Electrical and Computer Engineering 2277A/B Lecture 6: Boolean Algebra and Logic Gates

• School: Western University
• Department: Electrical and Computer Engineering
• Course: Electrical and Computer Engineering 2277A/B
• Professor: Duane Jacques

Document Summary

These theorems are restatements of the huntington postulates. Each theorem is a pair of dual statements. Constructing the truth table helps understand circuit"s behaviour: Cost = number of external input bits + number of internal input bits + number of logic gates. Complements of external inputs count as external input bits. Number of gates does not include not gates used to complement external inputs. Internal inputs are connections from output of a counted gate to input of another gate. Redesigned circuit has 4 external inputs, 2 internal inputs, and 3 gates. Simplified expression has same truth table for , which proves both expressions are equivalent. In binary logic, a dual expression is obtained by: Changing all to and vice versa is the dual of. Complement each literal in result from step 1. Literal: a single variable within a term, which may or may not be complemented. This procedure can be used to derive the generalized de morgan"s theorems.