## 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 and add it to x ^ y to get the required result.

```
#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;
}
```

Following is recursive implementation for the same approach.

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

Credits : http://www.geeksforgeeks.org