Lecture17CircuitMinimization

# Lecture17CircuitMinimization - Lecture 17 CS 2603 Applied...

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CS2603 Applied Logic for Hardware and Software Rex Page – University of Oklahoma 1 Lecture 17 — CS 2603 Applied Logic for Hardware and Software Circuit Minimization using Karnaugh maps

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CS2603 Applied Logic for Hardware and Software Rex Page – University of Oklahoma 2 Boolean Functions new name for same old animal Boolean function — a special kind of predicate Domain of discourse: tuples of {True, False} values Boolean functions truth tables F(a, b) — two-variable Boolean function Domain of discourse: pairs of Boolean values Specifies a Boolean output for each pair of Boolean inputs Representations we’ve already seen for 2-var Boolean functions 9 Truth table with four rows (unique: one per Boolean function) 9 Propositional WFF with two variables (not a unique rep'n) 9 Combinational circuit with two input lines, one output line F(a, b, c) — three-variable Boolean function Domain of discourse: triples of Boolean values 8-line truth table, 3-variable WFF, 3-input/1-output circuit F(x 1 , x 2 , … x n ) — n-variable Boolean function Domain of discourse: n-tuples of Boolean values 2 n -line truth table, n-variable WFF, n-input/1-output circuit