# RANDOMIZED ALGORITHMS 8

QUESTION

Write a function Add() that returns sum of two integers. The function should not use any of the arithmetic operators (+, ++, , -, .. etc).\n\nSum of two bits can be obtained by performing XOR (^) of the two bits. Carry bit can be obtained by performing AND (&) of two bits.\nAbove is simple Half Adder logic that can be used to add 2 single bits.\n\nWe can extend this logic for integers. If x and y dont 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>

{
// 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()
{
int m,n;
scanf("%d%d",&m,&n);  