# Add two numbers without using arithmetic operators in C++

## 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).

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

## Following is the program to add two numbers without using arithmetic operators:

```#include<iostream>

{
// 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()
{