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# FIGURES FOR CHAPTER 3 BOOLEAN ALGEBRA (continued) - PowerPoint PPT Presentation

This chapter in the book includes: Objectives Study Guide 3.1 Multiplying Out and Factoring Expressions 3.2 Exclusive-OR and Equivalence Operations 3.3 The Consensus Theorem 3.4 Algebraic Simplification of Switching Expressions 3.5 Proving the Validity of an Equation

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Presentation Transcript

Objectives

Study Guide

3.1 Multiplying Out and Factoring Expressions

3.2 Exclusive-OR and Equivalence Operations

3.3 The Consensus Theorem

3.4 Algebraic Simplification of Switching Expressions

3.5 Proving the Validity of an Equation

Programmed Exercises

Problems

FIGURES FORCHAPTER 3BOOLEAN ALGEBRA(continued)

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The consensus theorem can be stated as follows:

XY + X'Z + YZ = XY + X'Z

Proof:

XY + X'Z + YZ = XY + X'Z + (X + X')YZ

= (XY + XYZ) + (X'Z + X'YZ)

= XY(1 + Z) + X'Z(1 + Y) = XY + X'Z

A'BD' + BCD + ABC' + AB'D = BC'D' + AD + A'BC