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:

Aâ€²B(CDâ€²+D)+B(C+Aâ€²BD)Aâ€²B(CDâ€²+D)+B(C+Aâ€²BD)

=Aâ€²B(C+D)+B(C+Aâ€²BD)(âˆµx+xâ€²y=x+y)=Aâ€²B(C+D)+B(C+Aâ€²BD)(âˆµx+xâ€²y=x+y)

=Aâ€²BC+Aâ€²BD+BC+Aâ€²BD)(âˆµxx=x)=Aâ€²BC+Aâ€²BD+BC+Aâ€²BD)(âˆµxx=x)

=Aâ€²BC+BC+Aâ€²BD(âˆµx+x=x)=Aâ€²BC+BC+Aâ€²BD(âˆµx+x=x)

=BC(Aâ€²+1)+Aâ€²BD=BC(Aâ€²+1)+Aâ€²BD

=BC+Aâ€²BD(âˆµ1+x=1)

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