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.


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;
        return Add( x ^ y, (x & y) << 1);

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