JEE Main 2022 · 25 June · evening · Single correct · +4 / −1
Identify the logic operation performed by the given circuit:
- (a) AND gate
- (b) OR gate
- (c) NOR gate
- (d) NAND gate
Answer and solution
Answer (a) AND gate
Solution
Physics sir · 3 steps
Each input NOR with its legs tied is just a NOT gate, so the last NOR gets Ā and B̄.
- Inputs tied together. In each of the first two NOR gates both legs carry the same signal. A NOR fed A and A gives A + A̅ = Ā, so each of these gates works as a NOT gate.
- Final NOR gate. The last NOR gate receives Ā and B̄. Apply De Morgan's theorem: the bar over a sum becomes a product of the barred terms, and the double bars cancel.
Y = Ā + B̄̅ = Ā̄̄ · B̄̄̄ = A · B
A B Ā B̄ Y 0 0 1 1 0 0 1 1 0 0 1 0 0 1 0 1 1 0 0 1 - So. Y is 1 only when both A and B are 1. The circuit is an AND gate, option (a).
The idea to keep. A NOR with its inputs joined is a NOT gate. Invert both inputs and then NOR them, and De Morgan gives you AND. Do the same with NAND gates and you get OR.
Answer from the NTA final answer key. Solution by PrepWiser.