Answered: In K-Map, you might find some cells,…

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

In K-Map, you might find some cells, where each cell represents a minterm, filled with the letter X. This X is called “Don’t care”.

When forming groups of cells, don't care conditions (X) are considered as 1, if this allows us to form a larger group than would otherwise be possible without the don’t cares.

There is no requirement to group all or any of the don’t cares.

Rule: Only use the Don’t cares in a group if this simplifies the logic.

Based on the above note, and applying the same K-Map rules, you are asked to answer the below questions for the below 4-variable K-Map:

a- Encircle the groups that should be considered, using a minimum number of X’s where necessary to obtain the optimal solution.

N.B: Your solution is considered optimal, if you have involved the minimum number of minterms to simplify the function using K-map with the don’t cares.

b- Write the simplified equation of the function F.

c- Find the complement (F’) of the simplified F. Apply De Morgan’s law and show the steps. You can keep it in the POSform.

d- Draw the logic diagram of the simplified F using only NAND gates.

F	C'D'	C'D	CD	CD'
A'B'	X	1	1	X
A'B	0	X	1	0
AB	0	0	1	X
AB'	0	0	1	X

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