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Add two numbers without using arithmetic operators
  • Difficulty Level : Hard
  • Last Updated : 09 Apr, 2021

Write a function Add() that returns sum of two integers. The function should not use any of the arithmetic operators (+, ++, –, -, .. etc).
Sum of two bits can be obtained by performing XOR (^) of the two bits. Carry bit can be obtained by performing AND (&) of two bits. 

Above is simple Half Adder logic that can be used to add 2 single bits. We can extend this logic for integers. If x and y don’t have set bits at same position(s), then bitwise XOR (^) of x and y gives the sum of x and y. To incorporate common set bits also, bitwise AND (&) is used. Bitwise AND of x and y gives all carry bits. We calculate (x & y) << 1 and add it to x ^ y to get the required result. 

C++




// C++ Program to add two numbers
// without using arithmetic operator
#include <bits/stdc++.h>
using namespace std;
 
int Add(int x, int y)
{
    // Iterate till there is no carry
    while (y != 0)
    {
        // carry now contains common
        //set bits of x and y
        int carry = x & y;
 
        // Sum of bits of x and y where at
        //least one of the bits is not set
        x = x ^ y;
 
        // Carry is shifted by one so that adding
        // it to x gives the required sum
        y = carry << 1;
    }
    return x;
}
 
// Driver code
int main()
{
    cout << Add(15, 32);
    return 0;
}
 
// This code is contributed by rathbhupendra

C




// C Program to add two numbers
// without using arithmetic operator
#include<stdio.h>
 
int Add(int x, int y)
{
    // Iterate till there is no carry 
    while (y != 0)
    {
        // carry now contains common
        //set bits of x and y
        int carry = x & y; 
 
        // Sum of bits of x and y where at
        //least one of the bits is not set
        x = x ^ y;
 
        // Carry is shifted by one so that adding
        // it to x gives the required sum
        y = carry << 1;
    }
    return x;
}
 
int main()
{
    printf("%d", Add(15, 32));
    return 0;
}

Java




// Java Program to add two numbers
// without using arithmetic operator
import java.io.*;
 
class GFG
{
    static int Add(int x, int y)
    {
        // Iterate till there is no carry
        while (y != 0)
        {
            // carry now contains common
            // set bits of x and y
            int carry = x & y;
 
            // Sum of bits of x and
            // y where at least one
            // of the bits is not set
            x = x ^ y;
 
            // Carry is shifted by
            // one so that adding it
            // to x gives the required sum
            y = carry << 1;
        }
        return x;
    }
     
    // Driver code
    public static void main(String arg[])
    {
        System.out.println(Add(15, 32));
    }
}
 
// This code is contributed by Anant Agarwal.

Python3




# Python3 Program to add two numbers
# without using arithmetic operator
def Add(x, y):
 
    # Iterate till there is no carry
    while (y != 0):
     
        # carry now contains common
        # set bits of x and y
        carry = x & y
 
        # Sum of bits of x and y where at
        # least one of the bits is not set
        x = x ^ y
 
        # Carry is shifted by one so that  
        # adding it to x gives the required sum
        y = carry << 1
     
    return x
 
print(Add(15, 32))
 
# This code is contributed by
# Smitha Dinesh Semwal

C#




// C# Program to add two numbers
// without using arithmetic operator
using System;
 
class GFG
{
    static int Add(int x, int y)
    {
        // Iterate till there is no carry
        while (y != 0)
        {
            // carry now contains common
            // set bits of x and y
            int carry = x & y;
 
            // Sum of bits of x and
            // y where at least one
            // of the bits is not set
            x = x ^ y;
 
            // Carry is shifted by
            // one so that adding it
            // to x gives the required sum
            y = carry << 1;
        }
        return x;
    }
     
    // Driver code
    public static void Main()
    {
        Console.WriteLine(Add(15, 32));
    }
}
 
// This code is contributed by vt_m.

PHP




<?php
// PHP Program to add two numbers
// without using arithmetic operator
 
function Add( $x, $y)
{
     
    // Iterate till there is
    // no carry
    while ($y != 0)
    {
         
        // carry now contains common
        //set bits of x and y
        $carry = $x & $y;
 
        // Sum of bits of x and y where at
        //least one of the bits is not set
        $x = $x ^ $y;
 
        // Carry is shifted by one
        // so that adding it to x
        // gives the required sum
        $y = $carry << 1;
    }
    return $x;
}
 
    // Driver Code
    echo Add(15, 32);
 
// This code is contributed by anuj_67.
?>

Javascript




<script>
 
// Javascript Program to add two numbers
// without using arithmetic operator
 
   
    function Add(x, y) {
        // Iterate till there is no carry  
        while (y != 0)
        {
            // carry now contains common 
            //set bits of x and y
            let carry = x & y;  
   
            // Sum of bits of x and y where at 
            //least one of the bits is not set
            x = x ^ y; 
   
            // Carry is shifted by one so that adding
            // it to x gives the required sum
            y = carry << 1;
        }
        return x;
    }
   
     //driver code
    document.write(Add(15, 32));
  
// This code is contributed by Surbhi Tyagi
</script>

Output : 

47

Following is the recursive implementation for the same approach.

C




int Add(int x, int y)
{
    if (y == 0)
        return x;
    else
        return Add( x ^ y, (x & y) << 1);
}

Java




static int Add(int x, int y)
{
  if (y == 0)
    return x;
  else
    return Add(x ^ y, (x & y) << 1);
}
 
// This code is contributed by subham348

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

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