Answered: Write a sum-of-products Boolean…

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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Question

a. Write a sum-of-products Boolean expression bexp₃ for the output ? of this truth table.

b. Draw a circuit that is a direct translation of bexp₃ without any simplification. For the circuit, try to use the same input order and layout convention as in the example shown below

А A B C
ооо
0 1
1
0
011
100
101
110
1
О
0
0
1
1
Y
1
0
1
О
1
1
0
1

Expert Solution

Step 1: Some Overviews of the Boolean expression

In the given truth table, we have the variables A, B, and C, and we want to find the Boolean expression bexp3 for the output Y.

The sum-of-products Boolean expression is constructed by OR'ing together product terms for each row where the output is 1. A product term is an AND of the variables, where each variable is either complemented (i.e., A' instead of A) or not, based on the value in the row (0 or 1, respectively).

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