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Question
If A, B and C are the elements of Boolean algebra, simplify the expression (A’ + B’) (A + C’) + B’ (B + C). Draw the simplified circuit.
Solution
(A' + B')(A + C') + B'(B + C)
= A' (A + C') + B' (A + C') + B'B + B'C
= A'A + A'C' + B'A + B'C' + B'B + B'C
= 0 + A'C' + B'A + B'C' + 0 + B'C .....[∵ A'A = 0]
= A'C' + B'A + B' (C'+C)
= A'C'+B'A+B' .....[∵ A + A' = 1]
= A'C' + B' (A + 1)
= A'C' +B' ......[∵ A + 1 = 1]
simplified circuit :-
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