Answered: Using the laws of boolean algebra…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Using the laws of boolean algebra simplify these expressions and list the law(s) used to justify each step. And show a truth table for the original expression and verify that your final expression satisfies the same truth table.

a. ABC + ABC’ + A’C + A’B’C + AB’C

b. A'B' + A'BC' + (A + C')'

Expert Solution

Step 1: Simplify expression (a) and show truth table

(a.)

F₁ = ABC + ABC’ + A’C + A’B’C + AB’C

= AB(C+C') + A'C + (A + A')B'C .........(i)

We know that: X + X' = 1 (Complement Law)

Therefore, A + A' =1 & C+C' = 1

So our function become,

F₁ = AB + A'C + B'C

= AB +C(A' + B') ..........(ii)

Now let us assume original fuction as X₁ and reduced function as X₂

X₁ = ABC + ABC’ + A’C + A’B’C + AB’C

& X₂ = AB +C(A' + B')

Truth Table:

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