The GATE Grind

GATE 2022 EC – Question 49

Digital Circuits · Combinatorial Circuits · 2 marks · Multiple select

Consider a Boolean gate (D) where the output $Y$ is related to the inputs $A$ and $B$ as, $Y=A+\bar B$, where $+$ denotes logical OR operation. The Boolean inputs '0' and '1' are also available separately. Using instances of only D gates and inputs '0' and '1', ________ (select the correct option(s)).

  1. NAND logic can be implemented
  2. OR logic cannot be implemented
  3. NOR logic can be implemented
  4. AND logic cannot be implemented

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Show answer and explanation

Correct answer: (A) NAND logic can be implemented; (C) NOR logic can be implemented

Explanation

$D(0,B)=\bar B$ gives a NOT gate. Then $D(A,\bar B)=A+B$ gives OR. NOT and OR together are functionally complete, so AND $=\overline{\bar A+\bar B}$, NAND and NOR can all be built. Hence A and C are correct while B and D are false.