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XOR gate - Wikipedia

XOR gate

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The XOR gate (sometimes EOR, or EXOR and pronounced as exclusive OR, ksor or sometimes EX-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 ($\nleftrightarrow$) 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.¹²

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.³

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

Printed 2026-06-28.

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Footnotes

1. Broesch, James D. (2012). Practical Programmable Circuits: A Guide to PLDs, State Machines, and Microcontrollers. Elsevier Science. p. 20. ISBN 978-0323139267. ↩

2. Van Houtven, Laurens (2017). Crypto 101 (PDF). p. 17. ↩

3. Fletcher, William (1980). An engineering approach to digital design. Prentice-Hall. p. 98. ISBN 0-13-277699-5. ↩

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