# Appendix B: Digital Logic - PowerPoint PPT Presentation

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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

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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

A AND B = A‧B

A OR B = A + B

NOT A = A

D = A +(B‧C)

NOT AND OR

XOR NAND NOR

### Gates

See Page 704 (Figure B.1)

• Functional Complete Sets:

• AND, OR, NOT

• AND, NOT

• OR, NOT

• NAND

• NOR

### 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)

### Multiplexer

4-to-1

MUX

D0

D1

D2

D3

F

S2 S1

Figure B.13 (Page 699)

S1

S2

D0

D1

F

D2

D3

4-to-1 Multiplexer

B

A

00

01

10

11

2-to-4

Decoder

D0

D1

D2

D3

A

B

### Decoder

N-to-2N

Decoder

N-bit

Inputs

2N

Outputs

Figure B.15 (Page 700)

2-to-4

Decoder/Demultiplexer