computer architecture: Boolean Problem 1:For each of the following Boolean expressions create the truth table:a. (ā + b· d)· (c ·b•a+¯•d)b. (w + x)(zỹ + x)

Answered: For each of the following 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

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computer architecture: Boolean

Problem 1:
For each of the following Boolean expressions create the truth table:
a. (ā + b· d)· (c ·b•a+¯•d)
b. (w + x)(zỹ + x)

Expert Solution

Step 1

Truth table is a table which represents all the possible values of logical statements along with all the possible results of the given combinations of values.
a. F= $(\bar{a} + b . \bar{d}) . (c . b . a + \bar{c} . d)$
Here, the given boolean expression contain 4 variables, therefore the possible combinations are 2⁴=16.
The resultant truth table is:

a	b	c	d	$\bar{a}$	b. $\bar{d}$	$\bar{a}$ +b. $\bar{d}$	c.b.a	$\bar{c} . d$	c.b.a+ $\bar{c} . d$	F= $(\bar{a} + b . \bar{d}) . (c . b . a + \bar{c} . d)$
0	0	0	0	1	0	1	0	0	0	0
0	0	0	1	1	0	1	0	1	1	1
0	0	1	0	1	0	1	0	0	0	0
0	0	1	1	1	0	1	0	0	0	0
0	1	0	0	1	1	1	0	0	0	0
0	1	0	1	1	0	1	0	1	1	1
0	1	1	0	1	1	1	0	0	0	0
0	1	1	1	1	0	1	0	0	0	0
1	0	0	0	0	0	0	0	0	0	0
1	0	0	1	0	0	0	0	1	1	0
1	0	1	0	0	0	0	0	0	0	0
1	0	1	1	0	0	0	0	0	0	0
1	1	0	0	0	1	1	0	0	0	0
1	1	0	1	0	0	0	0	1	1	0
1	1	1	0	0	1	1	1	0	1	1
1	1	1	1	0	0	0	1	0	1	0

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