# Logical XOR

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Previous lesson: Logical OR

## Introducing the Exclusive OR!

[math]\oplus[/math] : This is the XOR operator. It is also called the **exclusive OR**, to distinguish it from the inclusive OR of the previous lesson. Like the inclusive OR, it is a diadic operator; unlike any other operator, it is true when one and only one input is true.

- Let [math]p[/math] represent the statement: It is raining.
- Let [math]q[/math] represent the statement: I am hungry.
- [math]p \oplus q[/math] represents the exclusive disjunction of statements [math]p[/math] and [math]q[/math]: It is raining OR I am hungry,
*But not both.*

- [math]p \oplus q[/math] represents the exclusive disjunction of statements [math]p[/math] and [math]q[/math]: It is raining OR I am hungry,

## Truth Table

Its truth table is unique. Here it is!

[math]p \,\![/math] | [math]q \,\![/math] | [math]p \oplus q[/math] |
---|---|---|

T | T | F |

T | F | T |

F | T | T |

F | F | F |

## Why XOR is Special

XOR is used for adding binary numbers, and is the fundamental arithmetic operation used by computers.

## Next Lesson

Your next lesson is called Conditional Operator.