Decimal to Binary Converter
Convert decimal numbers (including fractions) to binary with step-by-step explanation
Quick Reference Table
| Decimal | Binary |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 10 |
| 3 | 11 |
| 4 | 100 |
| 5 | 101 |
| 0.5 | 0.1 |
| 0.25 | 0.01 |
| 0.125 | 0.001 |
| 0.375 | 0.011 |
This guide explains the decimal to binary tool and how to use it. We keep things clear and simple. You will learn each step of the process.
What Are Decimal and Binary Numbers?
Decimal numbers use base 10 with digits 0 to 9. They are used every day.
Binary numbers use only 0 and 1. Computers use binary to perform tasks.
How to Use This Tool
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Enter a Decimal Number: Type a whole number or a number with a fraction into the input field. Examples include 42.375 or 10.5.
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Click the Convert Button: Press the button. This starts the conversion process.
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Check the Results: The tool shows the decimal number and its binary equivalent. It also shows the steps used for conversion.
Understanding the Output
The result area displays the original decimal number. It then shows the binary number in a monospace font.
You will see detailed steps for converting the integer part. If you entered a fraction, the tool lists steps that show how the fraction is handled.
The tool multiplies the fraction by 2 until it either reaches zero or runs for 20 steps. This helps when fractions may not end in a finite number of digits.
Limitations and Special Notes
The tool performs up to 20 iterations for fractional numbers. Non-terminating fractions may be approximated.
If you enter an invalid value, you will see a prompt asking for a correct decimal number.
Common Use Cases
This converter is useful for students learning number systems. It helps those in coding and digital electronics. The tool is also handy for quick checks.
Conclusion
This decimal to binary tool makes conversion clear. The step-by-step guide shows how each part is calculated. Give it a try by entering a number, and follow the process displayed below. Happy converting!