# Logic Gates: The NOR Gate

Document Reference: TN201009005 - Rev: 4.14 - Last Update: 14-11-2020 03:50 GMT - Downloaded: 27-May-2024 02:42 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 ShapeRectangular ShapeDIN 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

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