The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
+18 votes

Consider the following expression

$a\bar d + \bar a\bar c + b\bar cd$

Which of the following Karnaugh Maps correctly represents the expression?



asked in Digital Logic by Boss (16.3k points)
edited by | 1k views

2 Answers

+1 vote
Best answer

$a\bar d + \bar a \bar c+b \bar c d = \overset{m_8}{a\bar b \bar c \bar d} + \overset{m_{10}}{a\bar b  c \bar d} +\overset{m_{12}}{a b \bar c \bar d} + \overset{m_{14}}{a b  c \bar d} $

$\qquad + \overset{m_0}{\bar a \bar b \bar c \bar d} + \overset{m_4}{\bar a  b \bar c \bar d}+ \overset{m_1}{\bar a \bar b \bar c  d}+ \overset{m_5}{\bar a  b \bar c  d}$

$\qquad + \overset{m_5}{\bar ab \bar c d}+ \overset{m_{13}}{ab\bar c d}$

When we minimize a K-map, we can assume either $0$ or $1$ for don't cares. But here they have asked for the expression represented by the K-map. So we can consider $X$ as $1$ and not as a don't care. Also the given expression is equivalent to the above K-map but not the minimal one. Minimal expression will be $\bar a \bar c + b\bar c+ a\bar d.$

Hence, Option A. 

answered by Veteran (407k points)
selected by
+10 votes

Answer is a.

answered by Active (5k points)
edited by
But we can still derive this expression using (c) and (d) as well right? They didn't ask for a minimal don't care set of K-map or something.

Please explain how are you being confident of the option (a)?
Even the given expression is not the minimal for option A.

d can be removed from bc'd.

@Sunit Acharya 

I think the expression should be able to cover every minterm . And it does not cover every minterm from the kmap c and d . 

here X represents 1 or don't care

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
49,532 questions
54,126 answers
71,046 users