Binary Do It Your Self (253)10 = (…………)2 (756)10 = (…………)2 (1024)10 = (…………)2
  • 87. Decimal To Binary (107.625)10 = (…………)2
  • 88. Decimal To Binary (107.625)10 = (…………)2 107 2 53 1 2 26 1 2 13 0 2 6 1 2 3 0 2 1 1 0 1 (1101011)2
  • 89. Decimal To Binary (107.625)10 = (…………)2 107 0.625 x 2 = 1.250 2 53 1 2 26 1 2 13 0 2 6 1 2 3 0 2 1 1 0 1 (1101011)2
  • 90. Decimal To Binary (107.625)10 = (…………)2 107 0.625 x 2 = 1.250 2 53 1 2 26 1 0.250 x 2 = 0.500 2 13 0 2 6 1 2 3 0 2 1 1 0 1 (1101011)2
  • 91. Decimal To Binary (107.625)10 = (…………)2 107 0.625 x 2 = 1.250 2 53 1 2 26 1 0.250 x 2 = 0.500 2 13 0 0.500 x 2 = 1.000 2 6 1 2 3 0 2 1 1 0 1 (1101011)2 (101)2 (1101011.101)2
  • 92. Decimal To Binary (95.3)10 = (…………)2
  • 93. Decimal To Binary (95.3)10 = (…………)2 95 2 47 1 2 23 1 2 11 1 2 5 1 2 2 1 2 1 0 0 1 (1011111)2
  • 94. Decimal To Binary (95.3)10 = (…………)2 95 0.3 x 2 = 0.6 2 47 1 2 23 1 2 11 1 2 5 1 2 2 1 2 1 0 0 1 (1011111)2
  • 95. Decimal To Binary (95.3)10 = (…………)2 95 0.3 x 2 = 0.6 2 47 1 2 23 1 0.6 x 2 = 1.2 2 11 1 2 5 1 2 2 1 2 1 0 0 1 (1011111)2
  • 96. Decimal To Binary (95.3)10 = (…………)2 95 0.3 x 2 = 0.6 2 47 1 2 23 1 0.6 x 2 = 1.2 2 11 1 0.2 x 2 = 0.4 2 5 1 2 2 1 2 1 0 0 1 (1011111)2
  • 97. Decimal To Binary (95.3)10 = (…………)2 95 0.3 x 2 = 0.6 2 47 1 2 23 1 0.6 x 2 = 1.2 2 11 1 0.2 x 2 = 0.4 2 5 1 0.4 x 2 = 0.8 2 2 1 2 1 0 0 1 (1011111)2
  • 98. Decimal To Binary (95.3)10 = (…………)2 95 0.3 x 2 = 0.6 2 47 1 2 23 1 0.6 x 2 = 1.2 2 11 1 0.2 x 2 = 0.4 2 5 1 0.4 x 2 = 0.8 2 2 1 2 1 0 0.8 x 2 = 1.6 0 1 (1011111)2
  • 99. Decimal To Binary (95.3)10 = (…………)2 95 0.3 x 2 = 0.6 2 47 1 0.6 x 2 = 1.2 2 23 1 2 11 1 0.2 x 2 = 0.4 2 5 1 0.4 x 2 = 0.8 2 2 1 2 1 0 0.8 x 2 = 1.6 0 1 0.6 x 2 = 1.2 (1011111)2 (010011)2 (1011111.010011)2
  • 100. Decimal To Binary Do It Your Self (961.875)10 = (…………)2 (517.625)10 = (…………)2
  • 101.  Base – 16 Hexadecimal s;M/VSLf Base – 8 Octal sVQ8VSLf
  • 102.  VQ8VSL ;bIF5£lT :YFGEFZ5âlT K[ H[ _4!4Z4#4$454&4* V[JF ( lRíMGM p5IMU SZ[ K[P p5IMU YTM VQ8VSL 5âlTDF VF9 VSMGMCMJFYL T[G[ VQ8VSL (Octal) base – 8 ;bIF5âlT TZLS[ VM/BJFDF l£VSL ;bIFGF HD6[ YL 0FAL AFH] V[D +6VFJ[ K[P+6 VSMG] H}Y AGFJLG[ VQ8VSL ;bIF D[/JL XSFI K[P
  • 103. VQ8VSL l£VSL 0 000 1 001 2 010 3 011 4 100 5 101 6 110 7 111
  • 104. Octal To Binary (752)8 = (…………)2
  • 105. Octal To Binary  (752)8 = (…………)2VQ8VSL l£VSL 0 000 2 1 001 2 010 010 3 011 4 100 5 101 6 110 7 111
  • 106. Octal To Binary  (752)8 = (…………)2VQ8VSL l£VSL 0 000 5 2 1 001 101 010 2 010 3 011 4 100 5 101 6 110 7 111
  • 107. Octal To Binary  (752)8 = (…………)2VQ8VSL l£VSL 0 000 7 5 2 1 001 111 101 010 2 010 3 011 4 100 5 101 6 110 7 111
  • 108. Octal To Binary  (752)8 = (…………)2VQ8VSL l£VSL 0 000 7 5 2 1 001 111 101 010 2 010 3 011 4 100 (111101010)2 5 101 6 110 7 111
  • 109. Octal To Binary (604)8 = (…………)2
  • 110. Octal To Binary  (604)8 = (…………)2VQ8VSL l£VSL 0 000 4 1 001 2 010 100 3 011 4 100 5 101 6 110 7 111
  • 111. Octal To Binary  (604)8 = (…………)2VQ8VSL l£VSL 0 000 0 4 1 001 000 100 2 010 3 011 4 100 5 101 6 110 7 111
  • 112. Octal To Binary  (604)8 = (…………)2VQ8VSL l£VSL 0 000 6 0 4 1 001 2 010 110 000 100 3 011 4 100 5 101 6 110 7 111
  • 113. Octal To Binary  (604)8 = (…………)2VQ8VSL l£VSL 0 000 6 0 4 1 001 2 010 110 000 100 3 011 4 100 (110000100)2 5 101 6 110 7 111
  • 114. Octal To Binary (135)8 = (…………)2
  • 115. Octal To Binary  (135)8 = (…………)2VQ8VSL l£VSL 0 000 1 3 5 1 001 2 010 001 011 101 3 011 4 100 (001011101)2 5 101 6 110 7 111
  • 116. Binary To Octal (10100111)2 = (…………)8
  • 117. Binary To Octal  (10100111)2 = (…………)8VQ8VSL l£VSL 0 000 1 001 111 2 010 7 3 011 4 100 5 101 6 110 7 111
  • 118. Binary To Octal  (10100111)2 = (…………)8VQ8VSL l£VSL 0 000 1 001 100 111 2 010 4 7 3 011 4 100 5 101 6 110 7 111
  • 119. Binary To Octal  (10100111)2 = (…………)8VQ8VSL l£VSL 0 000 1 001 010 100 111 2 010 2 4 7 3 011 4 100 (247)8 5 101 6 110 7 111
  • 120. Binary To Octal (010110101)2 = (…………)8
  • 121. Binary To Octal  (010110101)2 = (…………)8VQ8VSL l£VSL 0 000 1 001 101 2 010 5 3 011 4 100 5 101 6 110 7 111
  • 122. Binary To Octal  (010110101)2 = (…………)8VQ8VSL l£VSL 0 000 1 001 110 101 2 010 6 5 3 011 4 100 5 101 6 110 7 111
  • 123. Binary To Octal  (010110101)2 = (…………)8VQ8VSL l£VSL 0 000 1 001 010 110 101 2 010 2 6 5 3 011 4 100 (265)8 5 101 6 110 7 111
  • 124. Binary To Octal (111000011)2 = (…………)8
  • 125. Binary To Octal  (111000011)2 = (…………)8VQ8VSL l£VSL 0 000 1 001 111 000 011 2 010 7 0 3 3 011 4 100 (703)8 5 101 6 110 7 111
  • 126. Octal To Decimal (456)8 = (…………)10
  • 127. Octal To Decimal (456)8 = (…………)10 6 6x80
  • 128. Octal To Decimal (456)8 = (…………)10 5 6 5x81 + 6x80
  • 129. Octal To Decimal (456)8 = (…………)10 4 5 6 4x82 + 5x81 + 6x80
  • 130. Octal To Decimal (456)8 = (…………)10 4 5 6 4x82 + 5x81 + 6x80 4x64 + 5x8 + 6x1
  • 131. Octal To Decimal (456)8 = (…………)10 4 5 6 4x82 + 5x81 + 6x80 4x64 + 5x8 + 6x1 256 + 40 + 6
  • 132. Octal To Decimal (456)8 = (…………)10 4 5 6 4x82 + 5x81 + 6x80 4x64 + 5x8 + 6x1 256 + 40 + 6 (302)10
  • 133. Octal To Decimal (267)8 = (…………)10
  • 134. Octal To Decimal (267)8 = (…………)10 7 7x80
  • 135. Octal To Decimal (267)8 = (…………)10 6 7 6x81 + 7x80
  • 136. Octal To Decimal (267)8 = (…………)10 2 6 7 2x82 + 6x81 + 7x80
  • 137. Octal To Decimal (267)8 = (…………)10 2 6 7 2x82 + 6x81 + 7x80 2x64 + 6x8 + 7x1
  • 138. Octal To Decimal (267)8 = (…………)10 2 6 7 2x82 + 6x81 + 7x80 2x64 + 6x8 + 7x1 128 + 48 + 7
  • 139. Octal To Decimal (267)8 = (…………)10 2 6 7 2x82 + 6x81 + 7x80 2x64 + 6x8 + 7x1 128 + 48 + 7 (183)10
  • 140. Octal To Decimal (3426)8 = (…………)10
  • 141. Octal To Decimal (3426)8 = (…………)10 6 6x80
  • 142. Octal To Decimal (3426)8 = (…………)10 2 6 2x81 + 6x80
  • 143. Octal To Decimal (3426)8 = (…………)10 4 2 6 4x82 + 2x81 + 6x80
  • 144. Octal To Decimal (3426)8 = (…………)10 3 4 2 6 3x83 + 4x82 + 2x81 + 6x80
  • 145. Octal To Decimal (3426)8 = (…………)10 3 4 2 6 3x83 + 4x82 + 2x81 + 6x80 3x512 + 4x64 + 2x8 + 6x1
  • 146. Octal To Decimal (3426)8 = (…………)10 3 4 2 6 3x83 + 4x82 + 2x81 + 6x80 3x512 + 4x64 + 2x8 + 6x1 1536 + 256 + 16 + 6
  • 147. Octal To Decimal (3426)8 = (…………)10 3 4 2 6 3x83 + 4x82 + 2x81 + 6x80 3x512 + 4x64 + 2x8 + 6x1 1536 + 256 + 16 + 6 (1814)10
  • 148. Octal To Decimal (3615)8 = (…………)10 (Do It Your Self)
  • 149. Octal To Decimal (3615)8 = (…………)10 3 6 1 5 3x83 + 6x82 + 1x81 + 5x80 3x512 + 6x64 + 1x8 + 5x1 1536 + 384 + 8 + 5 (1933)10
  • 150. Decimal To Octal (597)10 = (…………)8
  • 151. Decimal To Octal (597)10 = (…………)8 597 8 74 5
  • 152. Decimal To Octal (597)10 = (…………)8 597 8 74 5 8 9 2
  • 153. Decimal To Octal (597)10 = (…………)8 597 8 74 5 8 9 2 8 1 1
  • 154. Decimal To Octal (597)10 = (…………)8 597 8 74 5 8 9 2 8 1 1 0 1
  • 155. Decimal To Octal (597)10 = (…………)8 597 8 74 5 8 9 2 8 1 1 0 1 (1125)8
  • 156. Decimal To Octal (3856)10 = (…………)8
  • 157. Decimal To Octal (3856)10 = (…………)8 3856 8 482 0
  • 158. Decimal To Octal (3856)10 = (…………)8 3856 8 482 0 8 60 2
  • 159. Decimal To Octal (3856)10 = (…………)8 3856 8 482 0 8 60 2 8 7 4
  • 160. Decimal To Octal (3856)10 = (…………)8 3856 8 482 0 8 60 2 8 7 4 0 7
  • 161. Decimal To Octal (3856)10 = (…………)8 3856 8 482 0 8 60 2 8 7 4 0 7 (7420)8
  • 162. Decimal To Octal (4635)10 = (…………)8
  • 163. Decimal To Octal (4635)10 = (…………)8 4635 8 579 3
  • 164. Decimal To Octal (4635)10 = (…………)8 4635 8 579 3 8 72 3
  • 165. Decimal To Octal (4635)10 = (…………)8 4635 8 579 3 8 72 3 8 9 0
  • 166. Decimal To Octal (4635)10 = (…………)8 4635 8 579 3 8 72 3 8 9 0 8 1 1
  • 167. Decimal To Octal (4635)10 = (…………)8 4635 8 579 3 8 72 3 8 9 0 8 1 1 0 1
  • 168. Decimal To Octal (4635)10 = (…………)8 4635 8 579 3 8 72 3 8 9 0 8 1 1 0 1 (11033)8
  • 169.  ;M/VSL ;bIF5£lT :YFGEFZ5âlT K[ H[ _4!4Z4#4PPPPPPPPP)4 A,B,C,D,E,F V[JF !& lRíMGM p5IMU SZ[ K[P A,B,C,D,E,F GF ;DFG NXFX TZLS[ VG]S|D[ !_4 !!4 !Z4 !#4 !$ VG[ !5 WFZJFDF VFJ[ K[P ;M/VSL ;bIF5âlTGM VFWFZ !& GM CMI K[P
  • 170. ;M/V l£VS ;M/V l£VSSL0 L0000 SL8 L1000 1 0001 9 1001 2 0010 10=A 1010 3 0011 11=B 1011 4 0100 12=C 1100 5 0101 13=D 1101 6 0110 14=E 1110 7 0111 15=F 1111
  • 171. Hexadecimal To Binary (3B2D)16 = (…………)2
  • 172. Hexadecimal To Binary (3B2D)16 = (…………)2 ;M/V l£VS ;M/V l£VS SL0 L0000 SL8 L1000 D 1 0001 9 1001 1101 2 0010 10=A 1010 3 0011 11=B 1011 4 0100 12=C 1100 5 0101 13=D 1101 6 0110 14=E 1110 7 0111 15=F 1111
  • 173. Hexadecimal To Binary (3B2D)16 = (…………)2 ;M/V l£VS ;M/V l£VS SL0 L0000 SL8 L1000 2 D 1 0001 9 1001 0010 1101 2 0010 10=A 1010 3 0011 11=B 1011 4 0100 12=C 1100 5 0101 13=D 1101 6 0110 14=E 1110 7 0111 15=F 1111
  • 174. Hexadecimal To Binary (3B2D)16 = (…………)2 ;M/V l£VS ;M/V l£VS SL0 L0000 SL8 L1000 B 2 D 1 0001 9 1001 1011 0010 1101 2 0010 10=A 1010 3 0011 11=B 1011 4 0100 12=C 1100 5 0101 13=D 1101 6 0110 14=E 1110 7 0111 15=F 1111
  • 175. Hexadecimal To Binary  (3B2D)16 = (…………)2 ;M/V l£VS ;M/V l£VS SL0 L0000 SL8 L1000 3 B 2 D 1 0001 9 10010011 1011 0010 1101 2 0010 10=A 1010 3 0011 11=B 1011 4 0100 12=C 1100 5 0101 13=D 1101 6 0110 14=E 1110 7 0111 15=F 1111
  • 176. Hexadecimal To Binary (4F5A)16 = (…………)2
  • 177. Hexadecimal To Binary (4F5A)16 = (…………)2 ;M/V l£VS ;M/V l£VS SL0 L0000 SL8 L1000 A 1 0001 9 1001 1010 2 0010 10=A 1010 3 0011 11=B 1011 4 0100 12=C 1100 5 0101 13=D 1101 6 0110 14=E 1110 7 0111 15=F 1111
  • 178. Hexadecimal To Binary (4F5A)16 = (…………)2 ;M/V l£VS ;M/V l£VS SL0 L0000 SL8 L1000 5 A 1 0001 9 1001 0101 1010 2 0010 10=A 1010 3 0011 11=B 1011 4 0100 12=C 1100 5 0101 13=D 1101 6 0110 14=E 1110 7 0111 15=F 1111
  • 179. Hexadecimal To Binary (4F5A)16 = (…………)2 ;M/V l£VS ;M/V l£VS SL0 L0000 SL8 L1000 F 5 A 1 0001 9 1001 1111 0101 1010 2 0010 10=A 1010 3 0011 11=B 1011 4 0100 12=C 1100 5 0101 13=D 1101 6 0110 14=E 1110 7 0111 15=F 1111
  • 180. Hexadecimal To Binary  (4F5A)16 = (…………)2 ;M/V l£VS ;M/V l£VS SL0 L0000 SL8 L1000 4 F 5 A 1 0001 9 10010100 1111 0101 1010 2 0010 10=A 1010 3 0011 11=B 1011 4 0100 12=C 1100 5 0101 13=D 1101 6 0110 14=E 1110 7 0111 15=F 1111
  • 181. Hexadecimal To Binary (7C6E)16 = (…………)2
  • 182. Hexadecimal To Binary  (7C6E)16 = (…………)2 ;M/V l£VS ;M/V l£VS SL0 L0000 SL8 L1000 7 C 6 E 1 0001 9 10010111 1100 0110 1110 2 0010 10=A 1010 3 0011 11=B 1011 4 0100 12=C 1100 5 0101 13=D 1101 6 0110 14=E 1110 7 0111 15=F 1111
  • 183. Binary To Hexadecimal (10010110110)2 = (…………)16
  • 184. Binary To Hexadecimal (10010110110)2 = (…………)16 ;M/V l£VS ;M/V l£VS SL0 L0000 SL8 L1000 0110 1 0001 9 1001 2 0010 10=A 1010 6 3 0011 11=B 1011 4 0100 12=C 1100 5 0101 13=D 1101 6 0110 14=E 1110 7 0111 15=F 1111
  • 185. Binary To Hexadecimal (10010110110)2 = (…………)16 ;M/V l£VS ;M/V l£VS SL0 L0000 SL8 L1000 1011 0110 1 0001 9 1001 2 0010 10=A 1010 B 6 3 0011 11=B 1011 4 0100 12=C 1100 5 0101 13=D 1101 6 0110 14=E 1110 7 0111 15=F 1111
  • 186. Binary To Hexadecimal (10010110110)2 = (…………)16 ;M/V l£VS ;M/V l£VS SL0 L0000 SL8 L1000 0100 1011 0110 1 0001 9 1001 2 0010 10=A 1010 4 B 6 3 0011 11=B 1011 4 0100 12=C 1100 5 0101 13=D 1101 6 0110 14=E 1110 7 0111 15=F 1111
  • 187. Binary To Hexadecimal (10100110110)2 = (…………)16
  • 188. Binary To Hexadecimal (10100110110)2 = (…………)16 ;M/V l£VS ;M/V l£VS SL0 L0000 SL8 L1000 0110 1 0001 9 1001 2 0010 10=A 1010 6 3 0011 11=B 1011 4 0100 12=C 1100 5 0101 13=D 1101 6 0110 14=E 1110 7 0111 15=F 1111
  • 189. Binary To Hexadecimal (10100110110)2 = (…………)16 ;M/V l£VS ;M/V l£VS SL0 L0000 SL8 L1000 0011 0110 1 0001 9 1001 2 0010 10=A 1010 3 6 3 0011 11=B 1011 4 0100 12=C 1100 5 0101 13=D 1101 6 0110 14=E 1110 7 0111 15=F 1111
  • 190. Binary To Hexadecimal (10100110110)2 = (…………)16 ;M/V l£VS ;M/V l£VS SL0 L0000 SL8 L1000 0101 0011 0110 1 0001 9 1001 2 0010 10=A 1010 5 3 6 3 0011 11=B 1011 4 0100 12=C 1100 5 0101 13=D 1101 6 0110 14=E 1110 7 0111 15=F 1111
  • 191. Binary To Hexadecimal (111000111001)2 = (…………)16
  • 192. Binary To Hexadecimal (111000111001)2 = (…………)16 ;M/V l£VS ;M/V l£VS SL0 L0000 SL8 L1000 1110 0011 1001 1 0001 9 1001 2 0010 10=A 1010 E 3 9 3 0011 11=B 1011 4 0100 12=C 1100 5 0101 13=D 1101 6 0110 14=E 1110 7 0111 15=F 1111
  • 193. Hexadecimal To Decimal (3F9)16 = (…………)10
  • 194. Hexadecimal To Decimal (3F9)16 = (…………)10 9 9X160
  • 195. Hexadecimal To Decimal (3F9)16 = (…………)10 F=15 9 15X161 + 9X160
  • 196. Hexadecimal To Decimal (3F9)16 = (…………)10 3 F=15 9 3X162 + 15X161 + 9X160
  • 197. Hexadecimal To Decimal (3F9)16 = (…………)10 3 F=15 9 3X162 + 15X161 + 9X160 3X256 + 15X16 + 9X1
  • 198. Hexadecimal To Decimal (3F9)16 = (…………)10 3 F=15 9 3X162 + 15X161 + 9X160 3X256 + 15X16 + 9X1 768 + 240 + 9
  • 199. Hexadecimal To Decimal (3F9)16 = (…………)10 3 F=15 9 3X162 + 15X161 + 9X160 3X256 + 15X16 + 9X1 768 + 240 + 9 (1017)10
  • 200. Hexadecimal To Decimal (2E7)16 = (…………)10 7 7X160
  • 201. Hexadecimal To Decimal (2E7)16 = (…………)10 E=14 7 14X161 + 7X160
  • 202. Hexadecimal To Decimal (2E7)16 = (…………)10 2 E=14 7 2X162 + 14X161 + 7X160
  • 203. Hexadecimal To Decimal (2E7)16 = (…………)10 2 E=14 7 2X162 + 14X161 + 7X160 2X256 + 14X16 + 7X1
  • 204. Hexadecimal To Decimal (2E7)16 = (…………)10 2 E=14 7 2X162 + 14X161 + 7X160 2X256 + 14X16 + 7X1 512 + 224 + 7
  • 205. Hexadecimal To Decimal (2E7)16 = (…………)10 2 E=14 7 2X162 + 14X161 + 7X160 2X256 + 14X16 + 7X1 512 + 224 + 7 (743)10
  • 206. Hexadecimal To Decimal (1A8)16 = (…………)10
  • 207. Hexadecimal To Decimal (1A8)16 = (…………)10 (Do It Your Self) 1 A=10 8 1X162 + 10X161 + 8X160 1X256 + 10X16 + 8X1 256 + 160 + 8 (424)10
  • 208. Hexadecimal To Decimal Do It Your Self (A2)16 = (…………)10 (A24)16 = (…………)10 (2C6)16 = (…………)10
  • 209. Hexadecimal To Decimal (3A.7B)16 = (…………)10
  • 210. Hexadecimal To Decimal (3A.7B)16 = (…………)10 B=11 11X16-2
  • 211. Hexadecimal To Decimal (3A.7B)16 = (…………)10 7 B=11 7X16-1 + 11X16-2
  • 212. Hexadecimal To Decimal (3A.7B)16 = (…………)10 A=10 7 B=11 10X160 + 7X16-1 + 11X16-2
  • 213. Hexadecimal To Decimal (3A.7B)16 = (…………)10 3 A=10 7 B=113X161 + 10X160 + 7X16-1 + 11X16-2
  • 214. Hexadecimal To Decimal (3A.7B)16 = (…………)10 3 A=10 7 B=113X161 + 10X160 + 7X16-1 + 11X16-23X16 + 10X1 + 7X1/16 + 11X1/256
  • 215. Hexadecimal To Decimal (3A.7B)16 = (…………)10 3 A=10 7 B=113X161 + 10X160 + 7X16-1 + 11X16-23X16 + 10X1 + 7X1/16 + 11X1/25648 + 10 + 0.4375 + 0.042968
  • 216. Hexadecimal To Decimal (3A.7B)16 = (…………)10 3 A=10 7 B=113X161 + 10X160 + 7X16-1 + 11X16-23X16 + 10X1 + 7X1/16 + 11X1/25648 + 10 + 0.4375 + 0.042968(58.480468)10
  • 217. Decimal To Hexadecimal (91)10 = (…………)16
  • 218. Decimal To Hexadecimal (91)10 = (…………)16 91 16 5 11=B
  • 219. Decimal To Hexadecimal (91)10 = (…………)16 91 16 5 11=B 0 5 (5B)16
  • 220. Decimal To Hexadecimal (2679)10 = (…………)16
  • 221. Decimal To Hexadecimal (2679)10 = (…………)16 2679 16 167 7
  • 222. Decimal To Hexadecimal (2679)10 = (…………)16 2679 16 167 7 16 10 7
  • 223. Decimal To Hexadecimal (2679)10 = (…………)16 2679 16 167 7 16 10 7 0 10=A (A77)16
  • 224. Decimal To Hexadecimal (185)10 = (…………)16
  • 225. Decimal To Hexadecimal (185)10 = (…………)16 185 16 11 9 0 11=B (B9)16
  • 226. Decimal To Hexadecimal Do It Your Self (4635)10 = (…………)16 (256)10 = (…………)16 (1098)10 = (…………)16
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