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Logic Gates: The XNOR Gate

Document Reference: TN201009007 - Rev: 4.15 - Last Update: 14-11-2020 12:05 GMT - Downloaded: 26-Nov-2020 00:28 GMT

A standard XNOR (Exclusive-NOR) 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 low output.

XNOR Gate Symbols

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

Distinctive ShapeRectangular ShapeDIN Shape (Historic)
Distinctive Symbol of an XNOR logic-gate.Rectangle Symbol of an XNOR logic-gate.DIN40700 Symbol of an XNOR logic-gate.

XNOR Gate Test-It

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

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XNOR Gate Truth Tables

Truth Table for XNOR Gate with 2 Inputs

ABX
001
010
100
111

Truth Table for XNOR Gate with 3 Inputs

ABCX
0001
0010
0100
0111
1000
1011
1101
1110

XNOR Gate Logical Expressions

Word Equation

X = A XNOR B

Boolean Algebra

In boolean algebra the plus sign with a circular border () combined with the overbar sign ( ) stands for the XNOR operation, e.g.:

X = A ⊕ B

Alternative notation:     X = A  B     or     X = A B     or     X = AB

ABX = A ⊕ B
00X = 0 ⊕ 0 = 0 = 1
01X = 0 ⊕ 1 = 1 = 0
10X = 1 ⊕ 0 = 1 = 0
11X = 1 ⊕ 1 = 0 = 1

Note: X = A ⊕ B ⊕ C = (A ⊕ B) ⊕ C = A ⊕ (B ⊕ C)

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

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