Problem Statement

Convert a decimal number to binary number.

Examples

Example 1:

Input:  number = 13

Output: 1101

Explanation:

Decimal Number: 13

13 / 2 = 6  (Remainder = 1)
 6 / 2 = 3  (Remainder = 0)
 3 / 2 = 1  (Remainder = 1)
 1 / 2 = 0  (Remainder = 1)

Binary Equivalent: 1101

Theory

• Decimal System: The decimal system is a base-10 numeral system, which uses 10 symbols (0-9) to represent numbers.
• Binary System: The binary system is a base-2 numeral system, which uses only two symbols (0 and 1) to represent numbers.

Different Approaches

Approach 1: Using Division

Step 1: 13 / 2 = 6  (Remainder = 1)
        |
        V
        1

Step 2: 6 / 2 = 3  (Remainder = 0)
        |
        V
        0

Step 3: 3 / 2 = 1  (Remainder = 1)
        |
        V
        1

Step 4: 1 / 2 = 0  (Remainder = 1)
        |
        V
        1


Now append them in reverse order.
Binary Equivalent: 1101

#include <iostream>
#include <string>
using namespace std;

// Function to convert decimal to binary using division method
string decimalToBinaryDivision(int n) {
    string binary = ""; // Initialize an empty string to store binary digits

    // Divide the decimal number by 2 until quotient is 0
    while (n > 0) {
        int rem = n % 2; // Calculate remainder
        binary = to_string(rem) + binary; // Store the remainder
        n /= 2; // Update the quotient
    }
    return binary; // Return the binary equivalent
}

int main() {
    int decimal = 13;
    string binary = decimalToBinary(decimal);
    cout << "Binary equivalent of " << decimal << " is " << binary << endl;
    return 0;
}

Output:

Binary equivalent of 13 is 1101

Complexity Analysis

Time Complexity:O(log n)

Space Complexity:O(log n)

2 Approach 2: Using Bitwise Shift Operator

In this approach, we use the bitwise shift operator to convert the decimal number to binary.

Code Implementation in C++:

#include <iostream>
using namespace std;

// Function to convert decimal to binary using bitwise shift operator method
string decimalToBinaryBitwise(int n) {
    string binary = ""; // Initialize an empty string to store binary digits

    // Loop through each bit from left to right (from most significant to least significant)
    for (int i = 31; i >= 0; i--) {
        // Check if the bit at position i is set (1) or not (0)
        if (n & (1 << i))
            binary += "1"; // If set, append '1' to the binary string
        else
            binary += "0"; // If not set, append '0' to the binary string
    }
    return binary; // Return the binary equivalent
}

int main() {
    int decimal = 13;
     // Convert decimal to binary using bitwise shift operator method
    string binary_bitwise = decimalToBinaryBitwise(decimal);
    cout << "Binary equivalent of " << decimal << " using bitwise shift operator method: " << binary_bitwise << endl;
}

Output:

Binary equivalent of 13 is 00000000000000000000000000001101

Complexity Analysis:

Time Complexity:O(1)

Space Complexity:O(1)