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>
 
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()
{
    std::cout<<Add(15, 32);
    return 0;
}