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 Shape | Rectangular Shape | DIN Shape (Historic) |
---|---|---|
XNOR Gate Test-It
To test the gate, click the switch symbols in the image below.
XNOR Gate Truth Tables
Truth Table for XNOR Gate with 2 Inputs
A | B | X |
---|---|---|
0 | 0 | 1 |
0 | 1 | 0 |
1 | 0 | 0 |
1 | 1 | 1 |
Truth Table for XNOR Gate with 3 Inputs
A | B | C | X |
---|---|---|---|
0 | 0 | 0 | 1 |
0 | 0 | 1 | 0 |
0 | 1 | 0 | 0 |
0 | 1 | 1 | 1 |
1 | 0 | 0 | 0 |
1 | 0 | 1 | 1 |
1 | 1 | 0 | 1 |
1 | 1 | 1 | 0 |
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 = 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 = 0 = 1 |
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 = 1 |
0 | 0 | 1 | X = (0 ⊕ 0) ⊕ 1 = 0 ⊕ 1 = 1 = 0 |
0 | 1 | 0 | X = (0 ⊕ 1) ⊕ 0 = 1 ⊕ 0 = 1 = 0 |
0 | 1 | 1 | X = (0 ⊕ 1) ⊕ 1 = 1 ⊕ 1 = 0 = 1 |
1 | 0 | 0 | X = (1 ⊕ 0) ⊕ 0 = 1 ⊕ 0 = 1 = 0 |
1 | 0 | 1 | X = (1 ⊕ 0) ⊕ 1 = 1 ⊕ 1 = 0 = 1 |
1 | 1 | 0 | X = (1 ⊕ 1) ⊕ 0 = 0 ⊕ 0 = 0 = 1 |
1 | 1 | 1 | X = (1 ⊕ 1) ⊕ 1 = 0 ⊕ 1 = 1 = 0 |