1. NUMBER SYSTEM

2. Number System Number Base B => B symbols – Base 16(Hexa):0, 1,……9, A,…, E, F – Base 10 (Decimal): 0, 1, 2,……, 7, 8, 9 – Base 8(Octal): 0, 1, 2, 3, 4, 5, 6, 7 – Base 2 (Binary): 0, 1

3. Number System (cont) Number representation: d 31 d 30... d 2 d 1 d 0 is a 32 digit number value = d 31 x B 31 + d 30 x B 30 +... + d 2 x B 2 + d 1 x B 1 + d 0 x B 0

4. Decimal Numbers: Base 10 Base or Radix is 10 Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Example: 412 10 = 4x10 2 + 1x10 1 + 2x10 0 = 400 + 10 +2 = 412

5. Binary Numbers: Base 2 Base or Radix is 2 Digits: 0, 1 Example: 101 2 = 1x2 2 + 0x2 1 + 1x2 0 = 4 + 0 +1 = 5

6. Octal Numbers: Base 8 Base or Radix is 8 Digits: 0, 1, 2, 3, 4, 5, 6, 7 Example: 123 8 = 1x8 2 + 2x8 1 + 3x8 0 = 64 + 16 +3 = 83

7. Hexadecimal Numbers: Base 16 Digits:0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F: – A  10 – B  11 – C  12 – D  13 – E  14 – F  15 Example: 12 16 = 1x16 1 + 2x16 0 = 16 +2 = 18

8. Conversions Decimal to Base NBase N to Decimal Successive Division by N (Remainder Method) Multiplication with power of N

9. Decimal to Binary

10. Conversion of 25 10 to Binary 2 25 2 12 -1 2 6 - 0 2 3 - 0 1 - 1 25 10 =11001 2

11. Binary to decimal conversion 11001 1X2 0 = 1 0X2 1 = 0 0X2 2 = 0 1X2 3 = 8 1X2 4 = 16 25 10

12. Decimal to Octal

13. Conversion of 125 10 to Octal 8 125 8 15 - 5 1 - 7 125 10 =175 8

14. Octal to decimal conversion 175 5X8 0 = 5 7X8 1 = 56 1X8 2 = 64 125 175 8 = 125 10

15. Conversion of 84 10 to Octal 8 84 8 10 - 4 1 - 2 84 10 =124 8

16. Octal to decimal conversion 124 4X8 0 = 4 2X8 1 = 16 1X8 2 = 64 84 124 8 = 84 10

17. Decimal to Hexa

18. Conversion of 450 10 to Hexadecimal 16 450 16 28 - 2 1 - 12 450 10 =1C2 16

19. Hexa to decimal conversion 1C2 2X16 0 = 2 12X16 1 = 192 1X16 2 = 256 450 1C2 16 = 450 10

20. Conversion of 385 10 to Hexadecimal 16 385 16 24 - 1 1 - 8 385 10 =181 16

21. Hexa to decimal conversion 181 1X16 0 = 1 8X16 1 = 128 1X16 2 = 256 385 181 16 = 385 10

22. Other Conversions BINARY  OCTAL BINARY  HEXA OCTAL  HEXA etc,.

23. BINARY  OCTAL OCTAL – BASE 8 = 2 3 3 DIGIT BINARY NUMBER Example:11001 2  OCTAL 11 001 011 001 3 1 11001 2 =31 8

24. Example:1110011 2  OCTAL 1 110 011 001110 011 1 6 3 1110011 2 =163 8

25. BINARY  HEXA HEXA – BASE 16 = 2 4 4 DIGIT BINARY NUMBER Example:11001 2  HEXA 1 1001 0001 1001 1 9 11001 2 =19 16

26. Example:1110011 2  OCTAL 1 110 011 001110 011 1 6 3 1110011 2 =163 8

27. OCTAL  HEXA OCTAL  BINARY  HEXA Example:31 8  HEXA 3 1 011 001 0001 1001 1 9 31 8 =19 16

28. HEXA  OCTAL Example: 1BD  OCTAL 1 B D 0001 1011 1101 0 6 7 5 1BD = 675 8

29. Conversion of 25.125 10 to Binary 2 25 2 12 -1 2 6 - 0 2 3 - 0 1 - 1 25 10 =11001 2

30. 0.125 X 2 = 0.250 0.250 X 2 = 0.5 0.5 X 2 = 1.0 25.125 10 = 11001.001 2

31. Binary to decimal conversion 11001.001 1X2 -3 = 0.125 0X2 -2 = 0 0X2 -1 = 0 1X2 0 = 1 0X2 1 = 0 0X2 2 = 0 1X2 3 = 8 1X2 4 = 16 25.125 10

32. Conversion of 84.250 10 to Octal 8 84 8 10 - 4 1 - 2 84 10 =124 8

33. 0.250 X 8 = 2.000 25.123 10 = 124.2 8

34. Octal to decimal conversion 124.2 2X8 -1 = 0.25 4X8 0 = 1 2X8 1 = 0 1X8 2 = 0 25.250 10