# Logic Gates: The XOR Gate

Document Reference: TN201009006 - Rev: 4.14 - Last Update: 14-11-2020 03:57 GMT - Downloaded: 13-Apr-2024 00:13 GMT

## A standard XOR (Exclusive-OR) 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 high output.

### XOR Gate Symbols

The inputs (`A, B`) of an XOR gate are on the left, and the output (`X`) is on the right of the logic XOR gate symbol.

Distinctive ShapeRectangular ShapeDIN Shape (Historic)

### XOR Gate Truth Tables

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

`A``B``X`
`0``0``0`
`0``1``1`
`1``0``1`
`1``1``0`

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

`A``B``C``X`
`0``0``0``0`
`0``0``1``1`
`0``1``0``1`
`0``1``1``0`
`1``0``0``1`
`1``0``1``0`
`1``1``0``0`
`1``1``1``1`

### XOR Gate Test-It

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

### XOR Gate Logical Expressions

#### Word Equation

`X = A XOR B`

#### Boolean Algebra

In boolean algebra the plus sign with a circular border (`⊕`) stands for the XOR operation, e.g.:

`X = A ⊕ B`

Alternative notation:     `X = A ∨ B`

`A``B``X = A ⊕ B`
`0``0``X = 0 ⊕ 0 = 0`
`0``1``X = 0 ⊕ 1 = 1`
`1``0``X = 1 ⊕ 0 = 1`
`1``1``X = 1 ⊕ 1 = 0`

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

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