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XNOR gate

technology Maturity 11-13 Next article →

An XNOR gate is a fundamental component used in digital logic systems. It is also known by several other names, such as ENOR, EXNOR, NXOR, or XAND. In mathematical logic, the XNOR gate represents the material biconditional. This means it functions as a logical connective that evaluates the relationship between two statements. Because it compares two inputs to see if they match, it is often called an "equivalence gate."

XNOR ANSI Labelled
XNOR ANSI Labelled

The mechanism of a two-input XNOR gate is based on logical equality. The gate receives two separate signals, which are called inputs, labeled A and B. The gate produces a high output, represented by the number 1, only if both inputs are identical. For example, if both input A and input B are high, the output will be high. If both inputs are low, the output will also be high. However, if one input is high and the other is low, the gate produces a low output, or 0.

3 gate XNOR
3 gate XNOR

Engineers can implement XNOR logic using several different hardware configurations. One simple method is to use an XOR gate followed by a NOT gate, which inverts the result. Another method uses a combination of AND, OR, and NOT gates. While a direct construction using these three types of gates requires five separate gates, Boolean algebra and de Morgan's Law can reduce this. By applying these mathematical rules, a circuit can be built using only three gates.

XNOR from NAND
XNOR from NAND

There are also ways to build XNOR gates using universal gates. Universal gates are types of gates, like NAND or NOR, that can be used to create any other logical function. An XNOR gate can be constructed using exactly four NOR gates. It can also be built using a specific arrangement of five NAND gates. This five-NAND topology is useful because it can offer a shorter propagation delay. Propagation delay is the time it takes for an input change to result in an output change.

XNOR from NAND 2
XNOR from NAND 2

Different circuit designs offer different advantages depending on the needs of the machine. For instance, some NOR-based constructions require fewer gates to function. This can save space on a circuit board. Other designs might prioritize speed or the availability of certain parts. In CMOS technology, which is a common way to build chips, an XNOR gate can be realized with 10 transistors. If the design uses both normal and inverted inputs, it might use 8 transistors. If inverters must be added to the circuit, the count rises to 12 transistors.

XNOR from NOR
XNOR from NOR

Various semiconductor manufacturers produce XNOR gates in different integrated circuit families. The 4000 series CMOS IC family includes the 4077 chip, which contains four independent, two-input XNOR gates. The TTL family includes the 74266, which is an open-collector implementation. Another older device, the 74S135, was able to implement four two-input XOR/XNOR gates or two three-input XNOR gates. Companies like Texas Instruments and NXP manufacture these components. They are typically available in formats like through-hole DIP or SOIC-14 and TSSOP-14.

XNOR from NOR 2
XNOR from NOR 2

While two-input gates are common, the concept can be extended to more inputs. A three-input version, such as that found in the SN74S135, follows a different rule. In this case, the output is high if an even number of inputs are high. This is expressed by the formula Q = NOT ((A XOR B) XOR C). Unlike the two-input version, this three-input version does not implement a simple logical equivalence function. Instead, it serves as a way to process multiple signals through a single logical process.

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File:3 gate XNOR.svg
3 gate XNOR.svg
File:XNOR ANSI Labelled.svg
XNOR ANSI Labelled.svg
File:XNOR from NAND.svg
XNOR from NAND.svg
File:XNOR from NOR.svg
XNOR from NOR.svg
File:XNOR from NAND 2.svg
XNOR from NAND 2.svg
File:XNOR from NOR 2.svg
XNOR from NOR 2.svg
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