Document Reference: TN201009006 - Rev: 4.14 - Last Update: 14-11-2020 03:57 GMT - Downloaded: 13-Apr-2024 00:13 GMT

## A standard XOR (Exclusive-OR) gate is a logic gate with two or more inputs and one output. An odd number of inputs states must be high to produce a high output.

### XOR Gate Symbols

The inputs (`A, B`

) of an XOR gate are on the left, and the output (`X`

) is on the right of the logic XOR gate symbol.

Distinctive Shape | Rectangular Shape | DIN Shape (Historic) |
---|---|---|

### XOR Gate Truth Tables

#### Truth Table for XOR Gate with 2 Inputs

`A` | `B` | `X` |
---|---|---|

`0` | `0` | `0` |

`0` | `1` | `1` |

`1` | `0` | `1` |

`1` | `1` | `0` |

#### Truth Table for XOR Gate with 3 Inputs

`A` | `B` | `C` | `X` |
---|---|---|---|

`0` | `0` | `0` | `0` |

`0` | `0` | `1` | `1` |

`0` | `1` | `0` | `1` |

`0` | `1` | `1` | `0` |

`1` | `0` | `0` | `1` |

`1` | `0` | `1` | `0` |

`1` | `1` | `0` | `0` |

`1` | `1` | `1` | `1` |

### XOR Gate Test-It

To test the gate, click the switch symbols in the image below.

### XOR Gate Logical Expressions

#### Word Equation

`X = A XOR B`

#### Boolean Algebra

In boolean algebra the plus sign with a circular border (`⊕`

) stands for the XOR operation, e.g.:

`X = A ⊕ B`

Alternative notation: `X = A ∨ B`

`A` | `B` | `X = A ⊕ B` |
---|---|---|

`0` | `0` | `X = 0 ⊕ 0 = 0` |

`0` | `1` | `X = 0 ⊕ 1 = 1` |

`1` | `0` | `X = 1 ⊕ 0 = 1` |

`1` | `1` | `X = 1 ⊕ 1 = 0` |

Note: `X = A ⊕ B ⊕ C = (A ⊕ B) ⊕ C = A ⊕ (B ⊕ C) `

`A` | `B` | `C` | `X = (A ⊕ B) ⊕ C` |
---|---|---|---|

`0` | `0` | `0` | X = (0 ⊕ 0) ⊕ 0 = 0 ⊕ 0 = 0 |

`0` | `0` | `1` | X = (0 ⊕ 0) ⊕ 1 = 0 ⊕ 1 = 1 |

`0` | `1` | `0` | X = (0 ⊕ 1) ⊕ 0 = 1 ⊕ 0 = 1 |

`0` | `1` | `1` | X = (0 ⊕ 1) ⊕ 1 = 1 ⊕ 1 = 0 |

`1` | `0` | `0` | X = (1 ⊕ 0) ⊕ 0 = 1 ⊕ 0 = 1 |

`1` | `0` | `1` | X = (1 ⊕ 0) ⊕ 1 = 1 ⊕ 1 = 0 |

`1` | `1` | `0` | X = (1 ⊕ 1) ⊕ 0 = 0 ⊕ 0 = 0 |

`1` | `1` | `1` | X = (1 ⊕ 1) ⊕ 1 = 0 ⊕ 1 = 1 |