XNOR

XNOR, short for exclusive NOR, is a digital logic gate that outputs a true signal when its inputs are equal. It is the negation of the XOR operation. For two inputs A and B, the XNOR output is 1 when A equals B, and 0 otherwise.

The truth table for a two-input XNOR is:

A = 0, B = 0 -> 1

A = 0, B = 1 -> 0

A = 1, B = 0 -> 0

A = 1, B = 1 -> 1

Boolean expressions describe XNOR as XNOR(A,B) = (A AND B) OR (NOT A AND NOT B) and also XNOR(A,B) = NOT(A XOR B).

In multi-input form, an XNOR gate yields 1 when an even number of inputs are 1, and 0 when the number of 1s is odd.

Applications include equality testing, parity checking, and error detection, as well as use in comparators and certain arithmetic circuits. XNOR helps implement bitwise equality checks between data words and can be used in mask generation and data verification in digital systems.

Implementation notes: most practical designs realize XNOR as an XOR gate followed by a NOT gate, though dedicated XNOR gates or equivalent NAND/NOR constructions are common in integrated circuits and programmable logic.