ECE 362 Microprocessor Systems and Interfacing © 5-1

Lecture 1 Hexadecimal Computation

Outline Decimal Binary Octal Hexadecimal

How is the base-10 or decimal number represented?

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Base-10: each digit can be 0 to 9

weights

How is the base-2 or binary number represented?

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Base-2: each digit can be either 0 or 1

weights

How to convert Decimal to Binary?

Above decimal point Keep dividing by 2 Remainders are binary sequence of the given

decimal Below decimal point

Keep multiplying by 2 Binary sequence of values above decimal point

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How is the base-16 or hexadecimal number represented?

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Base-16: each digit can be 0 to F

How to convert Hexadecimal to Decimal?

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weights

ECE 362 Microprocessor Systems and Interfacing ©

How to represent common decimal numbers in hexadecimal?

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Decimal Hex25651151210231024 (1K)20472048 (2K)40954096 (4K)81918192 (8K)1638316384 (16K)3276732768 (32K)6553565536 (64K)

ECE 362 Microprocessor Systems and Interfacing ©

How to represent common decimal numbers in hexadecimal?

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Decimal Hex25651151210231024 (1K)20472048 (2K)40954096 (4K)81918192 (8K)1638316384 (16K)3276732768 (32K)6553565536 (64K)

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

How to perform Binary Addition?

Rules: 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 2 = 102 = 0 with 1 to carry

1 + 1 + 1 = 3 = 112 = 1 with 1 to carry

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 5510

+ 2810

8310

64 32 16 8 4 2 1 1 0 1 0 0 1 1 = 64 + 16 + 2 +1 = 8310

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?

How to perform Octal Addition?

1 1 6 4 3 78

+ 2 5 1 08 9 9 - 8 8 (subtract Base (8))

1 1 1 4 78

How to perform Octal Addition?

Ex)

3 5 3 68 + 2 4 5 78 - (subtract Base (8))

How to perform Hexadecimal Addition?

1 1 7 C 3 916 + 3 7 F 216 20 18 11 - 16 16 (subtract Base (16))

B 4 2 B16

8 A D 416

+ 5 D 616 - (subtract Base (16))

16

How to perform Hexadecimal Addition?

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

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 8310

- 2810

5510

64 32 16 8 4 2 1 1 1 0 1 1 1 = 32 + 16 + + 4 + 2 +1 = 5510

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

= =

How to perform Octal Subtraction?

8 0 0 8 1 1 1 4 78

8 9 - 6 4 3 78

2 5 1 08

ex

3 5 3 68 - 2 4 5 78

How to perform Octal Subtraction?

How to perform Hexadecimal Subtraction?

B 16 7 C 3 916 19

- 3 7 F 216 4 4 4 716

8 A D 416

- 5 D 616 16

How to perform Hexadecimal Subtraction?

Notations to distinguish

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.

For example, hexadecimal number 10AF may look as follows $10AF, 0x10AF or 10AFh.

Similarly, binary numbers usually get the suffix % or 0b,

ECE 362 Microprocessor Systems and Interfacing © 1-24