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XNOR gate

INPUT OUTPUT
A B A XNOR B
0 0 1
0 1 0
1 0 0
1 1 1

The XNOR gate (sometimes spelled "exnor" or "enor" and rarely written NXOR) is a digital logic gate whose function is the logical complement of the exclusive OR (XOR) gate. The two-input version implements logical equality, behaving according to the truth table to the right. 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.

Symbols

There are 2 symbols for XNOR gates: the 'distinctive' symbol and the 'rectangular' symbol. For more information see Logic Gate Symbols. The ANSI symbol for the XNOR gate is a standard XOR gate with an inversion bubble connected.

"Distinctive" XNOR symbol
"Rectangular" XNOR Symbol

The XNOR gate with inputs A and B implements the logical expression <math>A \cdot B + \overline{A} \cdot \overline{B}</math>.

Hardware description and pinout

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. Both include four independent, two-input, XNOR gates. The pinout diagram is as follows:

File:XNOR Pinout.png
Pinout diagram of a 74266 Quad XNOR DIP-format IC
 1  Input A1
 2  Input B1
 3  Output Q1
 4  Output Q2
 5  Input B2
 6  Input A2
 7  Vss
 8  Input A3
 9  Input B3
 10 Output Q3
 11 Output Q4
 12 I
 >

This device is available from most semiconductor manufacturers such as NXP. It is usually available in both through-hole DIP and SOIC format. Datasheets are readily available in most datasheet databases. DIL is a Dual In Line package, and SIL is a Single In Line package.

Alternatives

If no specific XNOR gates are available, one can be made from four NOR gates or five NAND gates in the configurations shown below. In fact, any logic gate can be made from combinations of only NAND gates or only NOR gates.

File:XNOR using NOR.svg
XNOR gate constructed using only NOR gates
File:XNOR Using NAND.png
XNOR gate constructed using only NAND gates

XNOR gate can be made with 3 gates (1x OR & 2x NAND gates)

File:Xnor.png
XNOR Gate made up of 3 gates

See also

References

it:Algebra di Boole#XNOR