Fast Mobile Fraction Only Exact Mapping 100% Free Browser-Based
Binary Fraction → Hexadecimal Fraction

Binary Fraction to Hex Converter

Convert a binary fraction to hexadecimal instantly. Enter a fraction-only binary value such as 0.1011 or .1011 and get the exact hexadecimal fraction, left-to-right 4-bit grouping, required right-side padding, and a clear conversion breakdown.

Fraction-only conversion Designed for binary values from 0 up to, but not including, 1.
Group from the point Fractional bits are grouped left to right after the radix point.
Right-side padding Incomplete final groups are padded with zeros on the right.
Exact bit mapping Hex output is created directly from 4-bit fractional groups.
Binary Fraction Converter
● LIVE
6 FRACTION BITS
FRACTION FORMAT ✓ VALID BINARY FRACTION
BINARY FRACTION 0.101101
GROUPED FRACTION .1011 0100
HEX FRACTION 0.B4
HEXADECIMAL FRACTION BASE 2 → BASE 16
0.B4
6 fraction bits · 2 hex fraction digits · 2 right-padding bits
.101101₂ → .1011 0100 → .B4₁₆
TRY AN EXAMPLE
Input Range 0 ≤ fraction < 1
Grouping Direction Left to right after point
Group Size 4 fractional bits
Padding Side Right side of fraction
Output Exact hexadecimal fraction

Binary Fraction to Hex Converter

The Binary Fraction to Hex Converter converts the fractional part of a binary number into an equivalent hexadecimal fraction. It is designed for values such as 0.1011, 0.0001, and .11101, where the numeric value is between zero and one.

Binary fractional conversion is closely related to binary integer conversion, but the grouping direction is different. Fractional bits are divided into groups of four beginning immediately after the binary point and moving toward the right.

For example, binary fraction 0.1011 contains one complete 4-bit fractional group. The binary group 1011 maps to hexadecimal B, so 0.1011₂ = 0.B₁₆.

How to Convert a Binary Fraction to Hexadecimal

Start immediately after the binary point and separate the fractional digits into groups of four while moving from left to right. Convert each 4-bit group into its hexadecimal equivalent.

Binary fraction:
0.101101₂

Fraction bits:
101101

Group from left to right:
1011 | 01

Pad the final group on the right:
1011 | 0100

1011 = B
0100 = 4

Result:
0.101101₂ = 0.B4₁₆

Why Binary Fraction Bits Are Grouped From Left to Right

For the fractional side of a positional number, place values begin immediately after the radix point and move toward increasingly smaller powers. The first four fractional binary positions therefore correspond to the first hexadecimal fractional digit.

Binary fractional positions:

2^-1 · 2^-2 · 2^-3 · 2^-4

These four binary positions form:
one hexadecimal fractional digit

This is the opposite directional emphasis from an integer, where grouping is anchored at the rightmost whole-number digit.

Example: Convert 0.1011 Binary to Hex

The binary fraction 0.1011 contains exactly four fractional bits, so no padding is necessary.

0.1011₂

Fraction group:
1011

1011 = B

Therefore:
0.1011₂ = 0.B₁₆

As a decimal fraction, both representations equal 11/16, or 0.6875.

Example: Convert 0.1 Binary Fraction to Hex

The fraction 0.1₂ has only one fractional bit. To form a complete 4-bit group, three zeros must be added to the right.

0.1₂

Fraction bits:
1

Right-pad to four bits:
1000

1000 = 8

Therefore:
0.1₂ = 0.8₁₆

Both values equal one half in decimal.

Example: Convert 0.0001 Binary to Hex

The four fractional digits 0001 already form a complete nibble and map directly to hexadecimal 1.

0.0001₂

0001 = 1

Result:
0.0001₂ = 0.1₁₆

Binary 0.0001 equals 1/16, and hexadecimal 0.1 also equals 1/16.

Binary Fraction to Hex 4-Bit Conversion Chart

Every group of four fractional binary digits maps to one hexadecimal fractional digit using the same nibble table used for whole binary values.

00000
00011
00102
00113
01004
01015
01106
01117
10008
10019
1010A
1011B
1100C
1101D
1110E
1111F

Common Binary Fraction to Hex Values

The table below shows common binary fractions together with their grouped binary form and exact hexadecimal equivalent.

Binary Fraction Grouped Fraction Hex Fraction Decimal Value
0.0001 .0001 0.1 0.0625
0.0010 .0010 0.2 0.125
0.0100 .0100 0.4 0.25
0.1000 .1000 0.8 0.5
0.1010 .1010 0.A 0.625
0.1011 .1011 0.B 0.6875
0.1111 .1111 0.F 0.9375
0.101101 .1011 0100 0.B4 0.703125

Live Binary Fraction Group Breakdown

After conversion, the calculator displays every four-bit fractional group and the hexadecimal digit that group represents. Padding bits are included in the display so the conversion can be checked visually.

1011 B
0100 4

How Right-Side Padding Works for Binary Fractions

If the number of fractional binary digits is not divisible by four, zeros are added after the final fractional bit until the last group contains exactly four digits.

Input:
0.101₂

Fraction group:
101

Add one zero on the right:
1010

1010 = A

Therefore:
0.101₂ = 0.A₁₆
For a fractional value, padding zeros belong on the right side. Adding zeros before the fractional digits would change their positional weights.

Why Trailing Zeros Do Not Change a Binary Fraction

Adding zeros after the final fractional binary digit does not change the numeric value, just as writing 0.5000 instead of 0.5 does not change an ordinary decimal fraction.

0.1₂ = 0.1000₂

0.1₂ = 1/2
0.1000₂ = 1/2

Both convert to:
0.8₁₆

Binary Fraction Place Values

Binary fractional digits represent negative powers of two. The first bit after the binary point has weight 2-1, the second has weight 2-2, and the pattern continues to the right.

Fraction Position Binary Weight Decimal Value
1st bit 2^-1 0.5
2nd bit 2^-2 0.25
3rd bit 2^-3 0.125
4th bit 2^-4 0.0625
5th bit 2^-5 0.03125
6th bit 2^-6 0.015625

Hexadecimal Fraction Place Values

Hexadecimal fractional positions use negative powers of sixteen. Because each hex digit summarizes four binary fractional positions, the first hexadecimal fraction digit has weight 16-1.

First hex fraction digit = 16^-1 = 1/16
Second hex fraction digit = 16^-2 = 1/256
Third hex fraction digit = 16^-3 = 1/4096

For example, hexadecimal 0.B means 11 × 1/16, which equals 11/16 or 0.6875 decimal.

Why Four Binary Fraction Bits Equal One Hex Fraction Digit

The relationship comes from the fact that hexadecimal base 16 is exactly 24. Four binary positions therefore contain the same amount of place-value information as one hexadecimal position.

16 = 2^4

4 binary fraction bits
=
1 hexadecimal fraction digit

This makes binary-to-hex fraction conversion exact and direct. There is no need to approximate the value using floating-point arithmetic.

Does Every Finite Binary Fraction Have a Finite Hex Fraction?

Yes. A finite binary fraction always converts to a finite hexadecimal fraction because hexadecimal is a power-of-two base. Any leftover binary digits can be completed by adding at most three trailing zeros.

A binary fraction with 1, 2, or 3 leftover bits needs 3, 2, or 1 padding zeros respectively. A fraction whose bit count is already divisible by four needs no padding.

Binary Fraction Bit Length and Hex Fraction Length

Each group of up to four binary fractional bits produces one hexadecimal fractional digit. Therefore the number of hex fraction digits is the binary fraction bit count divided by four and rounded upward.

Hex fraction digits = ceil(Binary fraction bits ÷ 4)

1-4 bits → 1 hex fraction digit
5-8 bits → 2 hex fraction digits
9-12 bits → 3 hex fraction digits
13-16 bits → 4 hex fraction digits

Binary Fraction vs Binary Number With a Fraction

A fraction-only binary value contains no non-zero integer portion. Values such as 0.1011 or .1011 belong to this category. A value such as 101.101 contains both a whole-number portion and a fractional portion and requires grouping on both sides of the binary point.

Binary Value Type Example Hex
0.1011 Binary fraction only 0.B
.1111 Binary fraction only 0.F
101.101 Integer + fraction 5.A

Where Binary Fraction to Hex Conversion Is Used

Fractional binary values appear in computing, digital systems, numerical representation, and educational work where powers-of-two fractions need to be expressed more compactly in hexadecimal.

  • Learning binary and hexadecimal fractional place values.
  • Studying fixed-point binary representations.
  • Inspecting fractional bit fields in digital systems.
  • Understanding hexadecimal forms of powers-of-two fractions.
  • Working with low-level numerical formats and bit-oriented data.
  • Checking manual binary-to-hex conversion exercises.
  • Analyzing mantissa or significand bit patterns conceptually.

Common Binary Fraction to Hex Conversion Mistakes

Fractional binary conversion has several rules that differ from integer conversion, especially the grouping direction and padding side.

  • Grouping fraction bits from right to left instead of starting at the binary point.
  • Adding zeros to the left of the fractional group instead of trailing zeros on the right.
  • Dropping the binary point and accidentally treating the fraction as an integer.
  • Using more than one binary point.
  • Entering digits other than 0 and 1.
  • Entering a non-zero integer part on a fraction-only converter.
  • Assuming a trailing zero changes the value of the fraction.
  • Using floating-point approximation when direct 4-bit mapping is exact.

Binary Fraction to Hex Converter FAQs

These FAQs explain binary fractional grouping, right-side padding, hexadecimal fraction notation, exactness, accepted input formats, and common examples.

How do I convert a binary fraction to hexadecimal?
Starting immediately after the binary point, divide the fractional bits into groups of four from left to right. Add trailing zeros to the final group if necessary, then convert each 4-bit group to its hexadecimal digit.
What is 0.1011 binary in hexadecimal?
The fractional group 1011 maps directly to hexadecimal B, so 0.1011 binary equals 0.B hexadecimal.
What is 0.1 binary in hexadecimal?
Pad the fraction to 1000. Binary 1000 maps to hexadecimal 8, so 0.1 binary equals 0.8 hexadecimal.
What is 0.1111 binary in hex?
Binary fraction 1111 maps directly to hexadecimal F, so 0.1111 binary equals 0.F hexadecimal.
What is 0.101 binary in hexadecimal?
Pad the fractional bits on the right to 1010. That group maps to hexadecimal A, so 0.101 binary equals 0.A hexadecimal.
Why are zeros added on the right of a binary fraction?
Trailing zeros after the existing fractional bits do not change their place-value weights. They simply complete the final four-bit group needed for hexadecimal conversion.
Can I enter .1011 instead of 0.1011?
Yes. The converter accepts a leading zero before the binary point as optional and normalizes the displayed result to the 0.x form.
Can I enter 1.101 on this page?
No. This page is specifically for fraction-only values below 1. A value with a non-zero integer portion requires conversion of both its integer and fractional sections.
Can I enter only 1011 without a binary point?
No. A binary fraction must include the radix point so the converter can distinguish fractional bits from integer bits.
Does 0.1000 have the same value as 0.1?
Yes. Trailing zeros do not change the value of a positional fraction. Both represent one half and both convert to hexadecimal 0.8.
Is binary fraction to hex conversion exact?
Yes for finite binary fractions. Hexadecimal is base 16, which equals 2^4, so finite binary fractional digits map exactly into groups of four.
How many binary fractional bits make one hex digit?
Exactly four binary fractional bits correspond to one hexadecimal fractional digit.
Can very long binary fractions be converted exactly?
Yes. The converter processes the fractional bit string directly in 4-bit groups, so the hexadecimal result does not require floating-point arithmetic.

Convert Binary Fractions to Hex Online

Enter a fraction-only binary value such as 0.101101 and select Convert Binary Fraction to Hex. The calculator validates the fraction format, extracts the fractional bits, groups them from left to right, adds any required trailing zero padding, and returns the exact hexadecimal fraction.

The result also includes the fractional bit count, hexadecimal fractional digit count, number of right-padding bits, grouped binary representation, and a live nibble-by-nibble conversion breakdown.

Scroll to Top