Question #232179

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

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

Expert's answer

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)

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