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.

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the **DSA Self Paced Course** at a student-friendly price and become industry ready.