Addition of two numbers without carry

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++

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    // 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;
    }

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    Java

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    // 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 */

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    Python3

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    # 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)

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    C#

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    // 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 */

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    PHP

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    <?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 
    ?>

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    Output :

    6180
    


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