1. 1. Number Systems

2. Common Number Systems No No 0, 1, … 9, A, B, … F 16 Hexa- decimal No No 0, 1, … 7 8 Octal Yes No 0, 1 2 Binary No Yes 0, 1, … 9 10 Decimal Used in computers? Used by humans? Symbols Base System

3. Quantities/Counting (1 of 3) p. 33 7 7 111 7 6 6 110 6 5 5 101 5 4 4 100 4 3 3 11 3 2 2 10 2 1 1 1 1 0 0 0 0 Hexa- decimal Octal Binary Decimal

4. Quantities/Counting (2 of 3) F 17 1111 15 E 16 1110 14 D 15 1101 13 C 14 1100 12 B 13 1011 11 A 12 1010 10 9 11 1001 9 8 10 1000 8 Hexa- decimal Octal Binary Decimal

5. Quantities/Counting (3 of 3) Etc. 17 27 10111 23 16 26 10110 22 15 25 10101 21 14 24 10100 20 13 23 10011 19 12 22 10010 18 11 21 10001 17 10 20 10000 16 Hexa- decimal Octal Binary Decimal

7. Quick Example 25 10 = 11001 2 = 31 8 = 19 16 Base

8. Decimal to Decimal (just for fun) Hexadecimal Decimal Octal Binary Next slide…

9. 125 10 => 5 x 10 0 = 5 2 x 10 1 = 20 1 x 10 2 = 100 125 Base Weight

10. Binary to Decimal Hexadecimal Decimal Octal Binary

12. Example 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”

13. Octal to Decimal Hexadecimal Decimal Octal Binary

15. Example 724 8 => 4 x 8 0 = 4 2 x 8 1 = 16 7 x 8 2 = 448 468 10

16. Hexadecimal to Decimal Hexadecimal Decimal Octal Binary

18. Example 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

19. Decimal to Binary Hexadecimal Decimal Octal Binary

21. Example 125 10 = ? 2 125 10 = 1111101 2 2 125 62 1 2 31 0 2 15 1 2 7 1 2 3 1 2 1 1 2 0 1

22. Octal to Binary Hexadecimal Decimal Octal Binary

24. Example 705 8 = ? 2 705 8 = 111000101 2 7 0 5 111 000 101

25. Hexadecimal to Binary Hexadecimal Decimal Octal Binary

27. Example 10AF 16 = ? 2 10AF 16 = 0001000010101111 2 1 0 A F 0001 0000 1010 1111

28. Decimal to Octal Hexadecimal Decimal Octal Binary

30. Example 1234 10 = ? 8 8 1234 154 2 1234 10 = 2322 8 8 19 2 8 2 3 8 0 2

31. Decimal to Hexadecimal Hexadecimal Decimal Octal Binary

33. Example 1234 10 = ? 16 1234 10 = 4D2 16 16 1234 77 2 16 4 13 = D 16 0 4

34. Binary to Octal Hexadecimal Decimal Octal Binary

36. Example 1011010111 2 = ? 8 1011010111 2 = 1327 8 1 011 010 111 1 3 2 7

37. Binary to Hexadecimal Hexadecimal Decimal Octal Binary

40. Octal to Hexadecimal Hexadecimal Decimal Octal Binary

42. Example 1076 8 = ? 16 1076 8 = 23E 16 1 0 7 6 001 000 111 110 2 3 E

43. Hexadecimal to Octal Hexadecimal Decimal Octal Binary

45. Example 1F0C 16 = ? 8 1F0C 16 = 17414 8 1 F 0 C 0001 1111 0000 1100 1 7 4 1 4

46. Exercise – Convert ... Skip answer Answer Don’t use a calculator! 1AF 703 1110101 33 Hexa- decimal Octal Binary Decimal

47. Exercise – Convert … Answer 1AF 657 110101111 431 1C3 703 111000011 451 75 165 1110101 117 21 41 100001 33 Hexa- decimal Octal Binary Decimal

50. Example In the lab… 1. Double click on My Computer 2. Right click on C: 3. Click on Properties / 2 30 =

61. Exercise – Convert ... Skip answer Answer Don’t use a calculator! C.82 3.07 101.1101 29.8 Hexa- decimal Octal Binary Decimal

62. Exercise – Convert … Answer C.82 14.404 1100.10000010 12.5078125 3.1C 3.07 11.000111 3.109375 5.D 5.64 101.1101 5.8125 1D.CC… 35.63… 11101.110011… 29.8 Hexa- decimal Octal Binary Decimal

63. Thank you