JEE Main 2021 · 25 July · morning · Single correct · +4 / −1
Identify the logic operation carried out.
- (a) OR
- (b) AND
- (c) NOR
- (d) NAND
Answer and solution
Answer (b) AND
Solution
Physics sir · 3 steps
Each NAND with its inputs tied is just a NOT gate, so the circuit is a NOR fed with A-bar and B-bar.
- First stage. Both inputs of each NAND gate are joined, so each gate gets the same signal twice. A · A̅ = A̅, so the top gate gives A̅ and the bottom gate gives B̅.
- Final NOR gate. The NOR gate gets A̅ and B̅. De Morgan's theorem then turns the output into a product of A and B.
Y = A̅ + B̅̅ = A̅̅̅ · B̅̅̅ = A · B
A, B A̅, B̅ Y (NOR of these) 0, 0 1, 1 0 0, 1 1, 0 0 1, 0 0, 1 0 1, 1 0, 0 1 - So. The output is 1 only when both inputs are 1. That is the AND operation, option (b).
The idea to keep. A NAND or NOR gate with its inputs tied together is a NOT gate. Inverted inputs into a NOR give AND. Inverted inputs into a NAND give OR.
Answer from the NTA final answer key. Solution by PrepWiser.