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Logic Gates: The XOR Gate

Document Reference: TN201009006 - Rev: 4.14 - Last Update: 14-11-2020 03:57 GMT - Downloaded: 26-Nov-2020 00:47 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)
Distinctive Symbol of an XOR logic-gate.Rectangle Symbol of an XOR logic-gate.DIN40700 Symbol of an XOR logic-gate.

XOR Gate Truth Tables

Truth Table for XOR Gate with 2 Inputs

ABX
000
011
101
110

Truth Table for XOR Gate with 3 Inputs

ABCX
0000
0011
0101
0110
1001
1010
1100
1111

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 = AB

Alternative notation:     X = A B

ABX = AB
00X = 0 ⊕ 0 = 0
01X = 0 ⊕ 1 = 1
10X = 1 ⊕ 0 = 1
11X = 1 ⊕ 1 = 0

Note: X = ABC = (AB) ⊕ C = A ⊕ (BC)

ABCX = (AB) ⊕ C
000X = (0 ⊕ 0) ⊕ 0 = 0 ⊕ 0 = 0
001X = (0 ⊕ 0) ⊕ 1 = 0 ⊕ 1 = 1
010X = (0 ⊕ 1) ⊕ 0 = 1 ⊕ 0 = 1
011X = (0 ⊕ 1) ⊕ 1 = 1 ⊕ 1 = 0
100X = (1 ⊕ 0) ⊕ 0 = 1 ⊕ 0 = 1
101X = (1 ⊕ 0) ⊕ 1 = 1 ⊕ 1 = 0
110X = (1 ⊕ 1) ⊕ 0 = 0 ⊕ 0 = 0
111X = (1 ⊕ 1) ⊕ 1 = 0 ⊕ 1 = 1

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