C++ Program For Decimal To Binary Conversion

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

Input: 33
Output: 100001

For Example: 
If the decimal number is 10. 
Step 1: Remainder when 10 is divided by 2 is zero. Therefore, arr[0] = 0. 
Step 2: Divide 10 by 2. New number is 10/2 = 5. 
Step 3: Remainder when 5 is divided by 2 is 1. Therefore, arr[1] = 1. 
Step 4: Divide 5 by 2. New number is 5/2 = 2. 
Step 5: Remainder when 2 is divided by 2 is zero. Therefore, arr[2] = 0. 
Step 6: Divide 2 by 2. New number is 2/2 = 1. 
Step 7: Remainder when 1 is divided by 2 is 1. Therefore, arr[3] = 1. 
Step 8: Divide 1 by 2. New number is 1/2 = 0. 
Step 9: Since number becomes = 0. Print the array in reverse order. Therefore the equivalent binary number is 1010.

The below diagram shows an example of converting the decimal number 17 to an equivalent binary number. 

Below is the implementation of the above idea.  

C++

// C++ program to convert a decimal
// number to binary number
#include <iostream>
using namespace std;

// Function to convert decimal
// to binary
void decToBinary(int n)
{
    // Array to store binary number
    int binaryNum[32];

    // Counter for binary array
    int i = 0;
    while (n > 0)
    {
        // Storing remainder in binary
        // array
        binaryNum[i] = n % 2;
        n = n / 2;
        i++;
    }

    // Printing binary array in reverse
    // order
    for (int j = i - 1; j >= 0; j--)
        cout << binaryNum[j];
}

// Driver code
int main()
{
    int n = 17;
    decToBinary(n);
    return 0;
}

Output:

10001

Time complexity: O(logn) 

Auxiliary Space: O(1)

We can use bitwise operators to do the above job. Note that bitwise operators work faster than arithmetic operators used above.

C++

// C++ program to Decimal to binary
// conversion using bitwise operator
// Size of an integer is assumed to
// be 32 bits
#include <iostream>
using namespace std;

// Function that convert Decimal
// to binary
int decToBinary(int n)
{
    // Size of an integer is assumed
    // to be 32 bits
    for (int i = 31; i >= 0; i--)
    {
        int k = n >> i;
        if (k & 1)
            cout << "1";
        else
            cout << "0";
    }
}

// Driver code
int main()
{
    int n = 32;
    decToBinary(n);
}

Output:

00000000000000000000000000100000

Time complexity: O(1) 

loop iterates constant(32) number of times everytime even for small number 

Auxiliary Space: O(1)

Efficient Approach: 

It’s another efficient approach to converting Decimal to binary using the right shift(>>) and And(&) operator. Here we’ll use only Binary Operators which usually are very fast in computation.

C++

// C++ program to implement
// the above approach
#include <bits/stdc++.h>
using namespace std;

string DecimalToBinary(int num)
{
    string str;
      while(num)
      {
      // 1
      if(num & 1)
        str+='1';

      // 0
      else
        str+='0';

      // Right Shift by 1
      num>>=1;
    }
      return str;
}

void reverse(string str)
{
  for(int i=str.size()-1 ; i>=0 ; i--)
   cout<< str[i];
}

// Driver code
int main()
{
    int num = 59;
    cout<< "Binary of num 59 is: ";
    reverse( DecimalToBinary(num));
    return 0;
}

Output:

Binary of num 59 is: 111011

Time Complexity:  O(log n)

Auxiliary Space: O(1)

Decimal to binary conversion can also be done without using arrays. 

C++

// C++ implementation of the approach
#include <cmath>
#include <iostream>
using namespace std;

#define ull unsigned long long int

// Function to return the binary
// equivalent of decimal value N
int decimalToBinary(int N)
{

    // To store the binary number
    ull B_Number = 0;
    int cnt = 0;
    while (N != 0)
    {
        int rem = N % 2;
        ull c = pow(10, cnt);
        B_Number += rem * c;
        N /= 2;

        // Count used to store exponent value
        cnt++;
    }

    return B_Number;
}

// Driver code
int main()
{
    int N = 17;
    cout << decimalToBinary(N);
    return 0;
}

Output:

10001

Time complexity: O(logn) 

Auxiliary Space: O(1)

Note that this method is similar to the one where we convert Binary to Decimal as discussed in this post.
There is yet another method that converts any Decimal Number to its Binary form. The idea is to use bitset.

Below is the implementation of the above approach. 

C++

// C++ program to convert a decimal number
// to its binary form.

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

// Function to convert a decimal number
// to its binary form
string decimalToBinary(int n)
{
    // Finding the binary form of the number
    // and converting it to string.
    string s = bitset<64> (n).to_string();

    // Finding the first occurrence of "1"
    // to strip off the leading zeroes.
    const auto loc1 = s.find('1');

    if(loc1 != string::npos)
        return s.substr(loc1);

    return "0";
}

// Driver Code
int main()
{
    int n = 17;

    // Function call
    cout << decimalToBinary(n);

    return 0;
}

Output:

10001

Time complexity: O(logn) 

Auxiliary Space: O(1)
Another Approach:

C++

// C++ program to convert Decimal
// to Binary Number
#include <bits/stdc++.h>
using namespace std;

// Driver code
int main()
{
    // Input number
    int number = 15;
    int n = (int)(log2(number));

    // Binary output
    // using the inbuilt function
    cout << "the binary number is : " <<
             bitset<64>(number).to_string().substr(64 - n - 1);
}

Output:

the binary number is : 1111

Time complexity: O(logn) 

Auxiliary Space: O(1)