# Exclusive-OR Gate with EX-OR Gate Truth Table

Last Updated on October 26, 2023 by Electricalvolt

The EX-OR gate also known as the Exclusive-OR gate is widely used in digital circuits. The XOR gate outputs high when its inputs are at different logic levels with respect to each other. For the two input XOR gates, the gate output is high if the input is either 01 or 10, and the gate output is low if the input is either 11 or 00.

This article describes Exclusive OR Gate along with its definition, logic symbol, truth table, and equivalent AOI circuit. So, let’s begin with the basics of Ex-OR Gate.

## What is an Exclusive OR Gate or EX–OR Gate?

Exclusive-OR Gate, also known as EX OR Gate or XOR Gate, is a type of derived logic gate that is obtained by combining standard logic gates. It is a logic gate having only two inputs and one output.

In the case of the XOR gate, the output is HIGH (Logic 1) only if its two inputs are dissimilar and the output is LOW (Logic 0) if its two inputs are the same.

## Ex–OR Gate symbol

The standard logic symbol of an Ex-OR gate is shown in the following figure.

## EX-OR Gate Truth Table

The truth table of a logic gate is a table that specifies the relationship between input combinations and output of the logic gate. The truth table of an XOR gate is given below:

## Boolean Expression of XOR Gate

Boolean expression is a logic function that provides the relationship between the input and output of a logic gate. The Boolean expression of an EX-OR gate is given below:

Therefore, the operation of the XOR gate as per the Boolean function will be as follows:

• When A = 0 and B = 0, the output Y = 1 . 0 + 0 . 1 = 0.
• When A = 0 and B = 1, the output Y = 1 . 0 + 1 . 1 = 1.
• When A = 1 and B = 0, the output Y = 0 . 0 + 1 .1 = 1.
• When A = 1 and B = 1, the output Y = 0 .1 + 1 .0 = 0.

## Equivalent Logic Circuit of XOR Gate

Since the XOR gate is a type of derived logic gate with 2 inputs. Hence, it can be implemented using AND-OR-Inverter (AOI) gates. The realization of an EX-OR gate using AOI logic is shown below.

The output of this logic circuit will be HIGH only if its two inputs (A and B) are different, either 0 and 1 or 1 and 0. If the two inputs are the same, i.e. 0 and 0 or 1 and 1, then the output will be LOW. Hence, this logic circuit is equivalent to an XOR gate.

## XOR Gate ICs in TTL and CMOS Logic

A list of EX-OR gate ICs in TTL (Transistor-Transistor Logic) and CMOS (Complementary Metal Oxide Semiconductor) Logic is given below:

## Applications of EX-OR Gate

Exclusive OR gate (XOR gate) is widely used in a variety of digital electronic circuits. Some key applications of XOR gates are listed below:

• Used to implement a pseudo-random code generator.
• They can also be used in logic devices like PLCs, to compare two logic states and make decisions.
• EX-OR gates are used to implement various types of computational circuits.

Hence, this is all about Exclusive OR Gate (XOR gate), its truth table, and applications