What logical operation is performed by a two-input exclusive NOR gate?

To deduce the function of an Exclusive NOR (XNOR) gate, it helps to start with the Exclusive OR (XOR) gate. A standard XOR gate looks for differences, producing a 1 at its output only if one and only one input is 1. The XNOR gate takes that XOR output and passes it through a NOT inversion. Because the XOR gate outputs a 1 when the inputs are different, the XNOR gate produces a 0 when the inputs are different (i.e., when one and only one input is 1). Conversely, the XNOR gate acts as an "equivalence" gate, producing a 1 when both inputs are identical (either both 0s or both 1s).