nxor

nxor is a logical operation, a variation of the exclusive OR (XOR) gate. While XOR outputs true if the inputs are different, nxor outputs true if the inputs are the same. It is also known as the XNOR gate, exclusive NOR, or equivalence gate. The truth table for nxor with two inputs, A and B, is as follows: If A is false and B is false, the output is true. If A is false and B is true, the output is false. If A is true and B is false, the output is false. If A is true and B is true, the output is true.

In Boolean algebra, nxor can be represented by the symbol $\odot$, $\equiv$, or $\sim \oplus$. Mathematically, for two inputs A and B, nxor can be expressed as A nxor B = (A AND B) OR (NOT A AND NOT B). This is equivalent to saying that A nxor B is true if and only if A and B are both true, or A and B are both false.

Nxor gates are fundamental components in digital electronics and computer hardware. They are used in various applications, including error detection and correction circuits, equality comparators, and data synchronization. For instance, in a comparator circuit, an nxor gate can determine if two binary numbers are identical. If the output of the nxor gate for each corresponding bit position is true, then the numbers are equal.