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.

## CPP

#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; }

## Java

// Java Program to add two // numbers without using // arithmetic operator import java.io.*; class GFG { static 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; } // Driver code public static void main(String arg[]) { System.out.println(Add(15, 32)); } } // This code is contributed by Anant Agarwal.

## Python3

def Add(x, y): # Iterate till there is no carry while (y != 0): # carry now contains common set bits of x and y 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 print(Add(15, 32)) # This code is contributed by # Smitha Dinesh Semwal

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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