## A standard XNOR (Exclusive-NOR) 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 low output.

### XNOR Gate Symbols

The inputs (`A, B`

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

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

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

### XNOR Gate Test-It

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

### XNOR Gate Truth Tables

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

### XNOR Gate Logical Expressions

#### Word Equation

`X = A XNOR B`

#### Boolean Algebra

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

) combined with the overbar sign (` `

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

`X = A ⊕ B`

Alternative notation: `X = A ∨ B`

or `X = A ∨ B`

or `X = A ⊙ B`

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

`0` | `0` | `X = 0 ⊕ 0 = 0 = 1` |

`0` | `1` | `X = 0 ⊕ 1 = 1 = 0` |

`1` | `0` | `X = 1 ⊕ 0 = 1 = 0` |

`1` | `1` | `X = 1 ⊕ 1 = 0 = 1` |

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 = 1 |

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

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

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

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

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

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

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