Which gate will have an off output when both inputs are the same?

The correct choice is the XOR gate, which stands for "exclusive OR." This gate produces a high output (or '1') only when the inputs are different. Therefore, when both inputs are the same—whether they are both high (1) or both low (0)—the output will be low (or '0'). Thus, when inputs are identical, the XOR gate guarantees an off output.

Understanding the behavior of the XOR gate in relation to its inputs is crucial. For example, if you take the two inputs as either 0 and 0 or 1 and 1, the output is 0 in both scenarios. This characteristic makes the XOR gate essential in digital circuits that require conditions to trigger based on difference rather than sameness.

In contrast, NAND, AND, and OR gates produce different outputs based on their combinations of inputs. For instance, the NAND gate, which outputs off only when both inputs are high, and the AND gate generates an on output only when both inputs are high. The OR gate outputs on when at least one input is high. Hence, none of these gates will specifically have an off output with both inputs being the same in all cases.