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: d = 7
Output: 111
Explanation: 2⁰ + 2¹ + 2² = 1+2+4 = 7.

Input: d = 10
Output: 1010
Explanation: 2¹ + 2³ = 2+8 = 10.

We previously discussed an iterative approach in the post Program for Decimal to Binary Conversion, Now, let's focus on the recursive solution.

Recursive Approach for Small Integers - O(log₂n) Time and O(log₂n) Space

The function recursively divides the decimal number by 2, appending the remainder as the next binary digit, constructing the binary representation from right to left.

For example

To convert 10 to binary

1. 10 % 2 = 0, continue with 10 / 2 = 5
2. 5 % 2 = 1, continue with 5 / 2 = 2
3. 2 % 2 = 0, continue with 2 / 2 = 1
4. 1 % 2 = 1, stop as 1 / 2 = 0

Reading remainders gives 1010 (binary).

#include <bits/stdc++.h>
using namespace std;

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

// Driver code 
int main()
{
    int d = 10;
    cout << decToBin(d);
    return 0;
}

#include <stdio.h>

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

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

// Decimal to binary conversion
// using recursion
public class DecimalToBinary {
    public static int decToBin(int d) {
        if (d == 0)
            return 0;
        else
            return (d % 2 + 10 * decToBin(d / 2));
    }

    // Driver code 
    public static void main(String[] args) {
        int d = 10;
        System.out.println(decToBin(d));
    }
}

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

# Driver code 
d = 10
print(dec_to_bin(d))

// Decimal to binary conversion
// using recursion
public class DecimalToBinary {
    public static int DecToBin(int d) {
        if (d == 0)
            return 0;
        else
            return (d % 2 + 10 * DecToBin(d / 2));
    }

    // Driver code 
    public static void Main(string[] args) {
        int d = 10;
        System.Console.WriteLine(DecToBin(d));
    }
}

// Decimal to binary conversion
// using recursion
function decToBin(d) {
    if (d === 0) 
        return 0; 
    else
        return (d % 2 + 10 * decToBin(Math.floor(d / 2)));
}

// Driver code 
let d = 10;
console.log(decToBin(d));

1010

Recursive Approach for Big Integers Using String - O(log₂n) Time and O(log₂n) Space

The previous approach fails for numbers above 1023 as their binary representation exceeds the int range. Even using long long unsigned is limited to 1048575. A better solution is storing binary digits in a bool vector for scalability.

#include <bits/stdc++.h>
using namespace std;

void decToBinRec(int d, string &res) {
    if (d > 1) {
        decToBinRec(d / 2, res);
    }
    res += (d % 2) + '0';
}

string decToBin(int d) {
    string res = "";
    decToBinRec(d, res);
    return res;
}

int main() {
    int d = 1048576;
    cout << decToBin(d) << endl;
    return 0;
}

// Java program to convert decimal to binary using recursion
class DecimalToBinary {
    public static String decToBinRec(int d) {
        if (d > 1) {
            return decToBinRec(d / 2) + (d % 2);
        }
        return String.valueOf(d);
    }

    public static void main(String[] args) {
        int d = 1048576;
        System.out.println(decToBinRec(d));
    }
}

def dec_to_bin_rec(d):
    if d > 1:
        dec_to_bin_rec(d // 2)
    return str(d % 2) + (dec_to_bin_rec(d // 2) if d > 1 else '')

def dec_to_bin(d):
    return dec_to_bin_rec(d)

if __name__ == '__main__':
    d = 1048576
    print(dec_to_bin(d))

// C# program to convert decimal to binary using recursion
using System;

class DecimalToBinary {
    static string DecToBinRec(int d) {
        if (d > 1) {
            return DecToBinRec(d / 2) + (d % 2);
        }
        return d.ToString();
    }

    static void Main() {
        int d = 1048576;
        Console.WriteLine(DecToBinRec(d));
    }
}

function decToBinRec(d) {
    if (d > 1) {
        decToBinRec(Math.floor(d / 2));
    }
    process.stdout.write((d % 2).toString());
}

function decToBin(d) {
    decToBinRec(d);
    console.log('');
}

const d = 1048576;
decToBin(d);

100000000000000000000