1. Conversion of Number System www.ustudy.in

2. Conversion Among Bases The possibilities: Hexadecimal DecimalOctal Binary www.ustudy.in

3. Binary to Decimal Hexadecimal DecimalOctal Binary www.ustudy.in

4. Binary to Decimal Technique – Multiply each bit by 2 n, where n is the “weight” of the bit – The weight is the position of the bit, starting from 0 on the right – Add the results www.ustudy.in

5. Example 1 101011 2 => 1 x 2 0 = 1 1 x 2 1 = 2 0 x 2 2 = 0 1 x 2 3 = 8 0 x 2 4 = 0 1 x 2 5 = 32 43 10 Bit “0” www.ustudy.in

6. Example2 www.ustudy.in

7. Octal to Decimal Hexadecimal DecimalOctal Binary www.ustudy.in

8. Octal to Decimal Technique – Multiply each bit by 8 n, where n is the “weight” of the bit – The weight is the position of the bit, starting from 0 on the right – Add the results www.ustudy.in

9. Example 1 724 8 => 4 x 8 0 = 4 2 x 8 1 = 16 7 x 8 2 = 448 468 10 www.ustudy.in

10. Example 2 www.ustudy.in

11. Hexadecimal to Decimal Hexadecimal DecimalOctal Binary www.ustudy.in

12. Hexadecimal to Decimal Technique – Multiply each bit by 16 n, where n is the “weight” of the bit – The weight is the position of the bit, starting from 0 on the right – Add the results www.ustudy.in

13. Example 1 ABC 16 =>C x 16 0 = 12 x 1 = 12 B x 16 1 = 11 x 16 = 176 A x 16 2 = 10 x 256 = 2560 2748 10 www.ustudy.in

14. Example 2 www.ustudy.in

15. Decimal to Binary Hexadecimal DecimalOctal Binary www.ustudy.in

16. Decimal to Binary Technique – Divide by two, keep track of the remainder – First remainder is bit 0 (LSB, least-significant bit) – Second remainder is bit 1 – Etc. www.ustudy.in

17. Example 1 125 10 = ? 2 2 125 62 1 2 31 0 2 15 1 2 7 1 2 3 1 2 1 1 2 0 1 125 10 = 1111101 2 www.ustudy.in

18. Example 2 www.ustudy.in

19. Octal to Binary Hexadecimal DecimalOctal Binary www.ustudy.in

20. Octal to Binary Technique – Convert each octal digit to a 3-bit equivalent binary representation www.ustudy.in

21. Example 1 705 8 = ? 2 7 0 5 111 000 101 705 8 = 111000101 2 www.ustudy.in

22. Example 2 www.ustudy.in

23. Hexadecimal to Binary Hexadecimal DecimalOctal Binary www.ustudy.in

24. Hexadecimal to Binary Technique – Convert each hexadecimal digit to a 4-bit equivalent binary representation www.ustudy.in

25. Example 1 10AF 16 = ? 2 1 0 A F 0001 0000 1010 1111 10AF 16 = 0001000010101111 2 www.ustudy.in

26. Example 2 www.ustudy.in

27. Decimal to Octal Hexadecimal DecimalOctal Binary www.ustudy.in

28. Decimal to Octal Technique – Divide by 8 – Keep track of the remainder www.ustudy.in

29. Example 1 1234 10 = ? 8 8 1234 154 2 8 19 2 8 2 3 8 0 2 1234 10 = 2322 8 www.ustudy.in

30. Example 2 www.ustudy.in

31. Decimal to Hexadecimal Hexadecimal DecimalOctal Binary www.ustudy.in

32. Decimal to Hexadecimal Technique – Divide by 16 – Keep track of the remainder www.ustudy.in

33. Example 1 1234 10 = ? 16 1234 10 = 4D2 16 16 1234 77 2 16 4 13 = D 16 0 4 www.ustudy.in

34. Example 2 www.ustudy.in

35. Binary to Octal Hexadecimal DecimalOctal Binary www.ustudy.in

36. Binary to Octal Technique – Group bits in threes, starting on right – Convert to octal digits www.ustudy.in

37. Example 1 1011010111 2 = ? 8 1 011 010 111 1 3 2 7 1011010111 2 = 1327 8 www.ustudy.in

38. Example 2 www.ustudy.in

39. Binary to Hexadecimal Hexadecimal DecimalOctal Binary www.ustudy.in

40. Binary to Hexadecimal Technique – Group bits in fours, starting on right – Convert to hexadecimal digits www.ustudy.in

41. Example 1 1010111011 2 = ? 16 10 1011 1011 2 B B 1010111011 2 = 2BB 16 www.ustudy.in

42. Example 2 www.ustudy.in

43. Octal to Hexadecimal Hexadecimal DecimalOctal Binary www.ustudy.in

44. Octal to Hexadecimal Technique – Use binary as an intermediary www.ustudy.in

45. Example 1 1076 8 = ? 16 1 0 7 6 001 000 111 110 2 3 E 1076 8 = 23E 16 www.ustudy.in

46. Example 2 Octal 8 -> hexadecimal 16 27 8 -> hexadecimal 16 First convert the octal number to binary. 2 7 421 010 111 27 8 -> 010 111 2 www.ustudy.in

47. Example2 Cont., Convert to hexadecimal. 0001 0111 8421 0+0+0+1 = 1 0+4+2+1 = 7 27 8 -> 17 16 www.ustudy.in

48. Hexadecimal to Octal Hexadecimal DecimalOctal Binary www.ustudy.in

49. Hexadecimal to Octal Technique – Use binary as an intermediary www.ustudy.in

50. Example 1 1F0C 16 = ? 8 1 F 0 C 0001 1111 0000 1100 1 7 4 1 4 1F0C 16 = 17414 8 www.ustudy.in

51. Example 2 We do not convert directly from hexadecimal to octal but instead first convert to binary and then to octal. 45 16 -> octal 8 First convert the hexadecimal number to binary. www.ustudy.in

52. Example2 Cont., Hexadecimal to Binary 4 5 8421 0100 0101 45 16 -> 01000101 2 www.ustudy.in

53. Example2 Cont., Then Convert to Octal 001 000 101 421 421 421 0+0+1 = 1 0+0+0 = 0 4+0+1 = 5 45 16 -> 105 8 www.ustudy.in

54. The End …..Thank you…. www.ustudy.in