Data Modelling & AI Data Structure & Algorithm

Find XOR of two number without using XOR operator

31 July 2024

7

Given two integers, find XOR of them without using the XOR operator, i.e., without using ^ in C/C++.

Examples :

Input:  x = 1, y = 2
Output: 3

Input:  x = 3, y = 5
Output: 6

A Simple Solution is to traverse all bits one by one. For every pair of bits, check if both are the same, set the corresponding bit like 0 in output, otherwise set it as 1.

C++

// C++ program to find XOR without using ^
#include <iostream>
using namespace std;
 
// Returns XOR of x and y
int myXOR(int x, int y)
{
    int res = 0; // Initialize result
     
    // Assuming 32-bit Integer 
    for (int i = 31; i >= 0; i--)                     
    {
       // Find current bits in x and y
       bool b1 = x & (1 << i);
       bool b2 = y & (1 << i);
        
        // If both are 1 then 0 else xor is same as OR
        bool xoredBit = (b1 & b2) ? 0 : (b1 | b2);          
 
        // Update result
        res <<= 1;
        res |= xoredBit;
    }
    return res;
}
 
// Driver program to test above function
int main()
{
   int x = 3, y = 5;
   cout << "XOR is " << myXOR(x, y);
   return 0; 
}

C

// C program to find XOR without using ^
#include <stdio.h>
#include <stdbool.h> //to use bool
 
// Returns XOR of x and y
int myXOR(int x, int y)
{
    int res = 0; // Initialize result
 
    // Assuming 32-bit Integer
    for (int i = 31; i >= 0; i--)
    {
       
        // Find current bits in x and y
        bool b1 = x & (1 << i);
        bool b2 = y & (1 << i);
 
        // If both are 1 then 0 else xor is same as OR
        bool xoredBit = (b1 & b2) ? 0 : (b1 | b2);
 
        // Update result
        res <<= 1;
        res |= xoredBit;
    }
    return res;
}
 
// Driver Code
int main()
{
    int x = 3, y = 5;
    printf("XOR is %d\n", myXOR(x, y));
    return 0;
}
 
// This code is contributed by phalashi.

Java

// Java program to find XOR without using ^
import java.io.*;
 
class GFG{
   
// Returns XOR of x and y
static int myXOR(int x, int y)
{
     
    // Initialize result
    int res = 0; 
 
    // Assuming 32-bit Integer 
    for(int i = 31; i >= 0; i--)                     
    {
         
        // Find current bits in x and y
        int b1 = ((x & (1 << i)) == 0 ) ? 0 : 1;  
        int b2 = ((y & (1 << i)) == 0 ) ? 0 : 1;  
 
        // If both are 1 then 0 else xor is same as OR
        int xoredBit = ((b1 & b2) != 0) ? 0 : (b1 | b2);          
 
        // Update result
        res <<= 1;
        res |= xoredBit;
    }
    return res;
}
 
// Driver Code
public static void main (String[] args)
{
    int x = 3, y = 5;
     
    System.out.println("XOR is " + myXOR(x, y));
}
}
 
// This code is contributed by math_lover

Python3

# Python3 program to find XOR without using ^
 
# Returns XOR of x and y
def myXOR(x, y):
    res = 0 # Initialize result
 
    # Assuming 32-bit Integer
    for i in range(31, -1, -1):
         
        # Find current bits in x and y
        b1 = x & (1 << i)
        b2 = y & (1 << i)
        b1 = min(b1, 1)
        b2 = min(b2, 1)
 
        # If both are 1 then 0 
        # else xor is same as OR
        xoredBit = 0
        if (b1 & b2):
            xoredBit = 0
        else:
            xoredBit = (b1 | b2)
 
        # Update result
        res <<= 1;
        res |= xoredBit
    return res
 
# Driver Code
x = 3
y = 5
print("XOR is", myXOR(x, y))
 
# This code is contributed by Mohit Kumar

C#

// C# program to find XOR
// without using ^
using System;
class GFG{
   
// Returns XOR of x and y
static int myXOR(int x, 
                 int y)
{    
  // Initialize result
  int res = 0; 
 
  // Assuming 32-bit int 
  for(int i = 31; i >= 0; i--)                     
  {
    // Find current bits in x and y
    int b1 = ((x & (1 << i)) == 0 ) ?
               0 : 1;  
    int b2 = ((y & (1 << i)) == 0 ) ? 
               0 : 1;  
 
    // If both are 1 then 0 else 
    // xor is same as OR
    int xoredBit = ((b1 & b2) != 0) ?
                     0 : (b1 | b2);          
 
    // Update result
    res <<= 1;
    res |= xoredBit;
  }
  return res;
}
 
// Driver Code
public static void Main(String[] args)
{
  int x = 3, y = 5;
  Console.WriteLine("XOR is " +
                     myXOR(x, y));
}
}
 
// This code is contributed by 29AjayKumar

Javascript

<script>
 
// JavaScript program to find XOR without using ^
 
// Returns XOR of x and y
function myXOR(x, y)
{
    let res = 0; // Initialize result
     
    // Assuming 32-bit Integer 
    for (let i = 31; i >= 0; i--)                     
    {
    // Find current bits in x and y
      let b1 = ((x & (1 << i)) == 0 ) ? 0 : 1;  
      let b2 = ((y & (1 << i)) == 0 ) ? 0 : 1;  
         
        // If both are 1 then 0 else xor is same as OR
        let xoredBit = (b1 & b2) ? 0 : (b1 | b2);         
 
        // Update result
        res <<= 1;
        res |= xoredBit;
    }
    return res;
}
 
// Driver program to test above function
 
let x = 3, y = 5;
document.write("XOR is " + myXOR(x, y));
 
// This code is contributed by Surbhi Tyagi.
 
</script>

Output

XOR is 6

Time Complexity: O(num), where num is the number of bits in the maximum of the two numbers.
Auxiliary Space: O(1)

Thanks to Utkarsh Trivedi for suggesting this solution.

A Better Solution can find XOR without using a loop.
1) Find bitwise OR of x and y (Result has set bits where either x has set or y has set bit). OR of x = 3 (011) and y = 5 (101) is 7 (111)
2) To remove extra set bits find places where both x and y have set bits. The value of the expression “~x | ~y” has 0 bits wherever x and y both have set bits.
3) bitwise AND of “(x | y)” and “~x | ~y” produces the required result.

Below is the implementation.

C++

// C++ program to find XOR without using ^
#include <iostream>
using namespace std;
 
// Returns XOR of x and y
int myXOR(int x, int y)
{
   return (x | y) & (~x | ~y);
}
 
// Driver program to test above function
int main()
{
   int x = 3, y = 5;
   cout << "XOR is " << myXOR(x, y);
   return 0; 
}

Java

// Java program to find
// XOR without using ^
import java.io.*;
 
class GFG 
{
 
// Returns XOR of x and y
static int myXOR(int x, int y)
{
    return (x | y) & 
           (~x | ~y);
}
 
// Driver Code
public static void main (String[] args) 
{
    int x = 3, y = 5;
    System.out.println("XOR is "+ 
                      (myXOR(x, y)));
}
}
 
// This code is contributed by ajit

Python3

# Python 3 program to 
# find XOR without using ^
 
# Returns XOR of x and y
def myXOR(x, y):
    return ((x | y) & 
            (~x | ~y))
 
# Driver Code
x = 3
y = 5
print("XOR is" , 
       myXOR(x, y))
 
# This code is contributed
# by Smitha

C#

// C# program to find
// XOR without using ^
using System;
 
class GFG
{
     
// Returns XOR of x and y
static int myXOR(int x, int y)
{
    return (x | y) & 
           (~x | ~y);
}
 
// Driver Code
static public void Main ()
{
    int x = 3, y = 5;
    Console.WriteLine("XOR is "+ 
                     (myXOR(x, y)));
}
}
 
// This code is contributed by m_kit

PHP

<?php
// PHP program to find 
// XOR without using ^
 
// Returns XOR of x and y
function myXOR($x, $y)
{
    return ($x | $y) & (~$x | ~$y);
}
 
// Driver Code
$x = 3;
$y = 5;
 
echo "XOR is " , myXOR($x, $y);
 
// This code is contributed by aj_36
?>

Javascript

<script>
// Javascript program to find XOR without using ^
 
// Returns XOR of x and y
function myXOR(x, y)
{
   return (x | y) & (~x | ~y);
}
 
// Driver program to test above function
   let x = 3, y = 5;
   document.write("XOR is " + myXOR(x, y));
 
// This code is contributed by subham348.
</script>

Output

XOR is 6

Time Complexity: O(1) i.e. simple calculation of arithmetic and bitwise operator.
Auxiliary Space: O(1)

Thanks to jitu_the_best for suggesting this solution.

Alternate Solution :

C++

// C++ program to find XOR without using ^
#include <iostream>
using namespace std;
 
// Returns XOR of x and y
int myXOR(int x, int y)
{
   return (x & (~y)) | ((~x )& y);
}
 
// Driver program to test above function
int main()
{
   int x = 3, y = 5;
   cout << "XOR is " << myXOR(x, y);
   return 0; 
}

Java

// Java program to find XOR without using ^
import java.io.*;
  
class GFG 
{
 
// Returns XOR of x and y
static int myXOR(int x, int y)
{
return (x & (~y)) | ((~x )& y);
}
 
// Driver Code
public static void main (String[] args) 
{
  
int x = 3, y = 5;
System.out.println("XOR is "+ 
                      (myXOR(x, y)));
} 
}
 
// This code is contributed by shivanisinghss2110

Python3

# Python3 program to 
# Returns XOR of x and y
def myXOR(x, y):
    return (x & (~y)) | ((~x )& y)
 
# Driver Code
x = 3
y = 5
print("XOR is" , 
    myXOR(x, y))
 
# This code is contributed by shivanisinghss2110

C#

// C# program to find XOR without using ^
using System;
 
class GFG{
 
// Returns XOR of x and y
static int myXOR(int x, int y)
{
    return (x & (~y)) | ((~x )& y);
}
 
// Driver program to test above function
public static void Main()
{
    int x = 3, y = 5;
    Console.WriteLine("XOR is " +myXOR(x, y));
} 
}
 
// This code is contributed by shivansinghss2110

Javascript

<script>
 
// Javascript program to find XOR without using ^
 
// Returns XOR of x and y
function myXOR(x, y)
{
   return (x & (~y)) | ((~x ) & y);
}
 
// Driver code
let x = 3, y = 5;
 
document.write("XOR is " + myXOR(x, y));
 
// This code is contributed by subhammahato348
 
</script>

Output

XOR is 6

Time Complexity: O(1) i.e. simple calculation of arithmetic and bitwise operator.
Auxiliary Space: O(1)

Another Solution: we can simply use one of the properties of the XOR bitwise operator i.e. a+b = a^b + 2*(a&b), with the help of this we can do the same for an operator variant also.

C++14

// C++ program to find XOR without using ^
#include <iostream>
using namespace std;
 
int XOR(int x, int y) { return (x + y - (2 * (x & y))); }
 
int main()
{
    int x = 3, y = 5;
    cout << XOR(x, y) << endl;
    return 0;
}
// this code is contributed by vishu05

Java

// Java program to find XOR without using ^
 
class GFG {
 
    static int XOR(int x, int y) {
        return (x + y - (2 * (x & y)));
    }
 
    public static void main(String[] args) {
        int x = 3, y = 5;
        System.out.print(XOR(x, y) + "\n");
    }
}
 
// This code is contributed by umadevi9616 

Python3

# Python3 program to return XOR of x and y without ^ operator
def XOR(x, y):
    return (x+y - (2*(x & y)))
 
 
# Driver Code
x = 3
y = 5
print("XOR of",x,'&',y,'is:',
      XOR(x, y))
 
# This code is contributed by vishu05

C#

// C# program to find XOR without using ^
using System;
 
class GFG{
 
static int XOR(int x, int y) 
{
    return(x + y - (2 * (x & y)));
}
 
// Driver code
public static void Main(String[] args)
{
    int x = 3, y = 5;
   
    Console.Write(XOR(x, y) + "\n");
}
}
 
// This code is contributed by gauravrajput1

Javascript

<script>
// javascript program to find XOR without using ^
   function XOR(x , y) {
        return (x + y - (2 * (x & y)));
    }
 
     
        var x = 3, y = 5;
        document.write(XOR(x, y) + "\n");
 
// This code contributed by umadevi9616
</script>

Output

Time Complexity: O(1) i.e. simple calculation of arithmetic and bitwise operator.
Auxiliary Space: O(1)

Another Solution: We can simply subtract the AND(&) of the two numbers from the OR(|) so that the common bit gets canceled and the opposite bits remain in the answer.

C++

// C++ program to find XOR without using ^
#include <iostream>
using namespace std;
 
int XOR(int x, int y) { return ((x|y)-(x&y)); }
 
int main()
{
    int x = 3, y = 5;
    cout << XOR(x, y) << endl;
    return 0;
}
// this code is contributed by Suvam Chatterjee

Java

// Java program to find XOR without using ^
 
class GFG {
 
    static int XOR(int x, int y)
    {
        return ((x | y) - (x & y));
    }
 
    public static void main(String[] args)
    {
        int x = 3, y = 5;
        System.out.print(XOR(x, y) + "\n");
    }
}
 
// This code is contributed by garg28harsh.

Python3

# Python program to find XOR without using ^
def XOR(x, y):
    return ((x | y) - (x & y))
 
x, y = 3, 5
print(XOR(x, y))
 
# This code is contributed by lokesh

C#

using System;
class GFG {
  static int XOR(int x, int y)
  {
    return ((x | y) - (x & y));
  }
  public static void Main(String[] args)
  {
 
    int x = 3, y = 5;
    Console.Write(XOR(x, y));
    return;
  }
}
 
// This code is contributed by garg28harsh.

Javascript

// Javascript program to find XOR without using ^
function XOR(x, y) 
{ return ((x | y) - (x & y)); }
 
let x = 3, y = 5;
console.log(XOR(x, y));
 
// This code is contributed by garg28harsh.

Output

Time Complexity: O(1) i.e. simple calculation of arithmetic and bitwise operator.
Auxiliary Space: O(1)

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

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