C++ Program For Decimal To Binary Conversion

Binary Numbers uses only 0 and 1 (base-2), while Decimal Number uses 0 to 9 (base-10). In this article, we will learn to implement a C++ program to convert Decimal numbers to Binary Numbers.

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

Decimal to Binary Conversion using Loop

• Create an array to store the binary representation of size 32, Since the binary representation of an integer can have at most 32 bits.
• Run a loop till n is greater than 0.
• Extract the remainder by taking the mod of number using the modulus operator and store the remainder in the array as a binary digit.
• Update the number by dividing it by 2 in each iteration.
• Print the array in reverse order.

C++ Program to Convert Decimal To Binary using Loop

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 = 10;
    decToBinary(n);
    return 0;
}

Output

1010

Explanation

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. The 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. The 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. The 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. The new number is 1/2 = 0. 
Step 9: Since the number becomes = 0.
Print the array in reverse order. Therefore the equivalent binary number is 1010.

Complexity Analysis

• Time complexity: O(log (n))
• Auxiliary Space: O(1)

Decimal to Binary Conversion using std::bitset

C++ Standard Template Library provides std::bitset class that is used to perform bitwise operations on binary numbers. It can be used to convert Decimal Numbers to Binary and vice versa.

C++ Program to Convert Decimal To Binary using std::bitset

In the below C++ program, a bitset of size 4 is created and initialized with 10. Now the bitset binaryRepresentation will store the binary representation of 10.

C++

// C++ program to convert decimal numbers to binary using
// bitset class
#include <bitset>
#include <iostream>
#include <math.h>
using namespace std;
int main()
{
    int decimalNumber = 10;

    // Assuming 32-bit representation
      const int sz = ceil(log2(10));
    bitset<sz> binaryRepresentation(decimalNumber);

    cout << "Binary representation: "
         << binaryRepresentation << endl;

    return 0;
}

Output

Binary representation: 1010

Complexity Analysis

• Time complexity: O(log(n)), where n is the decimal number.
• Auxiliary Space: O(1)

Refer to the complete article Program for Decimal to Binary Conversion for more methods to convert decimal numbers to binary numbers.