# XOR Gate – Definition, Symbol, Diagram

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The XOR gate or Exclusive-OR gate is achieved by combining standard logic gates. XOR gate is used extensively in error detection circuits, arithmetic logic circuits, and computational logic comparators.

The Exclusive OR gate gives the output only if its two inputs are not similar, namely if one of them is one (high) and the other is zero (low). In this article, we will learn about the Exclusive-OR Gate (XOR), its logical symbol, truth table, circuit diagram, applications and various properties.

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Table of content

## What is the XOR Gate?

An XOR gate is a two-input single-output logic gate whose output is assumed to be HIGH(one) only when one of its inputs is HIGH(one).

### XOR Gate Symbol

The logic symbol for a two-input XOR gate is shown below:

### XOR Gate Expression

If input variables are represented by A and B, then the logical expression for output is

_ _
Y = AB + AB = A ⊕ B

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## What is the Truth Table of XOR Gate?

Practically three or more input XOR gate does not exist. But when more than two variables are XOR, a number of two input XOR gates are cascaded where the output is assumed to be ‘1’ when the odd number of input variables is ‘1’.
The XOR gate is also known as the odd number of 1’s detector in the input.

Figure: XOR Gate Truth Table

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## Application of XOR Gate

The most important application of the XOR gate is in parity generation and detection. Hence, it is also known as the staircase switch. The switching circuit of the XOR gate is shown.

The Exclusive OR gate follows both commutative and associative law.

## Enable and Disable Inputs

For an XOR Gate

For control = 0;

 A Control Y 0 0 0 1 0 1

Thus, the EX-OR gate acts as a buffer for controlled input of logic ‘0’.
For control = 1;

 A Control Y 0 1 1 1 1 0

Thus, the XOR gate acts as an inverter for logic ‘1’ control input.

## Properties of XOR Gate

A ⊕ A = 0

A ⊕ 0 = A

A ⊕ A̅ = 1

A ⊕ 1 = A̅

A ⊕ A ⊕ A = A

The internal diagram of the EXOR or XOR gate is as follows:

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