Decimal to binary number using recursion

Given a decimal number as input, we need to write a program to convert the given decimal number into an equivalent binary number. 

Examples :

Input : 7                                                         
Output :111

Input :10
Output :1010

We have discussed one iterative solution in below post. 
Program for Decimal to Binary Conversion
Below is Recursive solution:

findBinary(decimal)
   if (decimal == 0)
      binary = 0
   else
      binary = decimal % 2 + 10 * (findBinary(decimal / 2))

Step-by-step process for a better understanding of how the algorithm works 
Let the decimal number be 10. 
Step 1-> 10 % 2 which is equal-too 0 + 10 * ( 10/2 ) % 2 
Step 2-> 5 % 2 which is equal-too 1 + 10 * ( 5 / 2) % 2
Step 3-> 2 % 2 which is equal-too 0 + 10 * ( 2 / 2 ) % 2
Step 4-> 1 % 2 which is equal-too 1 + 10 * ( 1 / 2 ) % 2

Recursion Tree for Decimal to Binary Conversion

C++

// C++ program for decimal to binary
// conversion using recursion
#include <bits/stdc++.h>
using namespace std;

// Decimal to binary conversion
// using recursion
int find(int decimal_number)
{
    if (decimal_number == 0)
        return 0;
    else
        return (decimal_number % 2 + 10 *
                find(decimal_number / 2));
}

// Driver code
int main()
{
    int decimal_number = 10;
    cout << find(decimal_number);
    return 0;
}
// This code is contributed by shivanisinghss2110

C

// C/C++ program for decimal to binary
// conversion using recursion
#include <stdio.h>

// Decimal to binary conversion
// using recursion
int find(int decimal_number)
{
    if (decimal_number == 0)
        return 0;
    else
        return (decimal_number % 2 + 10 *
                find(decimal_number / 2));
}

// Driver code
int main()
{
    int decimal_number = 10;
    printf("%d", find(decimal_number));
    return 0;
}

Java

// Java program for decimal to binary
// conversion using recursion
import java.io.*;

class GFG
{

    // Decimal to binary conversion
    // using recursion
    static int find(int decimal_number)
    {
        if (decimal_number == 0)
            return 0;

        else

        return (decimal_number % 2 + 10 *
                find(decimal_number / 2));
    }

// Driver Code
public static void main(String args[])
{
    int decimal_number = 10;
    System.out.println(find(decimal_number));
}

}

// This code is contributed by Nikita Tiwari

Python3

# Python3 code for decimal to binary
# conversion using recursion

# Decimal to binary conversion
# using recursion
def find( decimal_number ):
    if decimal_number == 0:
        return 0
    else:
        return (decimal_number % 2 + 10 *
                find(int(decimal_number // 2)))

# Driver Code
decimal_number = 10
print(find(decimal_number))

# This code is contributed
# by "Sharad_Bhardwaj"

C#

// C# program for decimal to binary
// conversion using recursion
using System;

class GFG
{

    // Decimal to binary conversion
    // using recursion
    static int find(int decimal_number)
    {
        if (decimal_number == 0)
            return 0;

        else

        return (decimal_number % 2 + 10 *
                find(decimal_number / 2));
    }

    // Driver Code
    public static void Main()
    {

        int decimal_number = 10;

        Console.WriteLine(find(decimal_number));
    }
}

// This code is contributed by vt_m

PHP

<?php
// PHP program for decimal to binary
// conversion using recursion

// Decimal to binary
// conversion using recursion
function find($decimal_number)
{
    if ($decimal_number == 0)
        return 0;
    else
        return ($decimal_number % 2 + 10 *
                find($decimal_number / 2));
}

// Driver Code
$decimal_number = 10;
echo(find($decimal_number));

// This code is contributed by Ajit.
?>

Javascript

<script>

// Javascript program for decimal to binary
// conversion using recursion

// Decimal to binary conversion
// using recursion
function find(decimal_number)
{
    if (decimal_number == 0)
        return 0;
    else
        return ((decimal_number % 2) + 10 *
                find(parseInt(decimal_number / 2)));
}

// Driver code
var decimal_number = 10;
document.write( find(decimal_number));

// This code is contributed by noob2000.
</script>

Output

1010

Time Complexity: O(log₂n), Here n is the decimal_number.
Auxiliary Space: O(1), As constant extra space is used.

The above approach works fine unless you want to convert a number greater than 1023 in decimal to binary. The binary of 1024 is 10000000000 (one 1 and ten 0’s) which goes out of the range of int. Even with long long unsigned as return type the highest you can go is 1048575 which is way less than the range of int. An easier but effective approach would be to store the individual digits of the binary number in a vector of bool.

C++

// C++ program for decimal to binary
// conversion using recursion
#include<bits/stdc++.h>
using namespace std;


// Function to convert decimal to binary
void deci_to_bin(int x, string & bin_num)
{

    // Base Case
    if (x <= 1)
        bin_num += (char)(x + '0');
    else {

        // Recursion call
        deci_to_bin(x / 2, bin_num);

        // If x is divisible by 2
        if(x%2)
          bin_num += '1';

        // otherwise
        else
          bin_num += '0';
    }
}

// Driver Code
int main()
{
    string bin_num = "";
    deci_to_bin(1048576, bin_num);

    cout<<bin_num;
    return 0;
}

Java

// Java program for decimal to binary
// conversion using recursion
public class Main
{
    static String bin_num = "";

    // Function to convert decimal to binary
    static void deci_to_bin(int x)
    {

        // Base Case
        if (x <= 1)
            bin_num += (char)(x + '0');
        else {

            // Recursion call
            deci_to_bin((int)(x / 2));

            // If x is divisible by 2
            if(x%2 != 0)
              bin_num += '1';

            // otherwise
            else
              bin_num += '0';
        }
    }

    public static void main(String[] args) {
        deci_to_bin(1048576);

        System.out.print(bin_num);
    }
}

// This code is contributed by divyesh072019.

Python3

# Python3 code for decimal to binary
# conversion using recursion

# Decimal to binary conversion
# using recursion
def getbinary(number):

    # Base case
    if number == 0:
        return 0

     # Recursion call and storing the result
    smallans = getbinary(number // 2)

    return number % 2 + 10 * smallans

# Driver Code
decimal_number = 1048576
print(getbinary(decimal_number))

# This code is contributed
# by "Sarthak Sethi"

C#

// C# program for decimal to binary
// conversion using recursion
using System;
class GFG {

    static string bin_num = "";

    // Function to convert decimal to binary
    static void deci_to_bin(int x)
    {

        // Base Case
        if (x <= 1)
            bin_num += (char)(x + '0');
        else {

            // Recursion call
            deci_to_bin((int)(x / 2));

            // If x is divisible by 2
            if(x%2 != 0)
              bin_num += '1';

            // otherwise
            else
              bin_num += '0';
        }
    }

  static void Main() {
    deci_to_bin(1048576);

    Console.Write(bin_num);
  }
}

// This code is contributed by mukesh07.

Javascript

<script>
    // Javascript program for decimal to binary
    // conversion using recursion

    let bin_num = "";

    // Function to convert decimal to binary
    function deci_to_bin(x)
    {

        // Base Case
        if (x <= 1)
            bin_num += String.fromCharCode(x + '0'.charCodeAt());
        else {

            // Recursion call
            deci_to_bin(parseInt(x / 2, 10));

            // If x is divisible by 2
            if(x%2 != 0)
              bin_num += '1';

            // otherwise
            else
              bin_num += '0';
        }
    }

    deci_to_bin(1048576);

    document.write(bin_num);

    // This code is contributed by divyeshrabadiya07.
</script>

Output

100000000000000000000

Time Complexity: O(log n), where n is given decimal number
Auxiliary Space: O(log n)