XNOR Gate: Properties and Applications

XNOR gate or equivalence gate operates on the principle of outputting a high signal when the number of high inputs is even. It can be used to implement complex functions when combined with other logic gates, facilitating the development of intricate digital circuits.

In this article, we will be studying XNOR gate, its properties, implementation and applications.

Table of Contents

• What is XNOR gate?
• Truth Table
• Properties
• Implementation
• Applications

What is XNOR gate?

An XNOR gate (Exclusive NOR gate), also known as an equivalence gate, is a digital logic gate that provides true or high signal (usually represented as 1) only when the number of true inputs is even. In the context of a two-input gate, it gives a high output when both inputs are either 0 or 1, i.e., when the inputs are equal. It is essentially the complement of the XOR (Exclusive OR) gate.

The mathematical representation of a two-input XNOR logic gate can be given as:

Here, “⊙” is the symbol representing the XNOR operation, “A” and “B” are inputs, and “Y” refers to output.

Truth table of XNOR Logic Gate

A two-input XNOR logic gate is as follows:

A	B	Output
0	0	1
0	1	0
1	0	0
1	1	1

This gate is utilized in various digital circuits for functions such as parity generation and checking, and in the construction of arithmetic circuits like adders and multipliers. It is implemented using a combination of other basic gates like AND, OR, and NOT, or using universal logic gates like NAND and NOR. It’s a fundamental component in digital electronics, facilitating the development of complex digital systems.

Properties of XNOR Gate

The following are the properties of the XNOR gate:

• Commutative Property: This gate is commutative, meaning that the order of the inputs does not affect the output. 
• Associative Property: The gate is associative, which allows grouping of inputs in any manner without changing the output.
• Identity Element: The identity element for the gate is 1. When any input is XNORed with 1, it returns the complement of the input, i.e., 
• Complement Property: This gate exhibits the complement property, where an input XNORed with its complement yields a low output (0).
• Idempotent Law: According to this law, an input XNORed with itself will yield a high output (1).
• Universal Gate: This gate can function as a universal gate, meaning it can be used to implement any kind of digital logic gate, including itself.
• Symmetry: The XNOR gate is symmetric, implying that the outputs remain the same if the inputs are swapped.
• Functionality as an Equivalence Gate: This gate serves as an equivalence gate, outputting a high signal when the inputs are equal, making it useful in circuits requiring comparison operations.
• Realization using Other Gates: This logic gate can be realized using combinations of other basic gates (AND, OR, NOT) or universal gates (NAND, NOR), showcasing its versatility in circuit design.
• Use in Error Detection and Correction: Due to its properties, the XNOR gate is commonly used in error detection and correction schemes, particularly in the construction of parity generators and checkers.

Implementation

Using Basic Gates (AND, OR, NOT)

An XNOR logic gate can be synthesized using basic gates in the following manner:

This equation demonstrates how the XNOR function can be achieved through a combination of AND, OR, and NOT gates, illustrating its compatibility with other basic gates in circuit design.

Using NAND or NOR Gates

The XNOR logic gate can also be realized using either NAND or NOR gates, which are known as universal gates. This implementation showcases the gate’s versatility and its ability to integrate seamlessly into various circuit designs, facilitating the creation of complex digital systems.

CMOS Implementation

In modern digital circuits, the gate can be implemented using Complementary Metal-Oxide-Semiconductor (CMOS) technology. This approach utilizes a combination of PMOS and NMOS transistors to achieve energy-efficient and high-speed operation, making it a preferred choice for contemporary digital systems.

Applications of XNOR Gate

Following are the applications of XNOR logic gate: