1. Chapter 1 Number Systems & Conversions
Location in course textbook
Chapter. 1
CNET 315 Microprocessor & Assembly Language

2. CNET 315 Microprocessor & Assembly Language
Common Number Systems
Number System
Base
Symbols
Used by humans?
Used in computers?
Decimal 10
0, 1, … 9
Yes No
Binary 2
0, 1
Octal 8
0, 1, … 7
Hexa- decimal 16
0, 1, … 9,
A, B, … F
CNET 315 Microprocessor & Assembly Language

3. Quantities/Counting (1 of 3)
Decimal
Binary
Octal
Hexa- decimal 1 2 10 3 11 4
100 5
101 6
110 7
111
p. 33
CNET 315 Microprocessor & Assembly Language

4. Quantities/Counting (2 of 3)
Decimal
Binary
Octal
Hexa- decimal 8
1000 10 9
1001 11
1010 12 A
1011 13 B
1100 14 C
1101 15 D
1110 16 E
1111 17 F
CNET 315 Microprocessor & Assembly Language

5. Quantities/Counting (3 of 3)
Decimal
Binary
Octal
Hexa- decimal 16
10000 20 10 17
10001 21 11 18
10010 22 12 19
10011 23 13
10100 24 14
10101 25 15
10110 26
10111 27
Etc.
CNET 315 Microprocessor & Assembly Language

6. Conversion Among Bases
The possibilities:
Decimal
Octal
Binary
Hexadecimal
CNET 315 Microprocessor & Assembly Language

7. CNET 315 Microprocessor & Assembly Language
Quick Example
2510 = = 318 = 1916
Base
CNET 315 Microprocessor & Assembly Language

8. CNET 315 Microprocessor & Assembly Language
Weight
12510 => 5 x 100 = x 101 = x 102 =
Base
CNET 315 Microprocessor & Assembly Language

9. CNET 315 Microprocessor & Assembly Language
Binary to Decimal
Decimal
Octal
Binary
Hexadecimal
CNET 315 Microprocessor & Assembly Language

10. CNET 315 Microprocessor & Assembly Language
Binary to Decimal
Technique
Multiply each bit by 2n, 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
CNET 315 Microprocessor & Assembly Language

11. CNET 315 Microprocessor & Assembly Language
Example
Bit “0”
=> 1 x 20 = x 21 = x 22 = x 23 = x 24 = x 25 = 32
4310
CNET 315 Microprocessor & Assembly Language

12. CNET 315 Microprocessor & Assembly Language
Octal to Decimal
Decimal
Octal
Binary
Hexadecimal
CNET 315 Microprocessor & Assembly Language

13. CNET 315 Microprocessor & Assembly Language
Octal to Decimal
Technique
Multiply each bit by 8n, 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
CNET 315 Microprocessor & Assembly Language

14. CNET 315 Microprocessor & Assembly Language
Example
7248 => 4 x 80 = x 81 = x 82 =
CNET 315 Microprocessor & Assembly Language

15. Hexadecimal to Decimal
Octal
Binary
Hexadecimal
CNET 315 Microprocessor & Assembly Language

16. Hexadecimal to Decimal
Technique
Multiply each bit by 16n, 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
CNET 315 Microprocessor & Assembly Language

17. CNET 315 Microprocessor & Assembly Language
Example
ABC16 => C x 160 = 12 x 1 = B x 161 = 11 x 16 = A x 162 = 10 x 256 = 2560
274810
CNET 315 Microprocessor & Assembly Language

18. CNET 315 Microprocessor & Assembly Language
Decimal to Binary
Decimal
Octal
Binary
Hexadecimal
CNET 315 Microprocessor & Assembly Language

19. CNET 315 Microprocessor & Assembly Language
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.
CNET 315 Microprocessor & Assembly Language

20. CNET 315 Microprocessor & Assembly Language
Example
12510 = ?2
12510 =
CNET 315 Microprocessor & Assembly Language

21. CNET 315 Microprocessor & Assembly Language
Octal to Binary
Decimal
Octal
Binary
Hexadecimal
CNET 315 Microprocessor & Assembly Language

22. CNET 315 Microprocessor & Assembly Language
Octal to Binary
Technique
Convert each octal digit to a 3-bit equivalent binary representation
CNET 315 Microprocessor & Assembly Language

23. CNET 315 Microprocessor & Assembly Language
Example
7058 = ?2
7058 =
CNET 315 Microprocessor & Assembly Language

24. CNET 315 Microprocessor & Assembly Language
Hexadecimal to Binary
Decimal
Octal
Binary
Hexadecimal
CNET 315 Microprocessor & Assembly Language

25. CNET 315 Microprocessor & Assembly Language
Hexadecimal to Binary
Technique
Convert each hexadecimal digit to a 4-bit equivalent binary representation
CNET 315 Microprocessor & Assembly Language

26. CNET 315 Microprocessor & Assembly Language
Example
10AF16 = ?2
A F
10AF16 =
CNET 315 Microprocessor & Assembly Language

27. CNET 315 Microprocessor & Assembly Language
Decimal to Octal
Decimal
Octal
Binary
Hexadecimal
CNET 315 Microprocessor & Assembly Language

28. CNET 315 Microprocessor & Assembly Language
Decimal to Octal
Technique
Divide by 8
Keep track of the remainder
CNET 315 Microprocessor & Assembly Language

29. CNET 315 Microprocessor & Assembly Language
Example
= ?8 8
19 2 8
2 3 8
0 2
= 23228
CNET 315 Microprocessor & Assembly Language

30. Decimal to Hexadecimal
Octal
Binary
Hexadecimal
CNET 315 Microprocessor & Assembly Language

31. Decimal to Hexadecimal
Technique
Divide by 16
Keep track of the remainder
CNET 315 Microprocessor & Assembly Language

32. CNET 315 Microprocessor & Assembly Language
Example
= ?16
77 2 16
= D
0 4
= 4D216
CNET 315 Microprocessor & Assembly Language

33. CNET 315 Microprocessor & Assembly Language
Binary to Octal
Decimal
Octal
Binary
Hexadecimal
CNET 315 Microprocessor & Assembly Language

34. CNET 315 Microprocessor & Assembly Language
Binary to Octal
Technique
Group bits in threes, starting on right
Convert to octal digits
CNET 315 Microprocessor & Assembly Language

35. CNET 315 Microprocessor & Assembly Language
Example
= ?8
= 13278
CNET 315 Microprocessor & Assembly Language

36. CNET 315 Microprocessor & Assembly Language
Binary to Hexadecimal
Decimal
Octal
Binary
Hexadecimal
CNET 315 Microprocessor & Assembly Language

37. CNET 315 Microprocessor & Assembly Language
Binary to Hexadecimal
Technique
Group bits in fours, starting on right
Convert to hexadecimal digits
CNET 315 Microprocessor & Assembly Language

38. CNET 315 Microprocessor & Assembly Language
Example
= ?16
B B
= 2BB16
CNET 315 Microprocessor & Assembly Language

39. CNET 315 Microprocessor & Assembly Language
Octal to Hexadecimal
Decimal
Octal
Binary
Hexadecimal
CNET 315 Microprocessor & Assembly Language

40. CNET 315 Microprocessor & Assembly Language
Octal to Hexadecimal
Technique
Use binary as an intermediary
CNET 315 Microprocessor & Assembly Language

41. CNET 315 Microprocessor & Assembly Language
Example
10768 = ?16 E
10768 = 23E16
CNET 315 Microprocessor & Assembly Language

42. CNET 315 Microprocessor & Assembly Language
Hexadecimal to Octal
Decimal
Octal
Binary
Hexadecimal
CNET 315 Microprocessor & Assembly Language

43. CNET 315 Microprocessor & Assembly Language
Hexadecimal to Octal
Technique
Use binary as an intermediary
CNET 315 Microprocessor & Assembly Language

44. CNET 315 Microprocessor & Assembly Language
Example
1F0C16 = ?8
1 F C
1F0C16 =
CNET 315 Microprocessor & Assembly Language

45. CNET 315 Microprocessor & Assembly Language
Exercise – Convert ...
Decimal
Binary
Octal
Hexa- decimal 33
703
1AF
Don’t use a calculator!
CNET 315 Microprocessor & Assembly Language

46. CNET 315 Microprocessor & Assembly Language
Exercise – Convert …
Answer
Decimal
Binary
Octal
Hexa- decimal 33
100001 41 21
117
165 75
451
703
1C3
431
657
1AF
CNET 315 Microprocessor & Assembly Language

47. CNET 315 Microprocessor & Assembly Language
Binary Addition (1 of 2)
Two 1-bit values A B
A + B 1 10
“two”
CNET 315 Microprocessor & Assembly Language

48. CNET 315 Microprocessor & Assembly Language
Binary Addition (2 of 2)
Two n-bit values
Add individual bits
Propagate carries
E.g., 1 1
CNET 315 Microprocessor & Assembly Language

49. Binary Subtraction
Have previously looked at the subtraction operation. A quick review.
Just like subtraction in any other base
Minuend
Subtrahand
Difference
And when a borrow is needed. Note that the borrow gives us 2 in the current bit position. .

50. CNET 315 Microprocessor & Assembly Language
Thank you
CNET 315 Microprocessor & Assembly Language