1. ECE 362 Microprocessor Systems and Interfacing ©5-1 Lecture 1 Hexadecimal Computation Outline n Decimal n Binary n Octal n Hexadecimal

2. How is the base-10 or decimal number represented? ECE 362 Microprocessor Systems and Interfacing ©1-2 Base-10: each digit can be 0 to 9 weights

3. How is the base-2 or binary number represented? ECE 362 Microprocessor Systems and Interfacing ©1-3 Base-2: each digit can be either 0 or 1 weights

4. How to convert Decimal to Binary? n Above decimal point u Keep dividing by 2 u Remainders are binary sequence of the given decimal n Below decimal point u Keep multiplying by 2 u Binary sequence of values above decimal point ECE 362 Microprocessor Systems and Interfacing ©1-4

5. How is the base-16 or hexadecimal number represented? ECE 362 Microprocessor Systems and Interfacing ©1-5 Base-16: each digit can be 0 to F

6. How to convert Hexadecimal to Decimal? ECE 362 Microprocessor Systems and Interfacing ©1-6 weights

7. ECE 362 Microprocessor Systems and Interfacing © How to represent common decimal numbers in hexadecimal? 1-7 Decimal Hex 256 511 512 1023 1024 (1K) 2047 2048 (2K) 4095 4096 (4K) 8191 8192 (8K) 16383 16384 (16K) 32767 32768 (32K) 65535 65536 (64K)

8. ECE 362 Microprocessor Systems and Interfacing © How to represent common decimal numbers in hexadecimal? 1-8 Decimal Hex 256 511 512 1023 1024 (1K) 2047 2048 (2K) 4095 4096 (4K) 8191 8192 (8K) 16383 16384 (16K) 32767 32768 (32K) 65535 65536 (64K)

9. How to perform Decimal Addition? 111 3758 + 4657 8415 What is going on? 1 1 1 (carry) 3 7 5 8 + 4 6 5 7 14 11 15 - 10 10 10 (subtract the base) 8 4 1 5

10. How to perform Binary Addition? Rules: u 0 + 0 = 0 u 0 + 1 = 1 u 1 + 0 = 1 u 1 + 1 = 2 = 10 2 = 0 with 1 to carry u 1 + 1 + 1 = 3 = 11 2 = 1 with 1 to carry

11. How to perform Binary Addition? 1 1 1 1 1 1 0 1 1 1 + 0 1 1 1 0 0 2 3 2 2 - 2 2 2 2 1 0 1 0 0 1 1 Verification 55 10 + 28 10 83 10 64 32 16 8 4 2 1 1 0 1 0 0 1 1 = 64 + 16 + 2 +1 = 83 10

12. ex) Verification 1 0 0 1 1 1 + 0 1 0 1 1 0 + ___ ___________ 128 64 32 16 8 4 2 1 = How to perform Binary Addition?

13. How to perform Octal Addition? 1 1 6 4 3 7 8 + 2 5 1 0 8 9 9 - 8 8 (subtract Base (8)) 1 1 1 4 7 8

14. How to perform Octal Addition? Ex) 3 5 3 6 8 + 2 4 5 7 8 - (subtract Base (8))

15. How to perform Hexadecimal Addition? 1 1 7 C 3 9 16 + 3 7 F 2 16 20 18 11 - 16 16 (subtract Base (16)) B 4 2 B 16

16. 8 A D 4 16 + 5 D 6 16 - (subtract Base (16)) 16 How to perform Hexadecimal Addition?

17. How to perform Decimal Subtraction? 7 13 10 8 4 1 15 - 4 6 5 7 3 7 5 8 How is it done? (add the base 10 when borrowing) 10 10 7 3 0 10 8 4 1 5 13 10 15 - 4 6 5 7 3 7 5 8

18. How to perform Binary Subtraction? 1 2 1 0 2 0 2 2 1 0 1 0 0 1 1 - 0 1 1 1 0 0 1 1 0 1 1 1 Verification 83 10 - 28 10 55 10 64 32 16 8 4 2 1 1 1 0 1 1 1 = 32 + 16 + + 4 + 2 +1 = 55 10

19. How to perform Binary Subtraction? ex Verification 1 0 0 1 1 1 - 0 1 0 1 1 0 - ___ ___________ 128 64 32 16 8 4 2 1 =

20. How to perform Octal Subtraction? 8 0 0 8 1 1 1 4 7 8 8 9 - 6 4 3 7 8 2 51 0 8

21. ex 3 5 3 6 8 - 2 4 5 7 8 How to perform Octal Subtraction?

22. How to perform Hexadecimal Subtraction? B 16 7 C 3 9 16 19 - 3 7 F 2 16 4 4 4 7 16

23. 8 A D 4 16 - 5 D 6 16 16 How to perform Hexadecimal Subtraction?

24. Notations to distinguish n In order to avoid misunderstanding, different prefixes and suffixes are directly added to the numbers. The prefix $ or 0x as well as the suffix h marks the numbers in hexadecimal system. n For example, hexadecimal number 10AF may look as follows $10AF, 0x10AF or 10AFh. n Similarly, binary numbers usually get the suffix % or 0b, ECE 362 Microprocessor Systems and Interfacing ©1-24