XNOR gate
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XNOR gate truth table  

Input  Output  
A  B  A XNOR B 
0  0  1 
0  1  0 
1  0  0 
1  1  1 
Logical connectives  



Related concepts  
Applications  
Category  
The XNOR gate (sometimes ENOR, EXNOR, NXOR, XAND and pronounced as Exclusive NOR) is a digital
The algebraic notation used to represent the XNOR operation is . The algebraic expressions and 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
Both the TTL
Datasheets are readily available in most datasheet databases and suppliers.
Implementation
ANDORInvert logic
An XNOR gate can be implemented using a NAND gate and an ORANDInvert gate, as shown in the following picture. ^{[3]} This is based on the identity
An alternative, which is useful when inverted inputs are also available (for example from a

XNOR implemention using a NAND and an OAI gate

XNOR implementation using a 22AOI gate with normal and inverted inputs
CMOS
CMOS implementations based on the OAI logic above can be realized with 10

An XNORgate in CMOS using a NAND and an ORANDInvert gate

An XNOR gate in CMOS using both normal and inverted inputs
Pinout
Both the 4077 and 74x266 devices (SN74LS266, 74HC266, 74266, etc.) have the same pinout diagram, as follows:
Pinout diagram of the 74HC266N, 74LS266 and CD4077 quad XNOR plastic
 Input A1
 Input B1
 Output Q1 (high if and only if A1 and B1 have the same logic level)
 Output Q2
 Input B2
 Input A2
 V_{ss} (GND) common power and signal ground pin
 Input A3
 Input B3
 Output Q3
 Output Q4
 Input B4
 Input A4
 V_{dd} for CMOS (V_{cc} for TTL) positive power supply (see datasheets for acceptable voltage ranges)
Alternatives
If a specific type of gate is not available, a circuit that implements the same function can be constructed from other available gates. A circuit implementing an XNOR function can be trivially constructed from an XOR gate followed by a NOT gate. If we consider the expression , we can construct an XNOR gate circuit directly using AND, OR and NOT gates. However, this approach requires five gates of three different kinds.
As alternative, if different gates are available we can apply Boolean algebra to transform as stated above, and apply
An XNOR gate circuit can be made from four NOR gates. In fact, both NAND and NOR gates are socalled "universal gates" and any logical function can be constructed from either NAND logic or NOR logic alone. If the four NOR gates are replaced by NAND gates, this results in an XOR gate, which can be converted to an XNOR gate by inverting the output or one of the inputs (e.g. with a fifth NAND gate).
Desired gate  NAND construction  NOR construction 

An alternative arrangement is of five NAND gates in a topology that emphasizes the construction of the function from , noting from
Desired gate  NAND construction  NOR construction 

For the NAND constructions, the lower arrangement offers the advantage of a shorter propagation delay (the time delay between an input changing and the output changing). For the NOR constructions, the upper arrangement requires fewer gates.
From the opposite perspective, constructing other gates using only XNOR gates is possible though XNOR is not a fully universal logic gate. NOT and XOR gates can be constructed this way.
More than two inputs
Although other gates (OR, NOR, AND, NAND) are available from manufacturers with three or more inputs per gate, this is not strictly true with XOR and XNOR gates. However, extending the concept of the
Input  Output  

A  B  C  Q 
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 
This is effectively Q = NOT ((A XOR B) XOR C). Another way to interpret this is that the output is true if an even number of inputs are true. It does not implement a logical "equivalence" function, unlike twoinput XNOR gates.
See also
 AND gate
 OR gate
 NOT gate
 NAND gate
 NOR gate
 XOR gate
 Kronecker delta function
 Logical biconditional
 If and only if
References
 ^ "ExclusiveNOR Gate Tutorial". Retrieved 6 May 2018.
 ^ "XNOR Logic Gates". Retrieved 6 May 2018.
 ^ Fischer, P. "Aussagenlogik und Gatter" (PDF). University of Heidelberg. Retrieved 20240121.