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Addition of two numbers without carry
  • Difficulty Level : Easy
  • Last Updated : 25 Mar, 2021

You are given two positive number n and m. You have to find simply addition of both number but with a given condition that there is not any carry system in this addition. That is no carry is added at higher MSBs.
Examples : 
 

Input : m = 456, n = 854
Output : 200

Input : m = 456, n = 4
Output : 450

Algorithm : 
 

Input n, m while(n||m)
    {
        // Add each bits 
        bit_sum = (n%10) + (m%10);

        // Neglect carry
        bit_sum %= 10;

        // Update result
        // multiplier to maintain place value
        res = (bit_sum * multiplier) + res;
        n /= 10;
        m /= 10;

        // Update multiplier
        multiplier *=10;
    } print res

 

Approach : 
To solve this problem we will need the bit by bit addition of number where we start adding two number from right most bit (LSB) and add integers from both nubers with same position. Also we will neglect carry at each position so that that carry will not affect further higher bit position. 
Start adding both numbers bit by bit and for each bit take sum of integers then neglect their carry by taking modulo of bit_sum by 10 further add bit_sum to res by multiplying bit_sum with a multiplier specifying place value. (Multiplier got incremented 10 times on each iteration.) 
Below is the implementation of above approach : 
 

C++




// CPP program for special
// addition of two number
#include <bits/stdc++.h>
using namespace std;
 
int xSum(int n, int m)
{
    // variable to store result  
    int res = 0;
 
    // variable to maintain
    // place value
    int multiplier = 1;
 
    // variable to maintain
    // each digit sum
    int bit_sum;
 
    // Add numbers till each
    // number become zero
    while (n || m) {
 
        // Add each bits
        bit_sum = (n % 10) + (m % 10);
         
        // Neglect carry
        bit_sum %= 10;
         
        // Update result
        res = (bit_sum * multiplier) + res;
        n /= 10;
        m /= 10;
         
        // Update multiplier
        multiplier *= 10;
    }
    return res;
}
 
// Driver program
int main()
{
    int n = 8458;
    int m = 8732;
    cout << xSum(n, m);
    return 0;
}

Java




// Java program for special
// addition of two number
import java.util.*;
import java.lang.*;
 
public class GfG {
 
    public static int xSum(int n, int m)
    {
        int res = 0;
        int multiplier = 1;
        int bit_sum;
 
        // Add numbers till each
        // number become zero
        while (true) {
                 
            if(n==0 && m==0)
            break;
 
            // Add each bits
            bit_sum = (n % 10) + (m % 10);
 
            // Neglect carry
            bit_sum %= 10;
 
            // Update result
            res = (bit_sum * multiplier) + res;
            n /= 10;
            m /= 10;
 
            // Update multiplier
            multiplier *= 10;
           
        }
        return res;
    }
 
    // Driver function
    public static void main(String args[])
    {
        int n = 8458;
        int m = 8732;
        System.out.println(xSum(n, m));
    }
}
/* This code is contributed by Sagar Shukla */

Python3




# Python3 program for special
# addition of two number
import math
 
def xSum(n, m) :
 
    # variable to
    # store result
    res = 0
 
    # variable to maintain
    # place value
    multiplier = 1
 
    # variable to maintain
    # each digit sum
    bit_sum = 0
 
    # Add numbers till each
    # number become zero
    while (n or m) :
 
        # Add each bits
        bit_sum = ((n % 10) +
                   (m % 10))
         
        # Neglect carry
        bit_sum = bit_sum % 10
         
        # Update result
        res = (bit_sum *
               multiplier) + res
        n = math.floor(n / 10)
        m = math.floor(m / 10)
         
        # Update multiplier
        multiplier = multiplier * 10
     
    return res
 
# Driver code
n = 8458
m = 8732
print (xSum(n, m))
 
# This code is contributed by
# Manish Shaw(manishshaw1)

C#




// C# program for special
// addition of two number
using System;
 
public class GfG {
 
    public static int xSum(int n, int m)
    {
        int res = 0;
        int multiplier = 1;
        int bit_sum;
 
        // Add numbers till each
        // number become zero
        while (true) {
 
            // Add each bits
            bit_sum = (n % 10) + (m % 10);
 
            // Neglect carry
            bit_sum %= 10;
 
            // Update result
            res = (bit_sum * multiplier) + res;
            n /= 10;
            m /= 10;
 
            // Update multiplier
            multiplier *= 10;
            if (n == 0)
                break;
            if (m == 0)
                break;
        }
        return res;
    }
 
    // Driver function
    public static void Main()
    {
        int n = 8458;
        int m = 8732;
        Console.WriteLine(xSum(n, m));
    }
}
 
/* This code is contributed by Vt_m */

PHP




<?php
// php program for special
// addition of two number
 
function xSum($n, $m)
{
     
    // variable to store result
    $res = 0;
 
    // variable to maintain
    // place value
    $multiplier = 1;
 
    // variable to maintain
    // each digit sum
    $bit_sum;
 
    // Add numbers till each
    // number become zero
    while ($n || $m) {
 
        // Add each bits
        $bit_sum = ($n % 10) +
                   ($m % 10);
         
        // Neglect carry
        $bit_sum %= 10;
         
        // Update result
        $res = ($bit_sum * $multiplier) + $res;
        $n =floor($n / 10);
        $m =floor($m / 10);
         
        // Update multiplier
        $multiplier *= 10;
    }
    return $res;
}
 
    // Driver code
    $n = 8458;
    $m = 8732;
    echo xSum($n, $m);
 
//This code is contributed by mits
?>

Javascript




<script>
 
// Javascript program for special
// addition of two number
function xSum(n, m)
{
    // variable to store result
    var res = 0;
 
    // variable to maintain
    // place value
    var multiplier = 1;
 
    // variable to maintain
    // each digit sum
    var bit_sum;
 
    // Add numbers till each
    // number become zero
    while (n || m) {
 
        // Add each bits
        bit_sum = (n % 10) + (m % 10);
         
        // Neglect carry
        bit_sum %= 10;
         
        // Update result
        res = (bit_sum * multiplier) + res;
        n = parseInt(n / 10);
        m = parseInt(m / 10);
         
        // Update multiplier
        multiplier *= 10;
    }
    return res;
}
 
// Driver program
var n = 8458;
var m = 8732;
document.write(xSum(n, m));
     
    // This code is contributed by noob2000.
</script>

Output : 
 

6180

 




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