JEE Main 2023 · 11 April · evening · Single correct · +4 / −1
The logic operations performed by the given digital circuit is equivalent to:
- (a) NOR
- (b) AND
- (c) NAND
- (d) OR
Answer and solution
Answer (b) AND
Solution
Physics sir · 3 steps
A NAND followed by a NOT is just an AND, so Y is the OR output ANDed with the AND output.
- Read the circuit. The top gate gives A + B and the bottom gate gives AB. Both go into a NAND, and the NOT after it undoes the NAND's bubble, so together they act as one AND gate.
Y = (A+B)· AB̅̅ = (A+B)· AB = AB
- Simplify. Expanding gives (A+B)· AB = AAB + ABB = AB + AB = AB, since A · A = A and B · B = B.
A B A+B AB NAND output Y 0 0 0 0 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 1 1 1 0 1 - So. Y = 1 only when both inputs are 1. That is the truth table of an AND gate, option (b).
The idea to keep. Two inversions in a row cancel, so NAND plus NOT is AND. Then use X · X = X to collapse the Boolean expression before you look at the options.
Answer from the NTA final answer key. Solution by PrepWiser.