1. Create a K-map for each of the followingfunctions:i.X1 X2| f0 0 1110 111ii. f (x1,x2, x3) = Em (1,2, 3, 7)Ση (1,2, 3, 7)iii. f (x1, x2, X3) = x1· X2 + x2· X3X2 + X2 · X3

Answered: 1. Create a K-map for each of the…

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

1. Create a K-map for each of the following
functions:
i.
X1 X2| f
0 0 1
1
1
0 1
1
1
ii. f (x1,x2, x3) = Em (1,2, 3, 7)
Ση (1,2, 3, 7)
iii. f (x1, x2, X3) = x1· X2 + x2· X3
X2 + X2 · X3

Expert Solution

Introduction

K-map:-

Without using any Boolean algebra theorems, we can easily minimize Boolean expressions of 3, 4 variables using K-map. The K-map is a table-like representation that provides more data than the TRUTH TABLE. We start by filling the grid of the K-map with 0s and 1s, then we solve it by forming groups.

6 steps to solve expression using k map:-

Choose a K-map according to the no. of variables.
Determine the minimum and maximum terms as specified in the problem.
Place 1s in K-map blocks that correspond to the minterms (0s elsewhere) for SOP.
Put 0s in the K-map blocks that correspond to the max terms(1s elsewhere) for POS.
Form rectangular groups with total terms in two-digit powers., such as 2,4,8,...(except 1), and try to cover as many elements in each group as possible.
Find the product terms from the groups you made in step 5 and summarise them for the SOP form.