How to convert a number from Decimal to Binary using recursion in C#?

Converting a decimal number to binary using recursion in C# involves repeatedly dividing the number by 2 and collecting the remainders. The recursive approach breaks down the problem into smaller subproblems until the base case is reached.

Syntax

Following is the basic syntax for the recursive binary conversion method −

public void ConvertToBinary(int decimalNumber) {
    if (decimalNumber > 0) {
        ConvertToBinary(decimalNumber / 2);
        Console.Write(decimalNumber % 2);
    }
}

How It Works

The recursive algorithm works by dividing the decimal number by 2 repeatedly. Each division produces a quotient (used for the next recursive call) and a remainder (which becomes a binary digit). The base case occurs when the number becomes 0.

Using Recursive Method for Display

Example

using System;

public class BinaryConverter {
    public void ConvertToBinary(int decimalNumber) {
        if (decimalNumber > 0) {
            ConvertToBinary(decimalNumber / 2);
            Console.Write(decimalNumber % 2);
        }
    }
}

public class Program {
    public static void Main(string[] args) {
        BinaryConverter converter = new BinaryConverter();
        int decimalNum = 30;
        
        Console.WriteLine("Decimal: " + decimalNum);
        Console.Write("Binary: ");
        converter.ConvertToBinary(decimalNum);
        Console.WriteLine();
        
        // Another example
        decimalNum = 45;
        Console.WriteLine("Decimal: " + decimalNum);
        Console.Write("Binary: ");
        converter.ConvertToBinary(decimalNum);
        Console.WriteLine();
    }
}

The output of the above code is −

Decimal: 30
Binary: 11110
Decimal: 45
Binary: 101101

Using Recursive Method with Return Value

Example

using System;

public class BinaryConverter {
    public string GetBinaryString(int decimalNumber) {
        if (decimalNumber == 0) {
            return "";
        }
        return GetBinaryString(decimalNumber / 2) + (decimalNumber % 2).ToString();
    }
}

public class Program {
    public static void Main(string[] args) {
        BinaryConverter converter = new BinaryConverter();
        
        int[] numbers = {10, 25, 100};
        
        foreach(int num in numbers) {
            string binary = converter.GetBinaryString(num);
            if (binary == "") binary = "0"; // Handle zero case
            Console.WriteLine($"Decimal {num} = Binary {binary}");
        }
    }
}

The output of the above code is −

Decimal 10 = Binary 1010
Decimal 25 = Binary 11001
Decimal 100 = Binary 1100100

Using Mathematical Approach with Recursion

Example

using System;

public class BinaryConverter {
    public long ConvertToNumericBinary(int decimalNumber) {
        if (decimalNumber == 0) {
            return 0;
        }
        return (decimalNumber % 2) + 10 * ConvertToNumericBinary(decimalNumber / 2);
    }
}

public class Program {
    public static void Main(string[] args) {
        BinaryConverter converter = new BinaryConverter();
        
        int decimalNum = 30;
        long binaryResult = converter.ConvertToNumericBinary(decimalNum);
        
        Console.WriteLine($"Decimal: {decimalNum}");
        Console.WriteLine($"Binary (as number): {binaryResult}");
        
        // Another example
        decimalNum = 15;
        binaryResult = converter.ConvertToNumericBinary(decimalNum);
        Console.WriteLine($"Decimal: {decimalNum}");
        Console.WriteLine($"Binary (as number): {binaryResult}");
    }
}

The output of the above code is −

Decimal: 30
Binary (as number): 11110
Decimal: 15
Binary (as number): 1111

Conclusion

Converting decimal to binary using recursion in C# involves dividing the number by 2 repeatedly and collecting remainders. The recursive approach naturally handles the reverse order of binary digits, making it an elegant solution for this conversion problem.