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GATE | GATE MOCK 2017 | Question 16

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  • Last Updated : 19 Nov, 2018
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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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