The Boolean function f implemented in the figure shown below, using two input multiplexers is:
(A)
AB’C + ABC’
(B)
A’B’C + A’BC’
(C)
A’BC + A’B’C’
(D)
ABC + AB’C’
Answer: (D)
Explanation:
The output of a multiplexer (2X1) can be expressed in the form of:
f= S’. L1 + S. L2
For the above diagram the output from the first multiplexer would be B’C + BC’ which acts a select line for the second multiplexer. Hence,
f= (B’C + BC’)’A + (B’C + BC’).0
= ((B’C)’ . (BC’)’)A + 0
= (B+C’)(B’ + C)A
= (BC + B’C’) A
= ABC + AB’C’
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