Decimal Base Converter Tool
Convert decimal numbers including fractions to binary, octal, and hexadecimal.
Options
Input
About Decimal Base Conversion
When converting decimals to other bases, some finite decimals in base 10 become infinite in base 2 (e.g., 0.1). This tool calculates approximations based on specified precision.
Examples
- 10.5 → 1010.1 (binary) ※Exact conversion
- 0.625 → 0.101 (binary) ※Exact conversion
- 0.1 → 0.0001100110... (binary) ※Infinite
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How to Use
1
Enter a number
Enter the decimal number you want to convert (fractions allowed).
2
Set precision
Set the precision (bit count) for the fractional part.
3
View results
Check the binary, octal, and hexadecimal results and copy them.
About This Tool
A free online tool to convert decimal numbers including fractions to binary, octal, and hexadecimal. Unlike integer-only converters, this handles decimals like 0.5 and 0.125 accurately.
Features
- Decimal fraction conversionConvert not just integers but also decimal fractions.
- Precision settingsSpecify the bit precision for the fractional part.
- Process visualizationView the division and multiplication steps.
- Infinite detectionShows whether the result is exact or an approximation.
Use Cases
- Understanding floating-point numbers
- Learning IEEE 754 standard
- Math and CS assignments
- Embedded programming
- Computer architecture study
FAQ
Why does 0.1 become infinite?
Decimal 0.1 represents 1/10, which cannot be exactly expressed as a sum of powers of 2, resulting in an infinite repeating fraction in binary.
What happens with higher precision?
More bits are used for the fractional part, giving a more accurate approximation. However, infinite fractions can never be perfectly accurate.
Which decimals convert exactly?
Decimals that can be expressed as sums of negative powers of 2 (0.5, 0.25, 0.125, etc.) convert exactly. Example: 0.625 = 0.5 + 0.125
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