# Add two numbers without using arithmetic operators using Cpp

Hello Folks,

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++ 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;`

`}`

Output :

47

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.

Thankyou