The GATE Grind

GATE 2014 EC (EC1) – Question 25

Digital Circuits · Combinatorial Circuits · 1 mark · Multiple choice

Simplify $(X+Y)(X+\overline Y)+\overline{(X\overline Y)+\overline X}$.

  1. $X$
  2. $Y$
  3. $XY$
  4. $X+Y$

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Show answer and explanation

Correct answer: (A) $X$

Explanation

The first product is (X+Y)(X+Ȳ)=X+YȲ=X. By De Morgan’s law the complemented second term is [(XȲ)+X̄]̄=(X̄+Y)X=XY. Finally X+XY=X by absorption. Therefore the complete expression reduces to **X,A**.