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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)

slide11

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)

slide13

2-to-4

Decoder/Demultiplexer

full adder
Full Adder

See Figure B.22

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