Question

Construct a circuit diagram for the following Boolean Function
$(BC+A)(A^{\prime }{B}^{\prime }+C^{\prime })+A^{\prime }{B}^{\prime }{C}^{\prime }$
Using laws of Boolean Algebra, simplify the function and draw the simplified circuit.

Answer 1

It can be simplified as
$(BC+A)(A^{\prime }{B}^{\prime }+C^{\prime })+A^{\prime }{B}^{\prime }{C}^{\prime }$
$BC{A}^{\prime }{B}^{\prime }+BC{C}^{\prime }+A{A}^{\prime }{B}^{\prime }+A{C}^{\prime }+A^{\prime }{B}^{\prime }{C}^{\prime }$
$A^{\prime }CB{B}^{\prime }+BC{C}^{\prime }+A{A}^{\prime }{B}^{\prime }+A{C}^{\prime }+A^{\prime }{B}^{\prime }{C}^{\prime }$
$0+0+0+A{C}^{\prime }+A^{\prime }{B}^{\prime }{C}^{\prime }$
$=C^{\prime }(A+A^{\prime }{B}^{\prime })$
$=\left[\right(A+A^{\prime }\left)\right(A+B^{\prime }\left)\right]C^{\prime }$
$=(A+B^{\prime })C^{\prime }$