MHT CET · Physics · Semiconductors

To get the truth table shown from the following logic circuit, the logic gate G should be

A AND
B OR
C NAND
D NOR

Verified Solution

Answer & Solution

Correct Answer

(C) NAND

Step-by-step Solution

Detailed explanation

In the circuit, one input to the OR gate is A and the other input is the output of the gate G. Since \(Y\) is always 1 regardless of \(A\) and \(B\), the gate \(G\) must output 1 when its input is fed into the OR gate. For this to happen, the output of \(G\) needs to be such that it outputs 1 when combined with A in the OR gate.
From the truth table, the logic gate \(G\) is a NAND gate, as the NAND gate will output 1 for all combinations except when both inputs are 1 , which would then be overruled by the OR gate which outputs 1 if either input is 1 .

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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