1. ITEC 1011 Introduction to Information Technologies 1. Number Systems Chapt. 2 Location in course textbook

2. ITEC 1011 Introduction to Information Technologies Common Number Systems SystemBaseSymbols Used by humans? Used in computers? Decimal100, 1, … 9YesNo Binary20, 1NoYes Octal80, 1, … 7No Hexa- decimal 160, 1, … 9, A, B, … F No

3. ITEC 1011 Introduction to Information Technologies Quantities/Counting (1 of 3) DecimalBinaryOctal Hexa- decimal 0000 1111 21022 31133 410044 510155 611066 711177 p. 33

4. ITEC 1011 Introduction to Information Technologies Quantities/Counting (2 of 3) DecimalBinaryOctal Hexa- decimal 81000108 91001119 10101012A 11101113B 12110014C 13110115D 14111016E 15111117F

5. ITEC 1011 Introduction to Information Technologies Quantities/Counting (3 of 3) DecimalBinaryOctal Hexa- decimal 16100002010 17100012111 18100102212 19100112313 20101002414 21101012515 22101102616 23101112717 Etc.

6. ITEC 1011 Introduction to Information Technologies Conversion Among Bases The possibilities: Hexadecimal DecimalOctal Binary pp. 40-46

7. ITEC 1011 Introduction to Information Technologies Quick Example 25 10 = 11001 2 = 31 8 = 19 16 Base

8. ITEC 1011 Introduction to Information Technologies 125 10 =>5 x 10 0 = 5 2 x 10 1 = 20 1 x 10 2 = 100 125 Base Weight

9. ITEC 1011 Introduction to Information Technologies Binary to Decimal Hexadecimal DecimalOctal Binary

10. ITEC 1011 Introduction to Information Technologies 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

11. ITEC 1011 Introduction to Information Technologies 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”

12. ITEC 1011 Introduction to Information Technologies Octal to Decimal Hexadecimal DecimalOctal Binary

13. ITEC 1011 Introduction to Information Technologies 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

14. ITEC 1011 Introduction to Information Technologies Example 724 8 => 4 x 8 0 = 4 2 x 8 1 = 16 7 x 8 2 = 448 468 10

15. ITEC 1011 Introduction to Information Technologies Hexadecimal to Decimal Hexadecimal DecimalOctal Binary

16. ITEC 1011 Introduction to Information Technologies 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

17. ITEC 1011 Introduction to Information Technologies 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

18. ITEC 1011 Introduction to Information Technologies Decimal to Binary Hexadecimal DecimalOctal Binary

19. ITEC 1011 Introduction to Information Technologies 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.

20. ITEC 1011 Introduction to Information Technologies Example 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

21. ITEC 1011 Introduction to Information Technologies Octal to Binary Hexadecimal DecimalOctal Binary

22. ITEC 1011 Introduction to Information Technologies Octal to Binary Technique –Convert each octal digit to a 3-bit equivalent binary representation

23. ITEC 1011 Introduction to Information Technologies Example 705 8 = ? 2 7 0 5 111 000 101 705 8 = 111000101 2

24. ITEC 1011 Introduction to Information Technologies Hexadecimal to Binary Hexadecimal DecimalOctal Binary

25. ITEC 1011 Introduction to Information Technologies Hexadecimal to Binary Technique –Convert each hexadecimal digit to a 4-bit equivalent binary representation

26. ITEC 1011 Introduction to Information Technologies Example 10AF 16 = ? 2 1 0 A F 0001 0000 1010 1111 10AF 16 = 0001000010101111 2

27. ITEC 1011 Introduction to Information Technologies Decimal to Octal Hexadecimal DecimalOctal Binary

28. ITEC 1011 Introduction to Information Technologies Decimal to Octal Technique –Divide by 8 –Keep track of the remainder

29. ITEC 1011 Introduction to Information Technologies Example 1234 10 = ? 8 8 1234 154 2 8 19 2 8 2 3 8 0 2 1234 10 = 2322 8

30. ITEC 1011 Introduction to Information Technologies Decimal to Hexadecimal Hexadecimal DecimalOctal Binary

31. ITEC 1011 Introduction to Information Technologies Decimal to Hexadecimal Technique –Divide by 16 –Keep track of the remainder

32. ITEC 1011 Introduction to Information Technologies Example 1234 10 = ? 16 1234 10 = 4D2 16 16 1234 77 2 16 4 13 = D 16 0 4

33. ITEC 1011 Introduction to Information Technologies Binary to Octal Hexadecimal DecimalOctal Binary

34. ITEC 1011 Introduction to Information Technologies Binary to Octal Technique –Group bits in threes, starting on right –Convert to octal digits

35. ITEC 1011 Introduction to Information Technologies Example 1011010111 2 = ? 8 1 011 010 111 1 3 2 7 1011010111 2 = 1327 8

36. ITEC 1011 Introduction to Information Technologies Binary to Hexadecimal Hexadecimal DecimalOctal Binary

37. ITEC 1011 Introduction to Information Technologies Binary to Hexadecimal Technique –Group bits in fours, starting on right –Convert to hexadecimal digits

38. ITEC 1011 Introduction to Information Technologies Example 1010111011 2 = ? 16 10 1011 1011 2 B B 1010111011 2 = 2BB 16

39. ITEC 1011 Introduction to Information Technologies Octal to Hexadecimal Hexadecimal DecimalOctal Binary

40. ITEC 1011 Introduction to Information Technologies Octal to Hexadecimal Technique –Use binary as an intermediary

41. ITEC 1011 Introduction to Information Technologies Example 1076 8 = ? 16 1 0 7 6 001 000 111 110 2 3 E 1076 8 = 23E 16

42. ITEC 1011 Introduction to Information Technologies Hexadecimal to Octal Hexadecimal DecimalOctal Binary

43. ITEC 1011 Introduction to Information Technologies Hexadecimal to Octal Technique –Use binary as an intermediary

44. ITEC 1011 Introduction to Information Technologies Example 1F0C 16 = ? 8 1 F 0 C 0001 1111 0000 1100 1 7 4 1 4 1F0C 16 = 17414 8

45. ITEC 1011 Introduction to Information Technologies Exercise – Convert... Don’t use a calculator! DecimalBinaryOctal Hexa- decimal 33 1110101 703 1AF Skip answer Answer

46. ITEC 1011 Introduction to Information Technologies Binary Addition (1 of 2) Two 1-bit values pp. 36-38 ABA + B 000 011 101 1110 “two”

47. ITEC 1011 Introduction to Information Technologies Binary Addition (2 of 2) Two n-bit values –Add individual bits –Propagate carries –E.g., 10101 21 + 11001 + 25 101110 46 11

48. ITEC 1011 Introduction to Information Technologies Multiplication (1 of 3) Decimal (just for fun) pp. 39 35 x 105 175 000 35 3675

49. ITEC 1011 Introduction to Information Technologies Multiplication (2 of 3) Binary, two 1-bit values AB A  B 000 010 100 111

50. ITEC 1011 Introduction to Information Technologies Multiplication (3 of 3) Binary, two n-bit values –As with decimal values –E.g., 1110 x 1011 1110 1110 0000 1110 10011010

51. ITEC 1011 Introduction to Information Technologies Fractions Decimal to decimal (just for fun) pp. 46-50 3.14 =>4 x 10 -2 = 0.04 1 x 10 -1 = 0.1 3 x 10 0 = 3 3.14

52. ITEC 1011 Introduction to Information Technologies Fractions Binary to decimal pp. 46-50 10.1011 => 1 x 2 -4 = 0.0625 1 x 2 -3 = 0.125 0 x 2 -2 = 0.0 1 x 2 -1 = 0.5 0 x 2 0 = 0.0 1 x 2 1 = 2.0 2.6875

53. ITEC 1011 Introduction to Information Technologies Fractions Decimal to binary p. 50 3.14579.14579 x 2 0.29158 x 2 0.58316 x 2 1.16632 x 2 0.33264 x 2 0.66528 x 2 1.33056 etc. 11.001001...

54. ITEC 1011 Introduction to Information Technologies Exercise – Convert... Don’t use a calculator! DecimalBinaryOctal Hexa- decimal 29.8 101.1101 3.07 C.82 Skip answer Answer

55. ITEC 1011 Introduction to Information Technologies Exercise – Convert … DecimalBinaryOctal Hexa- decimal 29.811101.110011…35.63…1D.CC… 5.8125101.11015.645.D 3.10937511.0001113.073.1C 12.50781251100.1000001014.404C.82 Answer

56. ITEC 1011 Introduction to Information Technologies Thank you Next topic