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Decimal to binary conversion without using arithmetic operators

Last Updated : 06 Dec, 2023
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Find the binary equivalent of the given non-negative number n without using arithmetic operators.

Examples: 

Input : n = 10
Output : 1010

Input : n = 38
Output : 100110

Note that + in below algorithm/program is used for concatenation purpose. 
Algorithm: 

decToBin(n)
    if n == 0
        return "0"
    Declare bin = ""
    Declare ch
    while n > 0
        if (n & 1) == 0
            ch = '0'
        else
            ch = '1'
        bin = ch + bin
        n = n >> 1
    return bin


 Below is the implementation of above approach:

C++ 
// C++ implementation of decimal to binary conversion
// without using arithmetic operators
#include <bits/stdc++.h>

using namespace std;

// function for decimal to binary conversion
// without using arithmetic operators
string decToBin(int n)
{
    if (n == 0)
        return "0";
    
    // to store the binary equivalent of decimal
    string bin = "";    
    while (n > 0)    
    {
        // to get the last binary digit of the number 'n'
        // and accumulate it at the beginning of 'bin'
        bin = ((n & 1) == 0 ? '0' : '1') + bin;
        
        // right shift 'n' by 1
        n >>= 1;
    }
    
    // required binary number
    return bin;
}

// Driver program to test above
int main()
{
    int n = 38;
    cout << decToBin(n);
    return 0;
}
Java 
// Java implementation of decimal 
// to binary conversion without
// using arithmetic operators
import java.io.*;

class GFG {
    
    // function for decimal to 
    // binary conversion without
    // using arithmetic operators
    static String decToBin(int n)
    {
        if (n == 0)
            return "0";
    
        // to store the binary 
        // equivalent of decimal
        String bin = ""; 
        
        while (n > 0) 
        {
            // to get the last binary digit 
            // of the number 'n' and accumulate 
            // it at the beginning of 'bin'
            bin = ((n & 1) == 0 ? '0' : '1') + bin;
            
            // right shift 'n' by 1
            n >>= 1;
        }
        
        // required binary number
        return bin;
    }

    // Driver program to test above
    public static void main (String[] args) {

    int n = 38;
    System.out.println(decToBin(n));
    }
} 

// This code is contributed by vt_m
Python3 
# Python3 implementation of 
# decimal to binary conversion
# without using arithmetic operators

# function for decimal to 
# binary conversion without 
# using arithmetic operators
def decToBin(n):
    if(n == 0):
        return "0";
        
    # to store the binary
    # equivalent of decimal
    bin = "";
    
    while (n > 0):
        
        # to get the last binary
        # digit of the number 'n'
        # and accumulate it at 
        # the beginning of 'bin'
        if (n & 1 == 0):
            bin = '0' + bin;
        else:
            bin = '1' + bin;
        
        # right shift 'n' by 1
        # It also gives n//2 .
        n = n >> 1;
    
    # required binary number
    return bin;

# Driver Code
n = 38;
print(decToBin(n));

# This code is contributed
# by mits
C# 
// C# implementation of decimal
// to binary conversion without
// using arithmetic operators
using System;

class GFG {
    
    // function for decimal to
    // binary conversion without
    // using arithmetic operators
    static String decToBin(int n)
    {
        if (n == 0)
            return "0";

        // to store the binary
        // equivalent of decimal
        String bin = "";

        while (n > 0) {
            
            // to get the last binary digit
            // of the number 'n' and accumulate
            // it at the beginning of 'bin'
            bin = ((n & 1) == 0 ? '0' : '1') + bin;

            // right shift 'n' by 1
            n >>= 1;
        }

        // required binary number
        return bin;
    }

    // Driver program to test above
    public static void Main()
    {

        int n = 38;
        Console.WriteLine(decToBin(n));
    }
}

// This code is contributed by Sam007
JavaScript 
<script>
// javascript implementation of decimal 
// to binary conversion without
// using arithmetic operators
   
// function for decimal to 
// binary conversion without
// using arithmetic operators
function decToBin(n)
{
    if (n == 0)
        return "0";

    // to store the binary 
    // equivalent of decimal
    var bin = ""; 
    
    while (n > 0) 
    {
        // to get the last binary digit 
        // of the number 'n' and accumulate 
        // it at the beginning of 'bin'
        bin = ((n & 1) == 0 ? '0' : '1') + bin;
        
        // right shift 'n' by 1
        n >>= 1;
    }
    
    // required binary number
    return bin;
}

// Driver program to test above
var n = 38;
document.write(decToBin(n));

// This code is contributed by shikhasingrajput 
</script>
PHP 
<?php
// PHP implementation of decimal 
// to binary conversion without 
// using arithmetic operators

// function for decimal to 
// binary conversion without 
// using arithmetic operators
function decToBin($n)
{
    if ($n == 0)
        return "0";
    
    // to store the binary 
    // equivalent of decimal
    $bin = ""; 
    while ($n > 0) 
    {
        // to get the last binary 
        // digit of the number 'n'
        // and accumulate it at
        // the beginning of 'bin'
        $bin = (($n & 1) == 0 ? 
                          '0' : '1') . $bin;
        
        // right shift 'n' by 1
        $n >>= 1;
    }
    
    // required binary number
    return $bin;
}

// Driver Code
$n = 38;
echo decToBin($n);

// This code is contributed
// by mits
?>

Output: 
 

100110


Time complexity: O(num), where num is the number of bits in the binary representation of n.
Auxiliary space: O(num), for using extra space for string bin.




 

METHOD 2:Using format()

APPROACH:

This code converts a decimal number to binary using the built-in format() function in Python. The function takes two arguments: the first is the number to be converted, and the second is the format specifier 'b', which tells the function to convert the number to binary.

ALGORITHM:

1. Take the decimal number as input.
2. Convert the decimal number to binary using the format() function with the format specifier 'b'.
3. Store the result in a variable.
4. Print the variable.

C++ 
// CPP code of the above approach
#include <bits/stdc++.h>
using namespace std;

int main()
{
    int n = 38;
    // Convert n to binary representation as a string
    string binary = bitset<32>(n).to_string();
    cout << "The binary representation of " << n
         << " is: " << stoi(binary) << endl;

    n = 10;
    // Convert n to binary representation as a string
    binary = bitset<32>(n).to_string();
    cout << "The binary representation of " << n
         << " is: " << stoi(binary) << endl;

    return 0;
}

// This code is contributed by Susobhan Akhuli
Java 
// Java code of the above approach
import java.util.Scanner;

public class GFG {
    public static void main(String[] args)
    {
        int n = 38;
        // Convert n to binary representation as a string
        String binary = Integer.toBinaryString(n);
        System.out.println("The binary representation of "
                           + n + " is: " + binary);

        n = 10;
        // Convert n to binary representation as a string
        binary = Integer.toBinaryString(n);
        System.out.println("The binary representation of "
                           + n + " is: " + binary);
    }
}

// This code is contributed by Susobhan Akhuli
Python3 
n = 38
binary = format(n, 'b')
print(f"The binary representation of {n} is: {binary}")

n = 10
binary = format(n, 'b')
print(f"The binary representation of {n} is: {binary}")
C# 
// C# code of the above approach
using System;

public class GFG {
    static void Main()
    {
        int n = 38;

        // Convert n to binary representation as a string
        string binary
            = Convert.ToString(n, 2);
        Console.WriteLine(
            $"The binary representation of {n} is: {binary}");

        n = 10;

        // Convert n to binary representation as a string
        binary = Convert.ToString(n, 2);
        Console.WriteLine(
            $"The binary representation of {n} is: {binary}");
    }
}

// This code is contributed by Susobhan Akhuli
JavaScript 
// JavaScript program for the above approach
function decimalToBinary(n) {
    // Convert n to binary representation as a string
    let binary = n.toString(2);
    return binary;
}

// Test cases
let n1 = 38;
console.log(`The binary representation of ${n1} is: ${decimalToBinary(n1)}`);

let n2 = 10;
console.log(`The binary representation of ${n2} is: ${decimalToBinary(n2)}`);

// This code is contributed by Susobhan Akhuli

Output
The binary representation of 38 is: 100110
The binary representation of 10 is: 1010

Time complexity: O(log n), where n is the decimal number, because the number of iterations required in the format() function depends on the number of bits required to represent the number in binary, which is log2(n).

Space complexity: O(log n), because the space required to store the binary representation of the number in the variable also depends on the number of bits required to represent the number in binary, which is log2(n).


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