GATE 2016 EC – Question 27

Digital Circuits · Combinatorial Circuits · 1 mark · Multiple choice

The output of the combinational circuit given below is

Two inputs go into a gate G1, an AND gate with inputs $A$ and $B$. A second AND gate G2 has inputs $B$ and $C$. A third AND gate G3 has inputs G1 and $C$. An exclusive-OR gate X1 takes G1 and G2. The output $Y$ is a second exclusive-OR gate with inputs G3 and X1.

$A + B + C$
$A(B + C)$
$B(C + A)$
$C(A + B)$

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Correct answer: (C) $B(C + A)$

Explanation

G1 $= AB$, G2 $= BC$ and G3 $= ABC$. The first exclusive-OR gives $AB \oplus BC = B(A \oplus C)$. The output is $Y = ABC \oplus B(A \oplus C) = B[AC \oplus (A \oplus C)]$. Since $A \oplus C \oplus AC = A + C$, the output is $Y = B(A + C)$.