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 recursionint 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 recursionint 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 recursionimport 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 Codepublic 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 recursiondef find( decimal_number ): if decimal_number == 0: return 0 else: return (decimal_number % 2 + 10 * find(int(decimal_number // 2)))# Driver Codedecimal_number = 10print(find(decimal_number))# This code is contributed# by "Sharad_Bhardwaj" |
C#
// C# program for decimal to binary// conversion using recursionusing 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 recursionfunction 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 recursionfunction 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 binaryvoid 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 Codeint main(){ string bin_num = ""; deci_to_bin(1048576, bin_num); cout<<bin_num; return 0;} |
Java
// Java program for decimal to binary// conversion using recursionpublic 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 recursiondef 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 Codedecimal_number = 1048576print(getbinary(decimal_number)) # This code is contributed# by "Sarthak Sethi" |
C#
// C# program for decimal to binary// conversion using recursionusing 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)
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