Concept

# XOR gate

Summary
XOR gate (sometimes EOR, or EXOR and pronounced as Exclusive OR) is a digital logic gate that gives a true (1 or HIGH) output when the number of true inputs is odd. An XOR gate implements an exclusive or () from mathematical logic; 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 "must have one or the other but not both". An XOR gate may serve as a "programmable inverter" in which one input determines whether to invert the other input, or to simply pass it along with no change. Hence it functions as a inverter (a NOT gate) which may be activated or deactivated by a switch. 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. The gate is also used in subtractors and comparators. The algebraic expressions or or all represent the XOR gate with inputs A and B. The behavior of XOR is summarized in the truth table shown on the right. There are three schematic symbols for XOR gates: the traditional ANSI and DIN symbols and the IEC symbol. In some cases, the DIN symbol is used with ⊕ instead of ≢. For more information see Logic Gate Symbols. The "=1" on the IEC symbol indicates that the output is activated by only one active input. The logic symbols ⊕, Jpq, and ⊻ can be used to denote an XOR operation in algebraic expressions. C-like languages use the caret symbol ^ to denote bitwise XOR. (Note that the caret does not denote logical conjunction (AND) in these languages, despite the similarity of symbol.) The XOR gate is most commonly implemented using MOSFETs circuits. Some of those implementations include: The Complementary metal–oxide–semiconductor (CMOS) implementation of the XOR gate.