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Binary Number → Hexadecimal

Binary Number with Fraction to Hex

Convert a binary number with an integer and fractional part to hexadecimal. Enter a value such as 101101.011 and get the exact hexadecimal result with separate integer and fraction grouping, left and right padding, and a clear conversion breakdown.

Two-sided grouping Integer and fraction bits are handled independently around the point.

Correct padding direction Integer pads left; fraction pads right.

Exact direct conversion Every 4-bit group maps directly to one hexadecimal digit.

Large values supported Conversion does not require floating-point number arithmetic.

Binary Number Converter

● LIVE

ENTER BINARY INTEGER + FRACTION

6 + 3 BITS

NUMBER FORMAT ✓ INTEGER + FRACTION DETECTED

BINARY INPUT 101101.011

GROUPED BINARY 0010 1101 . 0110

HEX 2D.6

HEXADECIMAL RESULT INTEGER + FRACTION

2D.6

6 integer bits · 3 fraction bits · 2 hex integer digits · 1 hex fraction digit

101101.011₂ → 0010 1101 . 0110 → 2D.6₁₆

TRY AN EXAMPLE

Integer Grouping Right to left

Integer Padding Zeros on the left

Fraction Grouping Left to right

Fraction Padding Zeros on the right

Mapping 4 binary bits = 1 hex digit

Binary Number with Fraction to Hex Converter

The Binary Number with Fraction to Hex Converter converts a binary value containing digits on both sides of the binary point into its exact hexadecimal representation. This includes values such as 101.101, 101101.011, and 11111111.1111.

The integer and fractional sections are converted independently because their grouping directions are different. Whole-number bits are grouped outward from the point toward the left, while fractional bits are grouped outward from the point toward the right.

For example, 101.101₂ becomes 0101 . 1010 after padding. Binary 0101 maps to hexadecimal 5 and binary 1010 maps to hexadecimal A, giving 5.A₁₆.

How to Convert a Binary Number with a Fraction to Hex

First split the binary value at the radix point. Convert the integer part using right-to-left 4-bit grouping, then convert the fractional part using left-to-right 4-bit grouping.

Binary number:
101101.011₂

Integer part:
101101 → 10 | 1101
Pad left → 0010 | 1101

Fraction part:
011 → 0110
Pad right → 0110

Convert groups:
0010 = 2
1101 = D
0110 = 6

Result:
101101.011₂ = 2D.6₁₆

The Two Binary-to-Hex Grouping Rules

When a binary number contains both a whole and fractional section, the binary point acts as the alignment boundary. Groups are built outward from that point in opposite directions.

Number Section	Grouping Direction	Padding Side	Example
Integer part	Right to left	Left	`10101 → 0001 0101`
Fraction part	Left to right	Right	`.101 → .1010`

Mixing these padding directions changes the place values. Integer padding belongs on the left; fraction padding belongs on the right.

Example: Convert 101.101 Binary to Hexadecimal

The binary number 101.101 has three integer bits and three fraction bits. Each side therefore needs one padding bit to complete a four-bit hexadecimal group.

101.101₂

Integer:
101 → 0101 → 5

Fraction:
101 → 1010 → A

Therefore:
101.101₂ = 5.A₁₆

The value is decimal 5.625. Hexadecimal 5.A represents exactly the same value because A/16 equals 0.625.

Example: Convert 101101.011 Binary to Hex

This example demonstrates padding on both sides of the binary point. The six-bit integer portion needs two leading zeros, while the three-bit fraction needs one trailing zero.

101101.011₂

Integer grouping:
10 | 1101
0010 | 1101

Fraction grouping:
011 → 0110

0010 = 2
1101 = D
0110 = 6

Result:
2D.6₁₆

Example: Convert 11111111.1111 Binary to Hex

When both sides already contain complete 4-bit groups, no padding is needed. This makes the conversion especially direct.

11111111.1111₂

1111 | 1111 . 1111

1111 = F
1111 = F
1111 = F

Result:
FF.F₁₆

Common Binary Numbers with Fractions and Their Hex Values

The following examples show how common mixed binary values convert to hexadecimal when the integer and fractional sections are grouped separately.

Binary	Padded / Grouped Binary	Hex	Decimal
`1.1`	`0001 . 1000`	`1.8`	1.5
`10.01`	`0010 . 0100`	`2.4`	2.25
`101.101`	`0101 . 1010`	`5.A`	5.625
`1111.1111`	`1111 . 1111`	`F.F`	15.9375
`10000.0001`	`0001 0000 . 0001`	`10.1`	16.0625
`101101.011`	`0010 1101 . 0110`	`2D.6`	45.375
`11111111.1111`	`1111 1111 . 1111`	`FF.F`	255.9375

Live Integer and Fraction Group Breakdown

After conversion, the calculator displays integer groups and fractional groups separately. This makes the opposite grouping and padding directions easy to verify visually.

Integer Groups

0010 2

1101 D

Fraction Groups

0110 6

Why the Binary Point Stays in the Same Position

The radix point separates place values greater than or equal to one from place values below one. During binary-to-hex conversion, each side is regrouped, but the boundary between integer and fractional values remains unchanged.

Binary:
101101 . 011

After grouping:
0010 1101 . 0110

Hex:
2D . 6

The point is not converted into a digit. It remains the separator between the whole hexadecimal digits and hexadecimal fractional digits.

How Integer Padding Works

If the integer part does not contain a multiple of four bits, zeros are placed before the leftmost integer bit. Leading zeros do not change the numeric value of the integer portion.

Integer portion:
10101

Group from the point toward the left:
1 | 0101

Pad on the left:
0001 | 0101

Hex:
15

How Fraction Padding Works

If the fractional section does not contain a multiple of four bits, zeros are placed after the final fractional bit. Trailing fractional zeros preserve the same value.

Fraction portion:
.101

Group from the point toward the right:
.101

Pad on the right:
.1010

Hex fraction:
.A

Why Four Binary Digits Equal One Hexadecimal Digit

Binary uses base 2 and hexadecimal uses base 16. Since 16 equals 2⁴, every sequence of exactly four binary bits maps to one hexadecimal digit.

16 = 2⁴

4 binary bits
=
1 hexadecimal digit

This relationship works equally well on both sides of the radix point, which is why mixed binary values can be converted exactly without passing through decimal first.

Binary and Hexadecimal Place Values Around the Radix Point

Both binary and hexadecimal are positional number systems. To the left of the point, place values use positive powers of the base. To the right, they use negative powers.

Position	Binary Weight	Hex Weight
First integer digit	`2⁰ = 1`	`16⁰ = 1`
Second integer digit	`2¹ = 2`	`16¹ = 16`
First fractional digit	`2⁻¹ = 1/2`	`16⁻¹ = 1/16`
Second fractional digit	`2⁻² = 1/4`	`16⁻² = 1/256`

Can Binary Numbers with Fractions Convert Exactly to Hex?

Yes. Any finite binary number converts exactly into a finite hexadecimal number because hexadecimal is a power-of-two base. No repeating hexadecimal fraction is required for a finite binary input.

At most three zero bits need to be added to either incomplete side to align it with a four-bit hexadecimal group. These padding bits do not alter the numeric value.

This direct relationship is one reason hexadecimal is especially convenient for displaying binary data: every hexadecimal digit corresponds to a fixed four-bit binary block.

Binary Fraction Converter vs Binary Number with Fraction Converter

A fraction-only converter focuses on values whose whole-number section is zero, such as 0.1011. A binary number with fraction converter handles a full mixed value containing both an integer section and a fractional section.

Input	Type	Hex
`0.1011`	Fraction-only binary	`0.B`
`101.1011`	Integer + fraction	`5.B`
`101101.011`	Integer + fraction	`2D.6`

Converting Large Binary Numbers with Long Fractions

A mixed binary value may contain hundreds or thousands of digits on either side of the radix point. Converting the complete value through ordinary floating-point arithmetic can lose precision, especially in the fractional portion.

This converter avoids that problem by processing the integer and fractional bit strings directly. Each side is padded independently and converted through exact 4-bit hexadecimal lookup.

The hexadecimal result therefore reflects the exact supplied binary digits rather than a rounded floating-point approximation.

Where Binary Numbers with Fractions Are Used

Binary values containing both whole and fractional portions appear in fixed-point arithmetic, numerical computing, digital hardware, educational work, and low-level representations of powers-of-two quantities.

Fixed-point numeric representations in embedded systems.
Digital signal processing values containing fractional bits.
Computer architecture and binary arithmetic education.
Manual verification of binary-to-hexadecimal calculations.
Analysis of low-level numeric formats.
Hardware designs that use explicit integer and fractional bit fields.
Debugging binary values where hexadecimal is easier to inspect.

Common Binary Number with Fraction Conversion Mistakes

The most frequent errors occur when the integer and fractional sections are grouped using the same direction or when padding is applied to the wrong side.

Grouping integer bits from left to right instead of from the radix point outward.
Grouping fractional bits from the far right instead of starting immediately after the point.
Adding integer padding zeros on the right.
Adding fractional padding zeros on the left.
Moving the radix point after grouping.
Using digits other than 0 and 1.
Entering more than one binary point.
Converting through floating-point decimal arithmetic and introducing rounding.

Binary Number with Fraction to Hex FAQs

These frequently asked questions cover two-sided grouping, padding direction, radix-point handling, exact conversion, examples, and large binary values.

How do I convert a binary number with a fraction to hex?

Split the value at the binary point. Group the integer bits from right to left and the fractional bits from left to right. Pad the integer side with leading zeros and the fraction side with trailing zeros when necessary, then convert every 4-bit group to hexadecimal.

What is 101.101 binary in hexadecimal?

Pad the integer side to 0101 and the fractional side to 1010. Binary 0101 equals hexadecimal 5 and binary 1010 equals A, so 101.101 binary equals 5.A hexadecimal.

What is 101101.011 binary in hex?

The integer part becomes 0010 1101, which maps to 2D. The fraction 011 is right-padded to 0110, which maps to 6. The final result is 2D.6.

Which direction do I group the integer bits?

Start at the binary point and group the integer bits in sets of four while moving toward the left.

Which direction do I group the fraction bits?

Start immediately after the binary point and group the fractional bits in sets of four while moving toward the right.

Where do I add zeros to the integer part?

Add any required padding zeros before the leftmost integer bit. Leading zeros do not alter the value.

Where do I add zeros to the fraction part?

Add padding zeros after the final fractional bit. Trailing fractional zeros do not alter the value.

What is 1.1 binary in hexadecimal?

The integer 1 pads to 0001, which maps to 1. The fraction 1 pads to 1000, which maps to 8. Therefore 1.1 binary equals 1.8 hexadecimal.

What is 1111.1111 binary in hex?

Both sides already form complete 4-bit groups. Integer 1111 maps to F and fraction 1111 maps to F, giving F.F hexadecimal.

Does the binary point become a hexadecimal point?

Yes. The radix-point boundary remains between the converted whole-number and fractional portions, so it appears in the corresponding position in the hex result.

Is binary-to-hex conversion exact for fractional numbers?

Yes for finite binary inputs. Hexadecimal has base 16 = 2⁴, so every finite binary integer and fractional sequence maps exactly into hexadecimal groups.

Can I enter spaces around binary groups?

Yes. Normal whitespace is ignored, allowing an input such as 1011 0101 . 1010 0011 for readability.

Can this converter handle a very long integer and fraction?

Yes. Both sections are processed directly as bit strings rather than through ordinary floating-point numeric conversion, allowing long values to be converted exactly.

Convert Binary Numbers with Fractions to Hex Online

Enter a binary value containing an integer and fractional section, such as 101101.011, then select Convert Binary Number to Hex. The calculator validates the binary format, separates the two sides, performs the correct directional grouping, applies left and right padding independently, and returns the exact hexadecimal result.

The output also shows integer and fraction bit counts, hexadecimal digit counts, grouping details, and separate live breakdowns for the whole-number and fractional portions.