Add two numbers without using arithmetic operators

Write a function Add() that returns sum of two integers. The function should not use any of the arithmetic operators (+, ++, –, -, .. etc).

Method 1:

C++

#include <iostream>
using namespace std;

int add(int a, int b)
{
    // for loop will start from 1 and move till the value of
    // second number , first number(a) is incremented in for
    // loop
    for (int i = 1; i <= b; i++)
        a++;
    return a;
}

int main()
{
    // first number is 10 and second number is 32 , for loop
    // will start from 1 and move till 32 and the value of a
    // is incremented 32 times which will give us the total
    // sum of two numbers

    int a = add(10, 32);
    cout << a;
    return 0;
}

// This code is contributed by Aditya Kumar (adityakumar129)

C

#include <stdio.h>

int add(int a, int b)
{
    // for loop will start from 1 and move till the value of
    // second number , first number(a) is incremented in for
    // loop
    for (int i = 1; i <= b; i++)
        a++;
    return a;
}

int main()
{
    // first number is 10 and second number is 32 , for loop
    // will start from 1 and move till 32 and the value of a
    // is incremented 32 times which will give us the total
    // sum of two numbers

    int a = add(10, 32);
    printf("%d", a);
    return 0;
}

// This code is contributed by Aditya Kumar (adityakumar129)

Java

import java.util.*;

class GFG {

    static int add(int a, int b)
    {
        // for loop will start from 1 and move till the
        // value of second number , first number(a) is
        // incremented in for loop
        for (int i = 1; i <= b; i++)
            a++;
        return a;
    }

    public static void main(String[] args)
    {
        // first number is 10 and second number is 32 , for
        // loop will start from 1 and move till 32 and the
        // value of a is incremented 32 times which will
        // give us the total sum of two numbers
        int a = add(10, 32);
        System.out.print(a);
    }
}

// This code is contributed by Aditya Kumar (adityakumar129)

Python3

# Python implementation
def add(a, b):
    # for loop will start from 1 and move till the value of second number ,
    # first number(a) is incremented in for loop
    for i in range(1, b + 1):
        a = a + 1
    return a


# driver code
# first number is 10 and second number is 32 , for loop
# will start from 1 and move till 32 and the value of a
# is incremented 32 times which will give us the total
# sum of two numbers
a = add(10, 32)
print(a)

# This code is contributed by Aditya Kumar (adityakumar129)

C#

using System;
public class GFG {

  static int add(int a, int b) {
    for (int i = 1; i <= b; i++) // for loop will start from 1 and move till the value of second
      // number , first number(a) is incremented in for loop
    {
      a++;
    }
    return a;
  }

  public static void Main(String[] args)
  {

    int a = add(10, 32); // first number is 10 and second number is 32 , for loop will start
    Console.Write(a); // from 1 and move till 32 and the value of a is incremented 32 times
    // which will give us the total sum of two numbers
  }
}

// This code is contributed by Rajput-Ji

Javascript

<script>
    function add(a , b)
    {
         // for loop will start from 1 and move till the value of second
        // number , first number(a) is incremented in for loop
        for (i = 1; i <= b; i++)
        {
            a++;
        }
        return a;
    }

    // first number is 10 and second number is 32 , for loop will start
    var a = add(10, 32);

    // from 1 and move till 32 and the value of a is incremented 32 times
    // which will give us the total sum of two numbers
    document.write(a);

// This code is contributed by Rajput-Ji
</script>

Output

42

Time Complexity: O(b)
Auxiliary Space: O(1)

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 should be unsigned to
        // deal with -ve numbers
        // carry now contains common
        //set bits of x and y
        unsigned 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(10, 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
        unsigned 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

42

Time Complexity: O(log y)
Auxiliary Space: O(1)

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,(unsigned) (x & y) << 1);
}

// This code is contributed by shubhamsingh10

C

int Add(int x, int y)
{
    if (y == 0)
        return x;
    else
        return Add( x ^ y, (unsigned)(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

Python3

def Add(x, y):

    if (y == 0):
        return x
    else
        return Add( x ^ y, (x & y) << 1)

# This code is contributed by subhammahato348

C#

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 subhammahato348

Javascript

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

// This code is contributed by Ankita saini

Time Complexity: O(log k), where k=x&y
Auxiliary Space: O(log k).

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