XOR gate

The XOR gate (sometimes EOR gate, or EXOR gate and pronounced as Exclusive OR gate) is a digital logic gate that gives a true (1/HIGH) output when the number of true inputs is odd. An XOR gate implements an exclusive or; that is, a true output results if one, and only one, of the inputs to the gate is true. If both inputs are false (0/LOW) or both are true, a false output results. XOR represents the inequality function, i.e., the output is true if the inputs are not alike otherwise the output is false. A way to remember XOR is "one or the other but not both".

XOR can also be viewed as addition modulo 2. As a result, XOR gates are used to implement binary addition in computers. A half adder consists of an XOR gate and an AND gate. Other uses include subtractors, comparators, and controlled inverters.

The algebraic expressions ${\displaystyle A\cdot {\overline {B}}+{\overline {A}}\cdot B}$ and ${\displaystyle (A+B)\cdot }$ ( ${\displaystyle {\overline {A}}+{\overline {B}}}$ ) both represent the XOR gate with inputs A and B. The behavior of XOR is summarized in the truth table shown on the right.

...
Wikipedia