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GATE 2026 EE – Question 45

Analog and Digital Electronics · VCOs and timers, combinatorial and sequential logic circuits, multiplexers, demultiplexers · 2 marks · Multiple choice

The digital circuit shown has 3 inputs ($x$, $y$, and $z$).

The simplified logical expression for the output (OUT) is:

Diagram for GATE 2026 EE question 45
  1. $\bar x\,\overline{yz}$
  2. 0
  3. $\bar x(y+z)$
  4. 1

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Show answer and explanation

Correct answer: (B) 0

Explanation

The NOR gate gives $\bar x\bar y\bar z$. The two AND gates give $\bar xy$ and $\bar xz$, and the OR combines them into $\bar x(y+z)$. The final AND is $\bar x\bar y\bar z\cdot\bar x(y+z)=\bar x\,(\bar y\bar z)(y+z)=0$, since $\bar y\bar z=\overline{y+z}$ and $(y+z)\overline{(y+z)}=0$. The output is always 0.