# Logical Gates: The AND Gate

Document Reference: TN201009002 - Rev: 4.14 - Last Update: 14-11-2020 03:18 GMT - Downloaded: 22-Jun-2024 17:16 GMT

## 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 ShapeRectangular ShapeDIN 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`.

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