Conversion of Decimal to Binary using Recursion

Introduction

Converting decimal numbers to binary is a common task in computer science and programming. Binary representation uses only two digits, 0 and 1, to express numbers, which is the foundational system for computers. The recursive approach for converting decimal to binary involves dividing the number by 2 and keeping track of the remainders. This method provides a clear and elegant solution to the problem.

#include <stdio.h>

// Function to convert decimal to binary using recursion
void decimalToBinary(int n) {
    if (n > 1) {
        decimalToBinary(n / 2); // Recursive call with quotient
    }
    printf("%d", n % 2); // Print the remainder (binary digit)
}

int main() {
    int decimalNumber;

    // Input: decimal number
    printf("Enter a decimal number: ");
    scanf("%d", &decimalNumber);

    printf("Binary representation: ");
    decimalToBinary(decimalNumber); // Call the recursive function
    printf("\n");

    return 0;
}

Explanation

1. Function Definition:
   • The function decimalToBinary takes an integer nnn as input.
   • Base Case: If nnn is greater than 1, the function calls itself with the value of nnn divided by 2. This continues until nnn is reduced to 1 or 0.
   • Recursive Case: After the recursive calls complete, the function prints the remainder of nnn divided by 2, which corresponds to the binary digits.
2. Main Function:
   • Prompts the user to enter a decimal number.
   • Calls the decimalToBinary function to perform the conversion and print the result.

Input

When the program runs, it prompts for input:

Enter a decimal number: 10

Output

The output will display the binary representation of the entered decimal number:

Binary representation: 1010

Conclusion

Using recursion to convert a decimal number to binary is an effective way to demonstrate the concept of recursive function calls. This method provides a clear and straightforward solution to the problem by breaking it down into smaller parts. While this recursive approach is elegant, it may not be the most efficient method for very large numbers due to function call overhead. However, it serves as a great example of how recursion can be used to solve problems in programming and enhances the understanding of number systems.