## A AND gate is a logic gate with two or more inputs and one output. All input states must be high to produce a high output.

### AND Gate Symbols

The inputs (`A, B`

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

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

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

### AND Gate Truth Tables

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

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

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

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

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

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

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

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

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

`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` | `1` |

### AND Gate Test-It

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

### AND Gate Logical Expressions

#### Word Equation

`X = A AND B`

#### Boolean Algebra

In boolean algebra the multiplication sign (`⋅`

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

`X = A ⋅ B`

or simplified: `X = AB`

Alternative notations: `X = A ∧ B`

or `X = A & B`

`A` | `B` | `X = AB` |
---|---|---|

`0` | `0` | `X = 0 ⋅ 0 = 0` |

`0` | `1` | `X = 0 ⋅ 1 = 0` |

`1` | `0` | `X = 1 ⋅ 0 = 0` |

`1` | `1` | `X = 1 ⋅ 1 = 1` |

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

`0` | `0` | `0` | X = 0 ⋅ 0 ⋅ 0 = 0 |

`0` | `0` | `1` | X = 0 ⋅ 0 ⋅ 1 = 0 |

`0` | `1` | `0` | X = 0 ⋅ 1 ⋅ 0 = 0 |

`0` | `1` | `1` | X = 0 ⋅ 1 ⋅ 1 = 0 |

`1` | `0` | `0` | X = 1 ⋅ 0 ⋅ 0 = 0 |

`1` | `0` | `1` | X = 1 ⋅ 0 ⋅ 1 = 0 |

`1` | `1` | `0` | X = 1 ⋅ 1 ⋅ 0 = 0 |

`1` | `1` | `1` | X = 1 ⋅ 1 ⋅ 1 = 1 |

#### AND Gate Circuit with Two Relays

By default, and without a signal on `Input A`

and `Input B`

, the `Output X`

will be pulled to `LOW`

(`0`

) via `R1`

.

A 12VDC (`1/HIGH`

) signal on terminal `Input A`

will light `LEDA`

and energize `RelayA`

. Energizing `RelayA`

will allow 12VDC to pass via switched contact `A`

from the terminal `12VDC IN`

to switched contact `B`

.

A 12VDC (`1/HIGH`

) signal on terminal `Input B`

will light `LEDB`

and energize `RelayB`

. Energizing `RelayB`

will allow 12VDC to pass via switched contact `B`

and via `DX`

from the switched contact `A`

to the terminal `Output X`

.

`LEDX`

will light and `Output X`

will be `HIGH`

as soon as 12VDC is allowed to pass via switched contacts `A`

and `B`

.