Which of the following gives a reversible operation?

Solution

Physics sir · 3 steps

Ask one question of each gate: from the output alone, can you tell me what the input was?

1. Meaning of reversible. A logic operation is reversible when you can work backwards from the output to the input. Each output value must come from exactly one input, so no information is lost.
2. Count the states. A gate with two independent inputs has 4 input combinations (00, 01, 10, 11), but one output wire has only 2 values. At least two inputs must share an output, so such a gate cannot be reversible.

   Option	Gate	Input to output	Reversible?
   (a)	two-input NOR	00 gives 1; 01, 10, 11 all give 0	No
   (b)	NOR with inputs joined, which is a NOT gate	0 gives 1, 1 gives 0	Yes
   (c)	two-input OR	00 gives 0; 01, 10, 11 all give 1	No
   (d)	two-input AND	11 gives 1; 00, 01, 10 all give 0	No

3. So. Joining the two inputs of the NOR gate in (b) gives Y = A + A̅ = A̅, a NOT gate. Its output always tells you the input, so (b) is the reversible operation.

The idea to keep. Reversible means one-to-one: every output traces back to a single input. If a gate has more input combinations than output values, information is lost and it cannot be reversible.

Answer from the NTA final answer key. Solution by PrepWiser.