Add two numbers without using arithmetic operators

Problem

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

Solution
We can get carry by &(and) operator and bit by ^ (xor) operator. We have already seen, how we can use bit-wise operators to replace arithmetic operators i.e. implement arithmetic operators using bitwise operators.

Method 1 - Iterative method

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;  
}

Method 2 - Recursive approach

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

Thanks.

See also