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Appendix B: Digital LogicPowerPoint Presentation

Appendix B: Digital Logic

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### Appendix B: Digital Logic

http://www.play-hookey.com/digital/

Boolean Algebra

- Boolean Algebra
- Algebra of logic
- Devised by the English mathematician George Boole.

- Everything in the digital world is based on the binary number system.
0 = false = no 1 = true = yes

- Digital Logic
- Using this two-valued logic system, every statement or condition must be either "true" or "false;"

Boolean Algebra

- Variables and Operations
- Variables
- A variable can take on the value 1(True) or 0(False).

- Operations
- Basic logical operations:
- AND
- OR
- NOT

- Basic logical operations:

- Variables

A AND B = A‧B

A OR B = A + B

NOT A = A

D = A +(B‧C)

Implementation of Boolean Functions

- Sum-of-Products
- Figure B.4 (page 688)

- Product-of-Sums
- Figure B.5 (page 689)

Simplified Implementation

Figure B.6 (Page 690)

A

00

01

10

11

2-to-4

Decoder

D0

D1

D2

D3

A

B

DecoderN-to-2N

Decoder

‧

‧

‧

N-bit

Inputs

2N

Outputs

‧

‧

‧

Figure B.15 (Page 700)

Decoder/Demultiplexer

Full Adder

See Figure B.22

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