Minimize the following functions using Boolean algebra:a) $ F = A'B'C'D' + A'BC'D + A'BC'D' + AB'C'D' + A'B'C'D + AB'CD' + AB'CD + A'B'CD' + A'B'C'D $b) $ F = A'B'C' + A'B'ABC' + AC $Here, $ ' $ means inversion of the variable.

Answered: Minimize the following functions using…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Minimize the following functions using Boolean algebra:

a) $ F = A'B'C'D' + A'BC'D + A'BC'D' + AB'C'D' + A'B'C'D + AB'CD' + AB'CD + A'B'CD' + A'B'C'D $

b) $ F = A'B'C' + A'B'ABC' + AC $

Here, $ ' $ means inversion of the variable.

Expert Solution

Step 1: Part1:

Certainly! Let's go through the minimization process for both functions :
a) $F equals A to the power of prime. B to the power of prime. C to the power of prime. D to the power of prime plus A to the power of prime. B. C to the power of prime. D plus A to the power of prime. B. C to the power of prime. D to the power of prime plus A. B to the power of prime. C to the power of prime. D to the power of prime plus A to the power of prime. B to the power of prime. C. D to the power of prime plus A. B to the power of prime. C. D to the power of prime plus A to the power of prime B to the power of prime C to the power of prime. D$

Group the terms and eliminate duplicates:

$F equals A to the power of prime. B to the power of prime. C to the power of prime. D to the power of prime plus A to the power of prime. B. C to the power of prime. D plus A. B to the power of prime. C to the power of prime. D to the power of prime plus A to the power of prime. B to the power of prime. C. D to the power of prime plus A. B to the power of prime. C. D to the power of prime plus A to the power of prime B to the power of prime C to the power of prime. D$

Apply the absorption law $X plus X to the power of prime Y equals X plus Y$ :

$F equals A to the power of prime. B. C to the power of prime. D plus A. B to the power of prime. C. D to the power of prime plus A to the power of prime B to the power of prime C to the power of prime. D$

So, the minimized expression is:

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