XNOR gate
logic gate
The XNOR gate (sometimes ENOR, EXNOR, NXOR, XAND and pronounced as exclusive NOR) is a digital logic gate whose function is the logical complement of the exclusive OR (XOR) gate. It is equivalent to the logical connective (
↔
{\displaystyle \leftrightarrow }
) from mathematical logic, also known as the material biconditional. The two-input version implements logical equality, behaving according to the truth table to the right, and hence the gate is sometimes called an "equivalence gate". A high output (1) results if both of the inputs to the gate are the same. If one but not both inputs are high (1), a low output (0) results.
The algebraic notation used to represent the XNOR operation is
S
=
A
⊙
B
{\displaystyle S=A\odot B}
. The algebraic expressions
(
A
+
B
¯
)
⋅
(
A
¯
+
B
)
{\displaystyle (A+{\overline {B}})\cdot ({\overline {A}}+B)}
and
A
⋅
B
+
A
¯
⋅
B
¯
{\displaystyle A\cdot B+{\overline {A}}\cdot {\overline {B}}}
both represent the XNOR gate with inputs A and B.
Symbols
There are two symbols for XNOR gates: one with distinctive shape and one with rectangular shape and label. Both symbols for the XNOR gate are that of the XOR gate with an added inversion bubble.
Hardware description
XNOR gates are represented in most TTL and CMOS IC families. The standard 4000 series CMOS IC is the 4077, and the TTL IC is the 74266 (although an open-collector implementation).
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