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Question
Write the Boolean function corresponding to the switching circuit given below:
A, B and C represent switches in ‘on’ position and A’, B’ and C’ represent them in ‘off position. Using Boolean algebra, simplify the function and construct an equivalent switching circuit.
Sum
Solution
A . (A'+B) + A' B + (A + B') . C
= AA' + AB + A'B + AC +B'C
= 0 + AB + A'B + AC + B'C ...(∵ aa' = 0)
= (A+A') . B + AC + B'C ...(Distributive law)
= 1.B + AC + B'C ...(∵ a + a' = 1)
= B + AC + B'C
= B + (A+B').C
Simplified switchging circuit is :
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Concept of Relation - Types of Relations - Identity Relation
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