Program for Decimal to Binary Conversion
Last Updated : 21 Jun, 2025
Given a non negative number n, the task is to convert the given number into an equivalent binary representation.
Examples:
Input: n = 12
Output: "1100"
Explanation: the binary representation of 12 is "1100", since 12 = 1×23 + 1×22 + 0×21+ 0×20 = 12
Input: n = 33
Output: "100001"
Explanation: the binary representation of 33 is "100001", since 1×25 + 0×24 + 0×23 + 0×22 + 0×21 + 1×20 = 33
[Approach - 1] Division by 2 - O(log₂(n)) Time and O(log₂(n)) Space
To convert a decimal number to binary, repeatedly divide it by 2 and record the remainders. Reading these remainders in reverse gives the binary representation.
C++ #include <iostream> #include <algorithm> using namespace std; string decToBinary(int n) { string bin = ""; while (n > 0) { // checking the mod int bit = n%2; bin.push_back('0' + bit); n /= 2; } // reverse the string reverse(bin.begin(), bin.end()); return bin; } int main() { int n = 12; cout << decToBinary(n); return 0; } #include <stdio.h> #include <string.h> // function to reverse the string void reverse(char *bin, int left, int right) { while (left < right) { char temp = bin[left]; bin[left] = bin[right]; bin[right] = temp; left++; right--; } } // function to convert decimal to binary char* decToBinary(int n) { int index = 0; char* bin = (char*) malloc(32 * sizeof(char)); while (n > 0) { int bit = n % 2; bin[index++] = '0' + bit; n /= 2; } bin[index] = '\0'; // Reverse the binary string reverse(bin, 0, index-1); return bin; } int main() { int n = 12; char* bin = decToBinary(n); printf("%s", bin); return 0; } import java.util.*; class GfG { static String decToBinary(int n) { StringBuilder bin = new StringBuilder(); while (n > 0) { int bit = n % 2; bin.append((char) ('0' + bit)); n /= 2; } // reverse the string bin.reverse(); return bin.toString(); } public static void main(String[] args) { int n = 12; System.out.println(decToBinary(n)); } } # function to convert decimal to binary def decToBinary(n): binArr = [] while n > 0: bit = n % 2 binArr.append(str(bit)) n //= 2 # reverse the string binArr.reverse() return "".join(binArr) if __name__ == "__main__": n = 12 print(decToBinary(n))
using System; using System.Collections.Generic; class GfG { // function to convert decimal to binary static string decToBinary(int n) { List<char> bin = new List<char>(); while (n > 0) { int bit = n % 2; bin.Add((char)('0' + bit)); n /= 2; } // reverse the string bin.Reverse(); return new string(bin.ToArray()); } static void Main() { int n = 12; Console.WriteLine(decToBinary(n)); } } // Function to convert decimal to binary function decToBinary(n) { let bin = []; while (n > 0) { let bit = n % 2; bin.push(String(bit)); n = Math.floor(n / 2); } // reverse the string bin.reverse(); return bin.join(""); } // Driver Code let n = 12; console.log(decToBinary(n)); [Approach - 2] Using Head Recursion - O(log₂(n)) Time and O(log₂(n)) Space
The idea is same as the previous approach, but we will use recursion to generate the binary equivalent number.
C++ #include <iostream> #include <algorithm> using namespace std; // Recursive function to convert decimal to binary void decToBinaryRec(int n, string &bin) { // Base Case if (n==0) return; // Recur for smaller bits. decToBinaryRec(n/2, bin); // Add MSB of current number to the binary string bin.push_back(n%2 + '0'); } // Function to convert decimal to binary string decToBinary(int n) { if (n == 0) return "0"; string bin = ""; decToBinaryRec(n, bin); return bin; } int main() { int n = 12; cout << decToBinary(n); return 0; } class GfG { // Recursive function to convert decimal to binary static void decToBinaryRec(int n, StringBuilder bin) { // Base Case if (n == 0) return; // Recur for smaller bits. decToBinaryRec(n / 2, bin); // Add MSB of current number to the binary string bin.append(n % 2); } // Function to convert decimal to binary static String decToBinary(int n) { if (n == 0) return "0"; StringBuilder bin = new StringBuilder(); decToBinaryRec(n, bin); return bin.toString(); } public static void main(String[] args) { int n = 12; System.out.println(decToBinary(n)); } } def decToBinaryRec(n, binArr): # Base Case if n == 0: return # Recur for smaller bits. decToBinaryRec(n // 2, binArr) # Add MSB of current number to the binary list binArr.append(str(n % 2)) # Function to convert decimal to binary def decToBinary(n): if n == 0: return "0" binArr = [] decToBinaryRec(n, binArr) return "".join(binArr) if __name__ == "__main__": n = 12 print(decToBinary(n))
using System; using System.Text; class GfG { // Recursive function to convert decimal to binary static void decToBinaryRec(int n, StringBuilder bin) { // Base Case if (n == 0) return; // Recur for smaller bits. decToBinaryRec(n / 2, bin); // Add MSB of current number to the binary string bin.Append(n % 2); } // Function to convert decimal to binary static string decToBinary(int n) { if (n == 0) return "0"; StringBuilder bin = new StringBuilder(); decToBinaryRec(n, bin); return bin.ToString(); } static void Main() { int n = 12; Console.WriteLine(decToBinary(n)); } } function decToBinaryRec(n, bin) { // Base Case if (n === 0) return; // Recur for smaller bits. decToBinaryRec(Math.floor(n / 2), bin); // Add MSB of current number to the binary string bin.push(n % 2); } // Function to convert decimal to binary function decToBinary(n) { if (n === 0) return "0"; let bin = []; decToBinaryRec(n, bin); return bin.join(""); } // Driver code let n = 12; console.log(decToBinary(n)); [Approach - 3] Using Bitwise Operators - O(log₂(n)) Time and O(log₂(n)) Space
Using bitwise operators, we can extract binary digits by checking the least significant bit (n & 1) and then right-shifting the number (n >> 1) to process the next bit.
This method is faster than arithmetic division and modulo, as bitwise operations are more efficient at the hardware level.
C++ #include <iostream> #include <algorithm> using namespace std; string decToBinary(int n) { // String to store the binary representation string bin = ""; while (n > 0) { // Finding (n % 2) using bitwise AND operator // (n & 1) gives the least significant bit (LSB) int bit = n & 1; bin.push_back('0' + bit); // Right shift n by 1 (equivalent to n = n / 2) // This removes the least significant bit (LSB) n = n >> 1; } reverse(bin.begin(), bin.end()); return bin; } int main() { int n = 12; cout << decToBinary(n); return 0; } #include <stdio.h> #include <string.h> // Function to Reverse the string void reverse(char *bin, int left, int right) { while (left < right) { char temp = bin[left]; bin[left] = bin[right]; bin[right] = temp; left++; right--; } } // function to convert decimal to binary char* decToBinary(int n) { int index = 0; char* bin = (char*) malloc(32 * sizeof(char)); while (n > 0) { // Finding (n % 2) using bitwise AND operator // (n & 1) gives the least significant bit (LSB) int bit = n & 1; bin[index++] = '0' + bit; // Right shift n by 1 (equivalent to n = n / 2) // This removes the least significant bit (LSB) n = n >> 1; } bin[index] = '\0'; // Reverse the binary string reverse(bin, 0, index-1); return bin; } int main() { int n = 12; char* bin = decToBinary(n); printf("%s", bin); return 0; } import java.util.*; class GfG { static String decToBinary(int n) { // String to store the binary representation StringBuilder bin = new StringBuilder(); while (n > 0) { // Finding (n % 2) using bitwise AND operator // (n & 1) gives the least significant bit (LSB) int bit = n & 1; bin.append(bit); // Right shift n by 1 (equivalent to n = n / 2) // This removes the least significant bit (LSB) n = n >> 1; } return bin.reverse().toString(); } public static void main(String[] args) { int n = 12; System.out.println(decToBinary(n)); } } def decToBinary(n): # String to store the binary representation bin = "" while n > 0: # Finding (n % 2) using bitwise AND operator # (n & 1) gives the least significant bit (LSB) bit = n & 1 bin += str(bit) # Right shift n by 1 (equivalent to n = n // 2) # This removes the least significant bit (LSB) n = n >> 1 return bin[::-1] if __name__ == "__main__": n = 12 print(decToBinary(n))
using System; using System.Text; class GfG { // Function to convert decimal to binary static string decToBinary(int n) { // String to store the binary representation StringBuilder bin = new StringBuilder(); while (n > 0) { // Finding (n % 2) using bitwise AND operator // (n & 1) gives the least significant bit (LSB) int bit = n & 1; bin.Append(bit); // Right shift n by 1 (equivalent to n = n / 2) // This removes the least significant bit (LSB) n = n >> 1; } char[] arr = bin.ToString().ToCharArray(); Array.Reverse(arr); return new string(arr); } static void Main() { int n = 12; Console.WriteLine(decToBinary(n)); } } function decToBinary(n) { // String to store the binary representation let bin = ""; while (n > 0) { // Finding (n % 2) using bitwise AND operator // (n & 1) gives the least significant bit (LSB) let bit = n & 1; bin += bit; // Right shift n by 1 (equivalent to n = Math.floor(n / 2)) // This removes the least significant bit (LSB) n = n >> 1; } return bin.split("").reverse().join(""); } // Driver code let n = 12; console.log(decToBinary(n)); [Approach - 4] Using Built-in Methods - O(log₂(n)) Time and O(log₂(n)) Space
The main idea is to leverage built-in functions provided by programming languages to directly convert a decimal number to its binary form. These functions abstract away the underlying logic and return the binary representation as a string, making the process quick, concise, and error-free.
C++ #include <iostream> #include <cmath> #include <bitset> #include <string> using namespace std; string decToBinary(int n) { int len = (int)(log2(n)); // Store in bitset to get the binary representation, // then convert it to string // and finally remove the prefix zeroes return bitset<64>(n).to_string().substr(64 - len - 1); } int main() { int n = 12; cout << decToBinary(n); return 0; } class GfG { static String decToBinary(int n) { int len = (int)(Math.log(n) / Math.log(2)); // Convert to binary string and remove leading zeros return String.format("%s", Integer.toBinaryString(n)); } public static void main(String[] args) { int n = 12; System.out.println(decToBinary(n)); } } import math def decToBinary(n): return bin(n)[2::] if __name__ == "__main__": n = 12 print(decToBinary(n))
using System; class GfG { static string decToBinary(int n) { // Convert the integer 'n' to its binary representation using base 2 // Convert.ToString(n, 2) converts the number to a string in binary return Convert.ToString(n, 2); } static void Main() { int n = 12; Console.WriteLine(decToBinary(n)); } } function decToBinary(n) { // Use toString(2) to convert the // number to a binary string return n.toString(2); } // Driver Code let n = 12; console.log(decToBinary(n)); Similar Reads
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