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Appendix B: Digital Logic

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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  1. Appendix B: Digital Logic http://www.play-hookey.com/digital/

  2. 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;"

  3. 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)

  4. Boolean Operators NOT AND OR XOR NAND NOR

  5. Key Identities of Boolean Algebra

  6. Gates See Page 704 (Figure B.1) • Functional Complete Sets: • AND, OR, NOT • AND, NOT • OR, NOT • NAND • NOR

  7. The Use of NAND Gates

  8. Implementation of Boolean Functions • Sum-of-Products • Figure B.4 (page 688) • Product-of-Sums • Figure B.5 (page 689)

  9. Simplified Implementation Figure B.6 (Page 690)

  10. Multiplexer 4-to-1 MUX D0 D1 D2 D3 F S2 S1 Figure B.13 (Page 699)

  11. S1 S2 D0 D1 F D2 D3 4-to-1 Multiplexer

  12. 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)

  13. 2-to-4 Decoder/Demultiplexer

  14. Half Adder

  15. Full Adder See Figure B.22

  16. 4-bit Adder

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