C# program to convert floating to binary

Converting a floating-point number to binary representation in C# involves separating the number into its integer and fractional parts, then converting each part separately using different algorithms.

The integer part is converted using repeated division by 2, while the fractional part is converted using repeated multiplication by 2.

Algorithm

The conversion process follows these steps −

• Separate the floating-point number into integer and fractional parts

• Convert the integer part by repeatedly dividing by 2 and collecting remainders

• Convert the fractional part by repeatedly multiplying by 2 and collecting integer parts

• Combine both parts with a binary point

Using Integer and Fractional Part Separation

Example

using System;

class Program {
    static void Main() {
        float number = 50.5f;
        Console.WriteLine("Converting " + number + " to binary:");
        
        string binaryResult = FloatToBinary(number);
        Console.WriteLine("Binary representation: " + binaryResult);
    }
    
    static string FloatToBinary(float number) {
        if (number == 0) return "0";
        
        // Separate integer and fractional parts
        int integerPart = (int)number;
        float fractionalPart = number - integerPart;
        
        // Convert integer part
        string integerBinary = IntegerToBinary(integerPart);
        
        // Convert fractional part
        string fractionalBinary = FractionalToBinary(fractionalPart);
        
        return integerBinary + "." + fractionalBinary;
    }
    
    static string IntegerToBinary(int number) {
        if (number == 0) return "0";
        
        string binary = "";
        while (number > 0) {
            binary = (number % 2) + binary;
            number = number / 2;
        }
        return binary;
    }
    
    static string FractionalToBinary(float fraction) {
        string binary = "";
        int precision = 10; // Limit precision to avoid infinite loop
        
        while (fraction > 0 && precision > 0) {
            fraction *= 2;
            if (fraction >= 1) {
                binary += "1";
                fraction -= 1;
            } else {
                binary += "0";
            }
            precision--;
        }
        
        return binary.Length > 0 ? binary : "0";
    }
}

The output of the above code is −

Converting 50.5 to binary:
Binary representation: 110010.1

Using BitConverter for IEEE 754 Representation

For the actual IEEE 754 binary representation used internally by computers −

Example

using System;

class Program {
    static void Main() {
        float number = 50.5f;
        Console.WriteLine("Float value: " + number);
        
        // Get IEEE 754 binary representation
        byte[] bytes = BitConverter.GetBytes(number);
        string binaryString = "";
        
        // Convert each byte to binary (reverse order for little-endian)
        for (int i = bytes.Length - 1; i >= 0; i--) {
            binaryString += Convert.ToString(bytes[i], 2).PadLeft(8, '0');
        }
        
        Console.WriteLine("IEEE 754 binary: " + binaryString);
        
        // Break down the IEEE 754 format
        Console.WriteLine("Sign bit: " + binaryString[0]);
        Console.WriteLine("Exponent: " + binaryString.Substring(1, 8));
        Console.WriteLine("Mantissa: " + binaryString.Substring(9));
    }
}

The output of the above code is −

Float value: 50.5
IEEE 754 binary: 01000010010010010000000000000000
Sign bit: 0
Exponent: 10000100
Mantissa: 10010010000000000000000

Handling Different Float Values

Example

using System;

class Program {
    static void Main() {
        float[] numbers = { 12.75f, 0.375f, 100.25f };
        
        foreach (float num in numbers) {
            Console.WriteLine(num + " ? " + FloatToBinary(num));
        }
    }
    
    static string FloatToBinary(float number) {
        if (number == 0) return "0";
        
        int integerPart = (int)number;
        float fractionalPart = number - integerPart;
        
        string integerBinary = IntegerToBinary(integerPart);
        string fractionalBinary = FractionalToBinary(fractionalPart);
        
        return integerBinary + "." + fractionalBinary;
    }
    
    static string IntegerToBinary(int number) {
        if (number == 0) return "0";
        string binary = "";
        while (number > 0) {
            binary = (number % 2) + binary;
            number /= 2;
        }
        return binary;
    }
    
    static string FractionalToBinary(float fraction) {
        string binary = "";
        int precision = 8;
        
        while (fraction > 0 && precision > 0) {
            fraction *= 2;
            if (fraction >= 1) {
                binary += "1";
                fraction -= 1;
            } else {
                binary += "0";
            }
            precision--;
        }
        
        return binary.Length > 0 ? binary : "0";
    }
}

The output of the above code is −

12.75 ? 1100.11
0.375 ? 0.011
100.25 ? 1100100.01

Conclusion

Converting floating-point numbers to binary requires handling integer and fractional parts separately. The integer part uses division by 2, while the fractional part uses multiplication by 2. For precise IEEE 754 representation, use BitConverter.GetBytes() to get the actual binary format used by the computer.