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Hexadecimal Fraction Converter

Hex Fraction to Binary Converter

Convert a hexadecimal fraction to binary instantly. Enter values such as A.F, 0.1, 2.BC, or FF.8 and get the exact binary value together with a digit-by-digit 4-bit mapping.

Exact 4-bit mapping Every hexadecimal digit maps directly to four binary bits.
Fraction support Handles hexadecimal digits before and after the radix point.
Leading-zero aware Fractional binary positions are preserved correctly.
Instant breakdown See the binary nibble corresponding to every entered hex digit.
Hex Fraction Converter
● LIVE
Use digits 0–9 and A–F. Optional 0x prefix supported.
BINARY RESULT BASE 2
Your binary fraction will appear here.
A.F₁₆ = 1010.1111₂
TRY AN EXAMPLE
HEX → 4-BIT BINARY 1 hex digit = 4 bits
Convert a value to see each hexadecimal digit mapped to binary.
Input Base Hexadecimal · Base 16
Output Base Binary · Base 2
Mapping 1 hex digit = 4 bits
Fractions Radix point supported
Example A.F = 1010.1111

Hex Fraction to Binary Converter

The Hex Fraction to Binary Converter converts hexadecimal values containing a fractional part into their exact binary equivalent. A hexadecimal fraction contains digits on either side of a radix point, such as A.F, 3.8, 0.25, or FF.C.

Because hexadecimal is base 16 and binary is base 2, each hexadecimal digit maps directly to a group of four binary bits. This makes hexadecimal fraction conversion particularly simple and exact.

Quick example: A.F16 = 1010.11112. A maps to 1010 and F maps to 1111.

How to Convert a Hex Fraction to Binary

Convert each hexadecimal digit independently using its four-bit binary equivalent. Keep the radix point in exactly the same position between the corresponding digit groups.

A.F₁₆ A = 1010 F = 1111 A.F₁₆ = 1010.1111₂

There is no need to repeatedly multiply the fractional portion by two as you would when converting a decimal fraction to binary.

Hexadecimal to Binary Digit Mapping

Every hexadecimal digit corresponds to one four-bit binary nibble. The same mapping applies whether the hexadecimal digit appears before or after the radix point.

Hex Binary Decimal Hex Binary Decimal
000000 810008
100011 910019
200102 A101010
300113 B101111
401004 C110012
501015 D110113
601106 E111014
701117 F111115

Example: Convert 2.BC to Binary

Convert each hexadecimal digit to four binary bits.

2 = 0010 B = 1011 C = 1100 2.BC₁₆ = 0010.1011 1100₂ = 10.10111100₂

The unnecessary integer-side leading zeros can be removed. The fractional binary groups remain aligned with their original hexadecimal positions.

Common Hex Fraction to Binary Values

Hex Fraction Binary Equivalent
0.1 0.0001
0.2 0.0010
0.4 0.0100
0.8 0.1000
1.A 1.1010
2.BC 10.10111100
A.F 1010.1111
F.5 1111.0101
10.25 10000.00100101
FF.8 11111111.1000

Why Hexadecimal Fractions Convert Exactly to Binary

The conversion is exact because hexadecimal and binary have a power-of-two relationship.

16 = 2⁴ Therefore: 1 hexadecimal digit = exactly 4 binary digits

This relationship continues after the radix point. For example, the first hexadecimal fractional position has a weight of 16-1, while four binary fractional positions represent the same subdivision.

0.1₁₆ = 1 / 16 = 0.0625₁₀ 0.0001₂ = 1 / 16 = 0.0625₁₀

Why Fractional Binary Zeros Matter

Zeros after the binary radix point can be important because they determine positional value. Hexadecimal 0.1 does not convert to binary 0.1.

0.1₁₆ = 0.0001₂ NOT 0.1₂

Binary 0.1 represents one-half, whereas hexadecimal 0.1 represents one-sixteenth. For this reason, the calculator preserves the complete four-bit mapping of every hexadecimal fractional digit.

Hexadecimal Integer vs Fractional Positions

Digits to the left of the hexadecimal point use non-negative powers of sixteen. Digits to the right use negative powers.

Integer positions: 16² · 16¹ · 16⁰ Fraction positions: 16⁻¹ · 16⁻² · 16⁻³

When converted to binary, every one of these hexadecimal positions expands into exactly four binary positions.

Where Hexadecimal Fractions Are Used

Hexadecimal fractional notation is useful whenever binary-aligned values must be represented more compactly.

  • Computer arithmetic and numerical analysis.
  • Low-level programming and debugging.
  • Fixed-point binary systems.
  • Floating-point investigation.
  • Embedded software and digital hardware.
  • Computer architecture education.
  • Binary data inspection.
  • Technical documentation involving base-16 numbers.

Common Hex Fraction Conversion Mistakes

  • Removing zeros immediately after the binary point.
  • Moving the radix point after conversion.
  • Using fewer than four bits for an internal hexadecimal digit.
  • Treating A through F as decimal characters rather than hexadecimal digits.
  • Using decimal fraction conversion rules unnecessarily.
  • Dropping fractional zeros that determine binary positional value.
  • Confusing ordinary hexadecimal fractions with IEEE 754 bit-pattern decoding.

Hex Fraction to Binary FAQs

How do I convert a hexadecimal fraction to binary?
Replace each hexadecimal digit with its four-bit binary equivalent and retain the radix point between the same digit groups.
What is 0.1 hexadecimal in binary?
0.1 hexadecimal equals 0.0001 binary.
What is A.F hexadecimal in binary?
A.F hexadecimal equals 1010.1111 binary.
Why does one hexadecimal digit equal four binary digits?
Hexadecimal has sixteen possible digit values and 16 equals 2 to the fourth power, so exactly four binary bits represent one hexadecimal digit.
Can hexadecimal fractions be represented exactly in binary?
Yes. Every finite hexadecimal fraction has a finite exact binary representation because each hexadecimal digit maps directly to four binary digits.
Does the converter accept lowercase hexadecimal letters?
Yes. Uppercase and lowercase A through F represent the same hexadecimal values.
Can I enter 0x before the hexadecimal value?
Yes. Inputs such as 0xA.F can be accepted by the calculator.
Why is hexadecimal 0.1 not binary 0.1?
Hexadecimal 0.1 represents one-sixteenth, while binary 0.1 represents one-half. One-sixteenth in binary is 0.0001.
Should binary zeros after the radix point be removed?
Not automatically. Some zeros identify the position of a fractional bit and preserve the original hexadecimal digit mapping.
Is this the same as converting IEEE 754 hexadecimal?
No. A regular hexadecimal fraction is direct positional base-16 notation. IEEE 754 hexadecimal bit patterns require separate sign, exponent, and significand interpretation.

Convert Hex Fractions to Binary Online

Enter a hexadecimal fraction in the calculator above and select Convert to Binary. The calculator validates the input, converts each hexadecimal digit into four binary bits, preserves the fractional positions, and displays both the complete binary result and the individual digit mapping.

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