Question

(i) Write the Boolean expression corresponding to the circuit given below.
(ii) Simplify the expression using laws of Boolean Algebra and construct the simplified circuit.

Answer 1

The statement of the given switching circuit is
$CA+A(B+C)(C+A)(C+B)$

$(CA+AB+AC)(C+A)(C+B)$
$(AC+AB)(C+A)(C+B)$
$=AC.C+ACA+ABC+ABA(C+B)$
$=AC+AC+ABC+AC(C+B)$
$=AC+ABC+ABC+ABB$
$=AC+ABC+AB$
$=AC+AB(1+C)$
$=AC+AB$
$=A(C+B)$
The simplified switching network is given in figure.