ITEC 1011 Introduction to Information Technologies

Transcription

1 Number Systems

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

3 Quantities/Counting (1 of 3) Decimal Binary Octal Hexadecimal p. 33

4 Quantities/Counting (2 of 3) Decimal Binary Octal Hexadecimal A B C D E F

5 Quantities/Counting (3 of 3) Decimal Binary Octal Hexadecimal Etc.

6 Conversion Among Bases The possibilities: Decimal Octal Binary Hexadecimal

7 Quick Example = = 31 8 = Base

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

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

10 Binary to Decimal Decimal Octal Binary Hexadecimal

11 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

12 Example Bit => 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 =

13 Octal to Decimal Decimal Octal Binary Hexadecimal

14 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

15 Example => 4 x 8 0 = 4 2 x 8 1 = 16 7 x 8 2 =

16 Hexadecimal to Decimal Decimal Octal Binary Hexadecimal

17 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

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 =

19 Decimal to Binary Decimal Octal Binary Hexadecimal

20 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.

21 Example =? =

22 Octal to Binary Decimal Octal Binary Hexadecimal

23 Octal to Binary Technique Convert each octal digit to a 3-bit equivalent binary representation

24 Example =? =

25 Hexadecimal to Binary Decimal Octal Binary Hexadecimal

26 Hexadecimal to Binary Technique Convert each hexadecimal digit to a 4-bit equivalent binary representation

27 Example 10AF 16 =? A F AF 16 =

28 Decimal to Octal Decimal Octal Binary Hexadecimal

29 Decimal to Octal Technique Divide by 8 Keep track of the remainder

30 Example =? =

31 Decimal to Hexadecimal Decimal Octal Binary Hexadecimal

32 Decimal to Hexadecimal Technique Divide by 16 Keep track of the remainder

33 Example =? = D = 4D2 16

34 Binary to Octal Decimal Octal Binary Hexadecimal

35 Binary to Octal Technique Group bits in threes, starting on right Convert to octal digits

36 Example =? =

37 Binary to Hexadecimal Decimal Octal Binary Hexadecimal

38 Binary to Hexadecimal Technique Group bits in fours, starting on right Convert to hexadecimal digits

39 Example =? B B = 2BB 16

40 Octal to Hexadecimal Decimal Octal Binary Hexadecimal

41 Octal to Hexadecimal Technique Use binary as an intermediary

42 Example =? E = 23E 16

43 Hexadecimal to Octal Decimal Octal Binary Hexadecimal

44 Hexadecimal to Octal Technique Use binary as an intermediary

45 Example 1F0C 16 =? 8 1 F 0 C F0C 16 =

46 Exercise Convert... Decimal Binary Octal Hexadecimal 1AF Don t use a calculator! Skip answer Answer

47 Exercise Convert Answer Decimal Binary Octal Hexadecimal C AF

48 Fractions Decimal to decimal (just for fun) 3.14 => 4 x 10-2 = x 10-1 = x 10 0 = pp

49 Fractions Binary to decimal => 1 x 2-4 = x 2-3 = x 2-2 = x 2-1 = x 2 0 = x 2 1 = pp

50 Fractions Decimal to binary x x x x x x etc. p. 50

51 Exercise Convert... Decimal Binary Octal Hexadecimal C.82 Don t use a calculator! Skip answer Answer

52 Exercise Convert Answer Decimal Binary Octal Hexadecimal D.CC D C C.82

53 Common Powers (1 of 2) Base 10 Power Preface Symbol pico p 10-9 nano n 10-6 micro 10-3 milli m 10 3 kilo k 10 6 mega M 10 9 giga G tera T Value

54 Common Powers (2 of 2) Base 2 Power Preface Symbol 2 10 kilo k 2 20 mega M 2 30 Giga G Value What is the value of k, M, and G? In computing, particularly w.r.t. memory, the base-2 interpretation generally applies

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

56 Exercise Free Space Determine the free space on all drives on a machine in the lab Drive Bytes Free space GB A: C: D: E: etc.

57 Review multiplying powers For common bases, add powers a b a c = a b+c = 2 16 = 65,536 or = = 64k

58 Thank you