Answer to Question #232179 in Electrical Engineering for Alock kumar

Question

Simplify the following boolean expression, using four-variable maps:

A' B' C' D' + A'CD' + AB'D'+ABCD + A' BD

Answer 1

The expression is: A' B' C' D' + A'CD' + AB'D'+ABCD + A' BD

We can begin by expanding it as follows:

A′B(CD′+D)+B(C+A′BD)A′B(CD′+D)+B(C+A′BD)

=A′B(C+D)+B(C+A′BD)(∵x+x′y=x+y)=A′B(C+D)+B(C+A′BD)(∵x+x′y=x+y)

=A′BC+A′BD+BC+A′BD)(∵xx=x)=A′BC+A′BD+BC+A′BD)(∵xx=x)

=A′BC+BC+A′BD(∵x+x=x)=A′BC+BC+A′BD(∵x+x=x)

=BC(A′+1)+A′BD=BC(A′+1)+A′BD

=BC+A′BD(∵1+x=1)

Our map is represented as follows: