GATE | GATE MOCK 2017 | Question 16

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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