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The XNOR gate, also known as the exclusive NOR or equivalence gate, is a digital logic gate that outputs '1' when inputs are equal. It is crucial for parity checking and data comparison in digital circuits. The gate's operation is defined by the Boolean expression A·B + ¬A·¬B, integrating NOT, AND, and OR operations. Its truth table and applications in digital systems highlight its importance in computing and digital logic design.

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## Introduction to XNOR Gate

### Definition of XNOR Gate

The XNOR gate is a type of digital logic gate that outputs a high level when the inputs are equal

### Distinction from Other Logic Gates

Comparison to XOR Gate

The XNOR gate's output is the complement of the XOR gate's output

Significance in Digital Systems

The XNOR gate is essential in digital circuits that perform functions such as parity checking and data comparison

### Boolean Expression and Truth Table

The operation of the XNOR gate can be understood through its Boolean expression and truth table, which show its behavior as an equivalence function

## Multi-Input XNOR Gate

### Extension to Gates with Multiple Inputs

The concept of the XNOR gate can be extended to gates with multiple inputs, such as a 3-input XNOR gate

### Rule for Multi-Input XNOR Gate

The output is high when there is an even number of high inputs

### Applications of Multi-Input XNOR Gate

Multi-Input XNOR gates are used in digital systems for error detection, data comparison, and equality operations

## Importance of XNOR Gate in Digital Systems

### Role in Parity Checking and Data Comparison

XNOR gates are critical in digital systems for functions such as parity checking and data comparison

### Practicality in Computing

XNOR gates serve as a basic yet essential component in various digital processes, such as determining an even number of TRUE values in a set of boolean variables

### Mastery in Computer Science and Digital Logic Design

Understanding the XNOR gate is crucial for those studying computer science and digital logic design

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