The GATE Grind

GATE 2016 EC (EC3) – Question 28

Digital Circuits · Combinatorial Circuits · 1 mark · Multiple choice

The minimum number of 2-input NAND gates needed to implement a 2-input XOR is

  1. 4
  2. 5
  3. 6
  4. 7

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Correct answer: (A) 4

Explanation

Use four NAND gates: $n_1=\overline{AB}$, $n_2=\overline{An_1}$, $n_3=\overline{Bn_1}$ and $Y=\overline{n_2n_3}$. The output is $A\oplus B$.

The first gate creates the shared product complement; two branches distinguish the unequal-input cases and the final gate combines them. This standard realization needs **four gates, A**; three 2-input NAND gates cannot implement the XOR truth table.

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