XOR Gate - Definition, Symbol, Diagram

By Priyanshu Vaish|Updated : September 30th, 2022

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:

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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.

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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.

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The Exclusive OR gate follows both commutative and associative law.

Enable and Disable Inputs

For an XOR Gate
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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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FAQs on XOR Gate Truth Table

  • The XOR gate is used extensively in digital data processing circuits and is known as the Exclusive-OR gate. The XOR gate has a high output only when an odd number of inputs are high. For example, for the two input XOR gates, the output will be high when the set of input is either 01 or 10.

  • The ability of the XOR gate to compare two logic levels and give an output dependent upon the input condition is advantageous in many computational circuits. Though it is not a basic logic gate, its versatility and usefulness have made it into a standard logic gate.

  • XOR gate (sometimes called as EOR, EXOR, and pronounced as the Exclusive OR) is the digital logic gate that results in true (either 1 or HIGH) output when the number of true inputs is the odd count. An XOR gate implements the exclusive OR that is a true output result if one of the inputs of the gate inputs is true.

  • The 2-input XOR gate is also recognized as the Inclusive-OR gate because when both inputs, say A and B, are set to logic one(high), the output appears as "0" or low that is, in the XOR function, the logic output "1" is achieved only when either A = " 1″ or B = " 1″ but not both together at the same point.

  • An exclusive OR gate (XOR gate) is the digital logic gate implemented using the transistors to act as an electronic switch used in implementing Boolean functions. It is built by combining standard logic gates such as the common NAND and NOR gates in order to produce the more complex function of this gate.

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