# Bitwise XOR, Computations, and Examples

A Bitwise XOR is a binary operation that takes two-bit patterns of equal length and performs the logical exclusive OR operation on each corresponding bits pair. Each position’s result is 0 if both bits are 0 or if both bits are 1. Otherwise, the result is 1.

Here, we will discuss the '^' operator in more detail.

## Introduction

A Bitwise XOR is a binary operation that takes two-bit patterns of equal length and performs the logical exclusive OR operation on each corresponding bits pair. Each position’s result is 0 if both bits are `0` or if both bits are `1`. Otherwise, the result is 1.

## Bitwise XOR

The Bitwise XOR operator does the following:

• It is a binary operator that takes two numbers.
• When we do Bitwise `^` of these two numbers, it considers the binary representation of these two numbers.
• Bitwise XOR compares bit by bit in binary representation, and whatever binary representation you get, the corresponding Integer is returned as an output.

The integer data type takes `4` bytes in C, C++, and Java programming languages.

``4 Bytes = 4 * (8 bits) = 32 bits. {1 Byte = 8 bits}``

For simplicity, we’ll represent these in 16-bit instead of 32-bit binary.

``````a = 12
b = 10
---------------------------------
a in binary : 0000 0000 0000 1100
b in binary : 0000 0000 0000 1010
---------------------------------
a ^ b       : 0000 0000 0000 0110
---------------------------------``````

The `^` operation happens from the rightmost bit traversing towards the leftmost bit in the 32-bit binary representation.

## Illustration

Let’s visualize the steps below:

Step #1:

``````a = 12
b = 10
---------------------------------
a in binary : 0000 0000 0000 1100
b in binary : 0000 0000 0000 1010
---------------------------------
a ^ b       :                   0
---------------------------------``````

Step #2:

``````a = 12
b = 10
---------------------------------
a in binary : 0000 0000 0000 1100
b in binary : 0000 0000 0000 1010
---------------------------------
a ^ b       :                  10
---------------------------------``````

Step #3:

``````a = 12
b = 10
---------------------------------
a in binary : 0000 0000 0000 1100
b in binary : 0000 0000 0000 1010
---------------------------------
a ^ b       :                 110
---------------------------------``````

Step #4:

``````a = 12
b = 10
---------------------------------
a in binary : 0000 0000 0000 1100
b in binary : 0000 0000 0000 1010
---------------------------------
a ^ b       : 0000 0000 0000 0110
---------------------------------``````

## Code

Below is the code representation of the `^` operator.

### Java

``````class XOROperation {
public static void main( String args[] ) {
int x = 12;
int y = 10;
System.out.println("Bitwise XOR of (x , y) is : " + (x ^ y)); // yields to 6
}
}``````

### Python

``````x=12
y=10
print("Bitwise XOR of (x,y) is : ",(x^y))``````

### JavaScript

``````const XOROperation = (x, y) => x ^ y;

const x = 12;
const y = 10;

console.log (`Bitwise XOR of (x , y) is : \${XOROperation (x, y)}`);
``````

### C++

``````#include <iostream>

using namespace std;

int main() {
int x = 12, y = 10;
cout << "Bitwise XOR of (x,y) is : " << (x ^ y);
return 0;
}``````

### TypeScript

``````const XOROperation = (x: number, y: number): number => x ^ y;

const x: number = 12;
const y: number = 10;

console.log(`Bitwise XOR of (x , y) is : \${XOROperation(x, y)}`);
``````

In the following lessons, we will apply the Bitwise approach to solve a few problems with XOR.

Let’s jump into our first problem using the Bitwise `^` operator in the next lesson.

Bit ManipulationData Structures and Algorithms

Gopi is an engineering leader with 12+ of experience in full-stack development—a specialist in Java technology stack. He worked for multiple startups, the European govt, and FAANG in India and Europe.

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