Bitwise recursive addition of two integers - GeeksforGeeks

05 May, 2021
When adding two binary numbers by hand we keep the carry bits in mind and add it at the same time. But to do same thing in program we need a lot of checks. Recursive solution can be imagined as addition of carry and a^b (two inputs) until carry becomes 0.
Examples : 
Input : int x = 45, y = 45
Output : 90

Input : int x = 4, y = 78
Output : 82
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.
One important observation is, if (x & y) becomes 0, then result is x ^ y. 
C
Java
Python3
C#
PHP
Javascript
// C program to do recursive addition// of two integers#include <stdio.h> int add(int x, int y) {    int keep = (x & y) << 1;    int res = x^y;     // If bitwise & is 0, then there    // is not going to be any carry.    // Hence result of XOR is addition.    if (keep == 0)        return res;     add(keep, res);} // Driver codeint main(){    printf("%d", add(15, 38));    return 0;}
// Java program to do recursive addition// of two integersimport java.io.*; class GFG {         static int add(int x, int y)    {        int keep = (x & y) << 1;        int res = x^y;             // If bitwise & is 0, then there        // is not going to be any carry.        // Hence result of XOR is addition.        if (keep == 0)            return res;                     return add(keep, res);    }     // Driver code    public static void main (String[] args)    {        System.out.println(add(15, 38));    }} // This code is contributed by Ajit.
     # Python program to do recursive addition# of two integers  def add(x, y):    keep = (x & y) << 1;    res = x^y;      # If bitwise & is 0, then there    # is not going to be any carry.    # Hence result of XOR is addition.    if (keep == 0):        return res;      return add(keep, res);   # Driver code print(add(15, 38)); #  This code is contributed by Princi Singh
// C# program to do recursive// addition of two integersusing System; class GFG {         static int add(int x, int y)    {        int keep = (x & y) << 1;        int res = x^y;             // If bitwise & is 0, then there        // is not going to be any carry.        // Hence result of XOR is addition.        if (keep == 0)            return res;                     return add(keep, res);    }     // Driver code    public static void Main ()    {        Console.Write(add(15, 38));    }} // This code is contributed by Smitha.
<?php// php program to do recursive addition// of two integers function add($x, $y) {    $keep = ($x & $y) << 1;    $res = $x^$y;     // If bitwise & is 0, then there    // is not going to be any carry.    // Hence result of XOR is addition.    if ($keep == 0)    {        echo $res;        exit(0);    }     add($keep, $res);} // Driver code$k= add(15, 38); // This code is contributed by mits.?>
<script> // Javascript program to do recursive// addition of two integersfunction add(x, y){    let keep = (x & y) << 1;    let res = x ^ y;       // If bitwise & is 0, then there    // is not going to be any carry.    // Hence result of XOR is addition.    if (keep == 0)        return res;               return add(keep, res);} // Driver codedocument.write(add(15, 38)); // This code is contributed by decode2207 </script>
53
 
jit_t
Smitha Dinesh Semwal
Mithun Kumar
princi singh
decode2207
Bit Magic
Recursion
Recursion
Bit Magic
Writing code in comment?
Please use ide.geeksforgeeks.org,
generate link and share the link here.
Set, Clear and Toggle a given bit of a number in C
Write an Efficient Method to Check if a Number is Multiple of 3
Swap two nibbles in a byte
Highest power of 2 less than or equal to given number
Swap bits in a given number
Write a program to print all permutations of a given string
Given an array A[] and a number x, check for pair in A[] with sum as x (aka Two Sum)
Recursion
Program for Tower of Hanoi
Backtracking | Introduction