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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 Python3 C# JavaScript PHP

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 Python3 C# JavaScript

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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