Simplify Boolean Expression ZWVZWSolutionGiven Boolean Expre

Simplify Boolean Expression (Z.W.V)+(~Z)+(~W)

Solution

Given Boolean Expression is F= (Z.W.V)+(~Z)+(~W)

=[ (Z.W.V)+(~Z) ] + (~W)

=[ (Z+~Z) ( W+~Z) ( V + ~Z ) ] + (~W)

{ According to distributive Law A + ( B.C.D )= (A + B) (A + C) (A + D) }

= [ ( 1 ) ( W+~Z) ( V + ~Z ) ] + (~W) { We know that Z.+~Z =1 }

=[ ( W+~Z) ( V + ~Z ) ] + (~W)

= [ ( W.V )+(~Z) ] + (~W)

{ According to Distributive Law (A + B) (A + C) = A + ( B.C ) }

= [ (~W) + ( W.V ) ] + (~Z)

= [ ( ~W + W ) (~W + V ) ] + (~Z)

{ According to Distributive Law A + ( B.C )= (A + B) (A + C) }

= [ ( 1 ) (~W + V ) ] + (~Z) { We know that W +~W =1 }

F = [ (~W + V ) ] + (~Z)

The Simplify Boolean Expression is F= (~W ) + V + (~Z)