Appendix B: Digital Logic

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 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 NOT AND OR XOR NAND NOR

Key Identities of Boolean Algebra

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

The Use of NAND Gates

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

Simplified Implementation Figure B.6 (Page 690)

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

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

Decoder 2-to-4 Decoder D0 D1 D2 D ABAB B A N-to-2 N Decoder ‧‧‧‧‧‧ N-bit Inputs ‧‧‧‧‧‧ 2 N Outputs Figure B.15 (Page 700)

2-to-4 Decoder/Demultiplexer

Half Adder

Full Adder See Figure B.22

4-bit Adder