JEE Main 2020 · 4 September · evening · Single correct · +4 / −1
Identify the operation performed by the circuit given below :
- (a) AND
- (b) NAND
- (c) OR
- (d) NOT
Answer and solution
Answer (a) AND
Solution
Physics sir · 4 steps
A NOR gate with its inputs tied together is a NOT gate, and then De Morgan finishes the job.
- Input gates. Each of A, B and C feeds both inputs of its own NOR gate. With both inputs equal, the output is A + A̅ = A̅, so each of these gates is just a NOT gate. The three outputs are A̅, B̅ and C̅.
- Final gate. These three go into a three-input NOR gate, so the output is the NOR of the three inverted inputs.
Y = A̅ + B̅ + C̅̅ = A̅̅̅ · B̅̅̅ · C̅̅̅ = A · B · C
- Quick check. If A, B and C are all 1, every inverted signal is 0, the NOR of three 0s is 1, and Y = 1. If any input is 0, its inverted signal is 1, the NOR output drops to 0, and Y = 0.
- So. The output is 1 only when all inputs are 1, which is the AND operation, option (a).
The idea to keep. Shorted inputs on a NOR or NAND gate make a NOT gate. Inverted inputs followed by a NOR give AND, and inverted inputs followed by a NAND give OR. That is De Morgan's theorem at work.
Answer from the NTA final answer key. Solution by PrepWiser.