Add two numbers without using arithmetic operators using Cpp

Software Development
#1

Hello Folks,

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.

// C++ Program to add two numbers

// without using arithmetic operator

#include <bits/stdc++.h>

using namespace std;

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

int main()

{

cout << Add(15, 32);

return 0;

}

Output :

47

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.

Thankyou