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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

Appendix B: Digital Logic

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


Boolean algebra
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 algebra1
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)


Boolean operators
Boolean Operators

NOT AND OR

XOR NAND NOR



Gates
Gates

See Page 704 (Figure B.1)

  • Functional Complete Sets:

    • AND, OR, NOT

    • AND, NOT

    • OR, NOT

    • NAND

    • NOR



Implementation of boolean functions
Implementation of Boolean Functions

  • Sum-of-Products

    • Figure B.4 (page 688)

  • Product-of-Sums

    • Figure B.5 (page 689)


Simplified implementation
Simplified Implementation

Figure B.6 (Page 690)


Multiplexer
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


Decoder

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



Full adder
Full Adder

See Figure B.22



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