Appendix B: Digital Logic

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

15. Half Adder

16. Full Adder See Figure B.22

17. 4-bit Adder