Number Systems. TA: Mamun. References: Lecture notes of Introduction to Information Technologies (ITEC 1011) by Dr Scott MacKenzie

Transcription

1 Number Systems TA: Mamun References: Lecture notes of Introduction to Information Technologies (ITEC 1011) by Dr Scott MacKenzie

2 Common Number Systems System Base Symbols Decimal 10 0, 1, 9 Binary 2 0, 1 Octal 8 0, 1, , 1, 9, A, B, F

3 Counting Decimal Binary Octal Decimal Binary Octal A B C D E F

4 Counting Decimal Binary Octal =? = = 30 8 = 18 16

5 Decimal to Decimal Decimal Octal Binary

6 =>? 10 - Multiply each bit by 10 n, where n is the weight of the bit - The weight is the position of the bit, starting from 0 on the right Weight => 5 x 10 0 = 5 2 x 10 1 = 20 1 x 10 2 = Add the results Base

7 Binary to Decimal Decimal Octal Binary

8 Binary to Decimal Technique 1. Multiply each bit by 2 n, where n is the weight of the bit 2. The weight is the position of the bit, starting from 0 on the right 3. Add the results

9 =>? => 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 =

10 Octal to Decimal Decimal Octal Binary

11 Octal to Decimal Technique 1. Multiply each bit by 8 n, where n is the weight of the bit 2. The weight is the position of the bit, starting from 0 on the right 3. Add the results

12 724 8 =>? => 4 x 8 0 = 4 2 x 8 1 = 16 7 x 8 2 =

13 to Decimal Decimal Octal Binary

14 to Decimal Technique 1. Multiply each bit by 16 n, where n is the weight of the bit 2. The weight is the position of the bit, starting from 0 on the right 3. Add the results

15 ABC 16 =>? 10 Decimal Binary Octal A B C D E F 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 =

16 Decimal to Binary Decimal Octal Binary

17 Decimal to Binary Technique 1. Divide by 2, keep track of the remainder 2. First remainder is LSB, least-significant bit 3. Last remainder is MSB, most-significant bit

18 =? =

19 Decimal to Octal Decimal Octal Binary

20 Decimal to Octal Technique 1. Divide by 8 2. Keep track of the remainder

21 =? =

22 Decimal to Decimal Octal Binary

23 Decimal to Technique 1. Divide by Keep track of the remainder

24 =? = D = 4D2 16

25 Any base to any base Base-x Base-y

26 Any base to any base Technique 1. Use Decimal as an intermediary Base-x Base-y Decimal

27 432 4 =? =>? 10 =>? => 2 x = 2 3 x = 12 4 x 4 2 = = = 141 7

28 Conversion Among Bases Division algorithm Base-y Decimal Octal Base-x Binary

29 Octal to Binary Decimal Octal Binary

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

31 705 8 =? 2 Decimal Binary Octal =

32 to Binary Decimal Octal Binary

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

34 10AF 16 =? 2 Decimal Binary Octal A B C D E F 1 0 A F AF 16 =

35 Binary to Octal Technique 1. Group bits in threes, starting on right 2. Convert to octal digits

36 =? 8 Decimal Binary Octal =

37 Binary to Decimal Octal Binary

38 Binary to Technique 1. Group bits in fours, starting on right 2. Convert to hexadecimal digits

39 =? 16 Decimal Binary Octal A B C D E F B B = 2BB 16

40 Octal to Decimal Octal Binary

41 Octal to Technique Use binary as an intermediary

42 =? Decimal Binary Octal A B C D E F E = 23E 16

43 to Octal Decimal Octal Binary

44 to Octal Technique Use binary as an intermediary

45 1F0C 16 =? 8 Decimal Binary Octal A B C D E F 1 F 0 C F0C 16 =

46 Conversion Among Bases Short-cut Octal Binary

47 Questions? Next tutorial ASCII UTF-8 Floating-point arithmetic