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);
}

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