Question

Write the Boolean expression corresponding to the circuit given below: 

Simplify the expression using laws of Boolean Algebra and construct the simplified circuit.

Answer 1

The statement using the given switching circuits is as: 

CA + A(B + C) (C + A) (C + B) ….. (i) 

using laws of Boolean Algebra, we have 

CA + A(B + C) (C + A) (C + B) = (CA + AB + AC) (C + A) (C + B) 

= (AC + AB + AC) (C + A) (C + B) 

= ACC + ACA + ABC + ABA (C + B) 

= AC + AC + ABC + AB (C + B) 

= AC + ABC + ABC + AB 

= AC + ABC + AB 

= AC + AB (1 + C) 

= AC + AB (1) 

= AC + AB 

= A(C + B) 

Hence, the simplified switching network can be shown as in the figure.