IEEE 754 FP16 16 Bits 1 / 5 / 10 Layout Half Precision NaN & Infinity

IEEE 754 Binary16 Decoder

FP16 Hex to Binary Converter

Convert a hexadecimal FP16 bit pattern into exact 16-bit binary and decode the IEEE 754 sign, 5-bit exponent and 10-bit fraction. The tool identifies normal values, subnormals, positive and negative zero, infinity and NaN.

Exact 16-bit pattern Exponent decoding Fraction decoding FP16 classification

FP16 Hex → IEEE 754 Binary

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FP16 HEX BIT PATTERN

Raw 16-bit FP16 pattern · 0000–FFFF · optional 0x prefix · exactly 4 normalized hex digits

EXACT FP16 BINARY S | EEEEE | FFFFFFFFFF

0011110000000000

Sign: 0 Exponent: 01111 Fraction: 0000000000 Class: Normal

FP16 value: 1

IEEE 754 BREAKDOWN 1 sign · 5 exponent · 10 fraction bits

3C00 → 0 | 01111 | 0000000000 · exponent 15 − bias 15 = 0 · value = +1 × 2⁰ = 1

TRY:

Format IEEE 754 binary16

Width 16 bits / 2 bytes

Sign 1 bit

Exponent 5 bits · bias 15

Fraction 10 stored bits

FP16 Hex to Binary Converter

The FP16 Hex to Binary Converter converts a 16-bit hexadecimal floating-point bit pattern into exact binary and interprets the result according to the IEEE 754 binary16 format, commonly called half-precision floating point or FP16.

Unlike an ordinary 16-bit integer conversion, FP16 assigns different roles to the individual bits: one sign bit, five exponent bits and ten stored fraction bits.

Example: hex 3C00 becomes 0011110000000000. Splitting the bits gives 0 | 01111 | 0000000000, which represents the FP16 value 1.0.

What Is FP16?

FP16 is the IEEE 754 binary16 floating-point format. A value occupies 16 bits, or two bytes.

FP16: S EEEEE FFFFFFFFFF S: 1 sign bit EEEEE: 5 exponent bits FFFFFFFFFF: 10 stored fraction bits

FP16 Bit Layout

Field	Bits	Purpose
Sign	1	Positive or negative
Exponent	5	Scale using exponent bias 15
Fraction	10	Stored significand fraction
Total	16	Complete FP16 pattern

How to Convert FP16 Hex to Binary

Each hexadecimal digit maps directly to four binary bits. Four hexadecimal digits therefore produce exactly sixteen FP16 bits.

Hex: 3C00 3 → 0011 C → 1100 0 → 0000 0 → 0000 Binary: 0011110000000000 Split: 0 | 01111 | 0000000000

How an FP16 Normal Number Is Decoded

For a normal finite number, the exponent field is neither 00000 nor 11111. The exponent bias is 15 and the significand has an implicit leading 1.

Value = (-1)^sign × (1 + fraction / 1024) × 2^(exponent – 15)

Example: 3C00 Hex Equals 1.0

3C00 → 0011110000000000 Sign: 0 Exponent: 01111 = 15 Fraction: 0000000000 = 0 Unbiased exponent: 15 − 15 = 0 Significand: 1 + 0/1024 = 1 Value: +1 × 2⁰ = 1

Example: C000 Hex Equals -2

C000 → 1100000000000000 Sign: 1 Exponent: 10000 = 16 Fraction: 0 Unbiased exponent: 16 − 15 = 1 Value: -1 × 2¹ = -2

Common FP16 Hex Values

Hex	Binary	Classification	Value
0000	0000000000000000	Positive zero	+0
8000	1000000000000000	Negative zero	-0
3C00	0011110000000000	Normal	1
4000	0100000000000000	Normal	2
4200	0100001000000000	Normal	3
C000	1100000000000000	Normal	-2
7BFF	0111101111111111	Normal	65504
0400	0000010000000000	Normal	0.00006103515625
0001	0000000000000001	Subnormal	5.960464477539063e-8
7C00	0111110000000000	Infinity	+Infinity
FC00	1111110000000000	Infinity	-Infinity
7E00	0111111000000000	NaN	NaN

FP16 Exponent Bias

For normal FP16 values, the five-bit exponent field is stored with a bias of 15.

Unbiased exponent = stored exponent − 15 Example: 10000₂ = 16 16 − 15 = 1

FP16 Subnormal Numbers

When the exponent bits are all zero and the fraction field is non-zero, the pattern represents a subnormal value. Subnormal numbers do not use the implicit leading 1.

Subnormal value: (-1)^sign × (fraction / 1024) × 2^-14

Hex 0001 is the smallest positive non-zero FP16 subnormal value.

Smallest Positive FP16 Subnormal

0001 → 0000000000000001 Exponent: 00000 Fraction integer: 1 Value: 2^-24 = 5.960464477539063 × 10^-8

Smallest Positive Normal FP16 Value

0400 → 0000010000000000 Exponent: 00001 Unbiased exponent: 1 − 15 = -14 Fraction: 0 Value: 2^-14 = 0.00006103515625

Maximum Finite FP16 Value

7BFF → 0 | 11110 | 1111111111 Exponent: 30 − 15 = 15 Significand: 1 + 1023/1024 Value: 65504

7BFF is the largest positive finite FP16 number. FBFF is its negative counterpart.

FP16 Positive and Negative Zero

IEEE 754 floating point includes separate positive-zero and negative-zero bit patterns.

Hex	Binary	Meaning
0000	0000000000000000	+0
8000	1000000000000000	-0

FP16 Infinity

An exponent of 11111 combined with a zero fraction represents infinity. The sign bit determines positive or negative infinity.

7C00 → 0 | 11111 | 0000000000 → +Infinity FC00 → 1 | 11111 | 0000000000 → -Infinity

FP16 NaN Values

An exponent field of 11111 combined with any non-zero fraction represents NaN, meaning “Not a Number.”

7E00 → 0 | 11111 | 1000000000 Exponent = all ones Fraction ≠ 0 Classification: NaN

FP16 vs Generic 16-Bit Hex Conversion

Both tools may produce the same sixteen binary digits, but the interpretation is completely different.

Input	Binary	Generic 16-Bit Meaning	FP16 Meaning
3C00	0011110000000000	Raw 16-bit pattern	1.0
C000	1100000000000000	Raw 16-bit pattern	-2.0
7C00	0111110000000000	Raw 16-bit pattern	+Infinity

FP16 vs Int16

FP16 and Int16 both occupy exactly sixteen bits, but they interpret those bits using entirely different numerical systems.

For example, hex C000 is FP16 -2, while interpreting the same raw bits as Int16 gives -16384. The bit pattern is identical; only the data type changes.

Optional 0x Prefix

The converter accepts a programming-style 0x or 0X prefix.

0x3C00 → 3C00 → 0011110000000000 → FP16 1

Common Uses for FP16

Machine-learning model weights and activations.
GPU and accelerator computation.
Graphics processing.
Compact floating-point storage.
Neural-network inference.
Binary file inspection.
Firmware and hardware debugging.
IEEE 754 education.
Floating-point reverse engineering.
Low-level numerical format analysis.

Common FP16 Conversion Mistakes

Treating the hexadecimal pattern as an ordinary unsigned integer.
Treating bit 15 as an Int16 sign bit instead of an FP16 sign field.
Forgetting the exponent bias of 15.
Using an implicit leading 1 for subnormal numbers.
Treating exponent 11111 as an ordinary exponent.
Ignoring positive and negative zero.
Treating NaN patterns as finite numeric values.
Confusing FP16 with BF16 even though both use 16 total bits.

FP16 Hex to Binary Converter FAQs

What does FP16 mean?

FP16 commonly refers to IEEE 754 binary16 half-precision floating point, which uses 16 total bits.

How many bits are in FP16?

FP16 contains 16 bits: 1 sign bit, 5 exponent bits and 10 stored fraction bits.

What is 3C00 in FP16?

3C00 becomes 0011110000000000 and represents exactly 1.0.

What is 4000 in FP16?

4000 becomes 0100000000000000 and represents exactly 2.0.

What is C000 in FP16?

C000 becomes 1100000000000000 and represents exactly -2.0.

What is the maximum finite FP16 value?

Hex 7BFF represents the maximum positive finite FP16 value, 65,504.

What is the smallest positive normal FP16 value?

Hex 0400 represents 2^-14, which equals 0.00006103515625.

What is the smallest positive FP16 value?

Hex 0001 is the smallest positive subnormal value and equals 2^-24, approximately 5.960464477539063e-8.

What does 7C00 mean in FP16?

7C00 represents positive infinity.

What does 7E00 mean in FP16?

7E00 is a NaN bit pattern because the exponent is all ones and the fraction is non-zero.

Does FP16 have negative zero?

Yes. Hex 8000 represents negative zero, while 0000 represents positive zero.

Is FP16 the same as BF16?

No. Both are 16-bit floating-point formats, but FP16 uses a 5-bit exponent and 10-bit fraction while BF16 uses a different field layout.

Convert FP16 Hex to Binary

Enter a raw FP16 hexadecimal bit pattern from 0000 through FFFF and select Decode FP16. The calculator converts all four hexadecimal digits to exactly sixteen binary bits, separates the sign, exponent and fraction fields, classifies the IEEE 754 value and displays its decoded floating-point meaning.