The Binary Fraction Converter makes it easy to convert decimal fractions to binary and binary fractions to decimal. Enter a number, choose the conversion type, and get your result instantly. It supports whole numbers, fractional values, and negative numbers, making it useful for students, programmers, and anyone learning about number systems.
Binary Fraction Converter
Convert decimal fractions to binary and binary fractions to decimal instantly as you type.
Try an example
Select an example to load it and see the result instantly.
Conversion Result
Your answer updates automatically when you enter a number or change the settings.
Result
10.625 (Decimal) = 1010.101 (Binary)
Conversion complete.
Conversion details
10.625 = 8 + 2 + 0.5 + 0.125 = 1010.101 in binary.
How binary fractions work
Each digit after the binary point represents a negative power of two: 1/2, 1/4, 1/8, 1/16, and so on. For example, 0.101 in binary equals 1/2 + 0/4 + 1/8 = 0.625 in decimal.
Precision note
Some decimal fractions have repeating binary representations. The selected precision controls how many fractional binary digits are displayed.
How to Use the Binary Fraction Converter
Using this converter is simple:
- Enter a decimal or binary number in the input field.
- Select Decimal to Binary or Binary to Decimal.
- Choose the fractional precision if needed.
- View the result instantly in the results panel.
- Use the example buttons to try different conversions or click Clear All to start again.
Examples of Binary Fraction Conversion
Here are a few examples to help you understand how decimal and binary fractions work.
| Decimal Number | Binary Equivalent |
|---|---|
| 0.5 | 0.1 |
| 0.75 | 0.11 |
| 0.625 | 0.101 |
| 1.25 | 1.01 |
| 10.625 | 1010.101 |
For example, the decimal number 0.625 is equal to 0.101 in binary. This is because the binary digits after the point represent fractions such as 1/2, 1/4, and 1/8.
What Is a Binary Fraction?
A binary fraction is a number that contains digits after the binary point. Unlike the decimal system, which uses powers of 10, the binary system uses powers of 2. Each position after the binary point represents a fraction such as 1/2, 1/4, 1/8, or 1/16.
Binary fractions are commonly used in computer science, digital electronics, and programming. Some decimal fractions have repeating binary representations, so they may require rounding when converted to a limited number of binary digits.
Frequently Asked Questions
1. What is a binary fraction converter?
A binary fraction converter is a tool that converts numbers with fractional parts between decimal and binary formats. It can convert decimal values such as 0.625 into binary (0.101) and binary fractions back into decimal.
2. How do I convert a decimal fraction to binary?
Separate the whole-number and fractional parts. Convert the whole-number part using repeated division by 2, then convert the fractional part by repeatedly multiplying it by 2 and recording the integer digits. The converter performs these steps automatically.
3. How do I convert a binary fraction to decimal?
Multiply each digit by its corresponding power of 2 and add the results. For example, binary 0.101 equals 1/2 + 0/4 + 1/8, which gives 0.625 in decimal.
4. Can I convert numbers such as 10.625 to binary?
Yes. The converter handles numbers containing both whole and fractional parts. For example, 10.625 in decimal is 1010.101 in binary.
5. Why do some binary fractions have long results?
Some decimal fractions cannot be represented exactly with a finite number of binary digits. In these cases, the converter displays a rounded result according to the selected precision.
6. Can I convert negative binary fractions?
Yes. You can enter negative decimal or binary fractions, such as -10.5 or -1010.1, and convert them using the appropriate conversion option.
7. Is this binary fraction converter free to use?
Yes. You can use the converter directly in your browser without installing software or using an external conversion service.