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Appendix B: Digital LogicPowerPoint Presentation

Appendix B: 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
- 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;"

- 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)

NOT AND OR

XOR NAND NOR

See Page 704 (Figure B.1)

- Functional Complete Sets:
- AND, OR, NOT
- AND, NOT
- OR, NOT
- NAND
- NOR

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

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

Figure B.6 (Page 690)

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

N-to-2N

Decoder

‧

‧

‧

N-bit

Inputs

2N

Outputs

‧

‧

‧

Figure B.15 (Page 700)

2-to-4

Decoder/Demultiplexer

See Figure B.22