Document Reference: TN201009005 - Rev: 4.14 - Last Update: 14-11-2020 03:50 GMT - Downloaded: 16-Jan-2021 02:01 GMT

## A NOR gate is a logic gate with two or more inputs and one output. All inputs states must be low to produce a high output.

### NOR Gate Symbols

The inputs (`A, B`

) of an NOR gate are on the left, and the output (`X`

) is on the right of the logic NOR gate symbol.

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

### NOR Gate Truth Tables

#### Truth Table for NOR Gate with 2 Inputs

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

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

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

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

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

#### Truth Table for NOR Gate with 3 Inputs

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

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

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

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

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

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

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

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

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

### NOR Gate Test-It

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

### NOR Gate Logical Expressions

#### Word Equation

`X = NOT (A OR B)`

#### Boolean Algebra

In boolean algebra the plus sign (`+`

) combined with the overbar sign (` `

) stands for the NOR operation, e.g.:

`X = A + B`

Alternative notations: `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 = 1 = 0` |

`A` | `B` | `C` | `X = A + B + C` |
---|---|---|---|

`0` | `0` | `0` | X = 0 + 0 + 0 = 0 = 1 |

`0` | `0` | `1` | X = 0 + 0 + 1 = 1 = 0 |

`0` | `1` | `0` | X = 0 + 1 + 0 = 1 = 0 |

`0` | `1` | `1` | X = 0 + 1 + 1 = 1 = 0 |

`1` | `0` | `0` | X = 1 + 0 + 0 = 1 = 0 |

`1` | `0` | `1` | X = 1 + 0 + 1 = 1 = 0 |

`1` | `1` | `0` | X = 1 + 1 + 0 = 1 = 0 |

`1` | `1` | `1` | X = 1 + 1 + 1 = 1 = 0 |