Question

Write the Boolean function corresponding to the switching circuit given below:

Answer 1

The required Boolean expression is
$A(A^{\prime }+B)+A^{\prime }B+C(A+B^{\prime })=A{A}^{\prime }+AB+A^{\prime }B+AC+B^{\prime }C$
$=0+B(A+A^{\prime })+AC+B^{\prime }C$ $[\because$ $A{A}^{\prime }=0]$
$=B+AC+B^{\prime }C$ $[\because$ $A{A}^{\prime }=1]$
$=(B+B^{\prime })(B+C)+AC$ $[\because a+bc=(a+b\left)\right(a+c\left)\right]$
$=B+C+AC$ $[\because B+B^{\prime }=1]$
$=B+C$ $[\because$ By law of absorption, $C+AC=C$]
which is the simplified circuit whose switching circuit is shown in the figure.