1. MicroProcessors Dr. Tamer Samy Gaafar Dept. of Computer & Systems Engineering Faculty of Engineering Zagazig University

2. Course Web Page http://www.tsgaafar.faculty.zu.edu.eg Email: tsgaafar@yahoo.com

4.  Grading: Course workGrade distribution Assignments + Sections 12pt 30 Midterm Exam 18pt Final Exam 70pt Total Points100

6. SystemBaseSymbols Decimal100, 1, … 9 Binary20, 1 Octal80, 1, … 7 Hexa- decimal 160, 1, … 9, A, B, … F BCD (Binary Coded Decimal) 10 0 --  9 in binary representation 0000, 0001,…… 1001

7. Hexadecimal DecimalOctal Binary

8. Hexadecimal DecimalOctal Binary

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

10. Hexadecimal DecimalOctal Binary

11.  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.  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. Hexadecimal DecimalOctal Binary

14. 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. 724 8 => 4 x 8 0 = 4 2 x 8 1 = 16 7 x 8 2 = 448 468 10

16. Hexadecimal to Decimal Hexadecimal DecimalOctal Binary

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 = 2560 2748 10

19. Decimal to Binary Hexadecimal DecimalOctal Binary

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 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

22. Octal to Binary Hexadecimal DecimalOctal Binary

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

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

25. Hexadecimal to Binary Hexadecimal DecimalOctal Binary

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

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

28. Decimal to Octal Hexadecimal DecimalOctal Binary

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

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

31. Decimal to Hexadecimal Hexadecimal DecimalOctal Binary

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

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 DecimalOctal Binary

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

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

37. Binary to Hexadecimal Hexadecimal DecimalOctal Binary

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

39. Example 1010111011 2 = ? 16 10 1011 1011 2 B B 1010111011 2 = 2BB 16

40. Octal to Hexadecimal Hexadecimal DecimalOctal Binary

41. Octal to Hexadecimal Technique – Use binary as an intermediary

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

43. Hexadecimal to Octal Hexadecimal DecimalOctal Binary

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

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

46. Common Powers (1 of 2) Base 10 PowerPrefaceSymbol 10 -12 picop 10 -9 nanon 10 -6 micro  10 -3 millim 10 3 kilok 10 6 megaM 10 9 gigaG 10 12 teraT Value.000000000001.000000001.000001.001 1000 1000000 1000000000 1000000000000

47. Common Powers (2 of 2) Base 2 PowerPrefaceSymbol 2 10 kilok 2 20 megaM 2 30 GigaG Value 1024 1048576 1073741824 What is the value of “k”, “M”, and “G”? In computing, particularly w.r.t. memory, the base-2 interpretation generally applies

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

49. Review – multiplying powers For common bases, add powers 2 6  2 10 = 2 16 = 65,536 or… 2 6  2 10 = 64  2 10 = 64k a b  a c = a b+c

50. Binary Addition (1 of 2) Two 1-bit values ABA + B 000 011 101 1110 “two”

51. Binary Addition (2 of 2) Two n-bit values – Add individual bits – Propagate carries – E.g., 10101 21 + 11001 + 25 101110 46 11

52. Multiplication (1 of 3) Decimal 35 x 105 175 000 35 3675

53. Multiplication (2 of 3) Binary, two 1-bit values AB A  B 000 010 100 111

54. Multiplication (3 of 3) Binary, two n-bit values – As with decimal values – E.g., 1110 x 1011 1110 1110 0000 1110 10011010

55. Fractions Decimal to decimal 3.14 =>4 x 10 -2 = 0.04 1 x 10 -1 = 0.1 3 x 10 0 = 3 3.14

56. Fractions Binary to decimal 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

57. Fractions Decimal to binary 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...

58. Exercise – Convert... Don’t use a calculator! DecimalBinaryOctal Hexa- decimal 29.8 101.1101 3.07 C.82

59. 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

60. DecimalBinaryOctal Hexa- decimal 0000 1111 21022 31133 410044 510155 611066 711177 Quantities/Counting (1 of 3)

61. DecimalBinaryOctal Hexa- decimal 81000108 91001119 10101012A 11101113B 12110014C 13110115D 14111016E 15111117F Quantities/Counting (2 of 3)

62. DecimalBinaryOctal Hexa- decimal 16100002010 17100012111 18100102212 19100112313 20101002414 21101012515 22101102616 23101112717 Quantities/Counting (3 of 3)

63. The BCD code With this BCD code, each individual digit of the decimal number system is represented by a corresponding binary number So the digits from 0 to 9 can be represented in 4 – bit each (why?)

64. BCDDecimal Number 00000 00011 00102 00113 01004 01015 01106 01117 10008 10019

65. The BCD code 4 digits in binary notation are therefore required for each digit in the decimal system Example: Decimal number 7133. 54 is thus represented 0111 0001 0011 0011. 0101 0100 (BCD code)

66. The BCD code Example: Number 0101 0010 0111 in BCD code represents 527 decimal number BCD coded numbers are often used for seven segment displays and coding switches

67. Thank you