Consider three 4 -variable functions {f}_{1}, {f}_{2} and {f}_{3}, which are expressed in sum-of-min-terms as {f}_{1}=\sum(0,2,5,8,14), {f}_{2}=\sum(2,3,6,8,14 15), f_{3}=\sum(2,7,11,14) For the following circuit with one AND gate and one XOR gate, the output function f can be expressed as:

GATE Computer Science (CS) 2019 Solved Papers

Question : 40 of 65

Marks: +1, -0

Consider three 4 -variable functions

{f}_{1}, {f}_{2}

and

{f}_{3}

, which are expressed in sum-of-min-terms as

{f}_{1}=Σ(0,2,5,8,14), {f}_{2}=Σ(2,3,6,8,14

15),

f_{3}=Σ(2,7,11,14)

For the following circuit with one AND gate and one XOR gate, the output function f can be expressed as:

Solution:

{f}_{1} ⋅ {f}_{2} \;\; =Σ(2,8,14)

{f}_{1} \;\; = {f}_{3} ⊕( {f}_{1} ⋅ {f}_{2})

\;\; =Σ(7,8,11)

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