Decimal Base Converter Tool

Convert decimal numbers including fractions to binary, octal, and hexadecimal.

Last updated: 2025/01/15 Calculate
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
AD 728×90

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
AD 336×280