Which gate only outputs 1 when both inputs are 1?

The correct answer is the gate that outputs 1 only when both inputs are 1, which is the AND gate. The AND gate operates on the principle of conjunction, meaning that it requires all its inputs to be true to produce a true output. When both inputs to an AND gate are 1 (true), it yields an output of 1. If either or both inputs are 0, the output will be 0 (false).

In contrast, an OR gate produces an output of 1 if at least one of its inputs is 1, while a XOR gate outputs 1 only when the inputs differ (one is 1, the other is 0). A NAND gate, on the other hand, outputs the inverse of the AND gate; it outputs 0 only when both inputs are 1, and outputs 1 for all other combinations. This delineation of how each gate functions highlights why the AND gate is the only one that meets the criteria presented in the question.