Example Data Table
| Format |
Binary |
Hex |
Class |
Decimal Meaning |
| Binary16 |
0011110000000000 |
0x3C00 |
Normal |
1 |
| Binary16 |
1100000000000000 |
0xC000 |
Normal |
-2 |
| Binary16 |
0111110000000000 |
0x7C00 |
Infinity |
Positive infinity |
| Binary16 |
0000000000000001 |
0x0001 |
Subnormal |
About 5.960464477539063E-8 |
| Binary16 |
0111111000000000 |
0x7E00 |
NaN |
Not a number |
| Bfloat16 |
0011111110000000 |
0x3F80 |
Normal |
1 |
Formula Used
Sign: sign value = (-1)sign bit
Bias: bias = 2exponent bits - 1 - 1
Normal value: decimal = sign value × 2raw exponent - bias × (1 + fraction / 2fraction bits)
Subnormal value: decimal = sign value × 21 - bias × (fraction / 2fraction bits)
Special values: all exponent bits set means infinity when fraction is zero. It means NaN when fraction is not zero.
How To Use This Calculator
Enter a 16 bit value in binary, hexadecimal, or unsigned integer form.
Select the float layout. Use Binary16 for half precision data.
Select Bfloat16 when your data uses one sign bit, eight exponent bits, and seven fraction bits.
Use custom layout when a device or file format uses another 16 bit split.
Enable byte swapping only when your two bytes appear in reversed order.
Press the calculate button. The result appears above the form.
Use CSV or PDF export to save the decoded fields.
Understanding 16 Bit Floating Numbers
A 16 bit floating number stores a real value in three fields. The first bit is the sign. The exponent field sets the scale. The fraction field stores the significant part. This layout allows very small and very large numbers to fit inside only sixteen bits. It is useful in graphics, machine learning, embedded devices, and file formats.
Why This Converter Helps
Manual conversion is easy to misread. One wrong bit can change the value, create infinity, or create NaN. This calculator separates every field. It shows the unbiased exponent, significand, class, and decimal value. You can enter binary, hexadecimal, or an unsigned integer. You can also swap bytes when data comes from a different memory order.
Handling Normal And Subnormal Values
Normal numbers use an implied leading one. Subnormal numbers do not. This matters near zero because subnormal values fill the underflow gap. The calculator detects zero, subnormal, normal, infinity, and NaN cases. It then uses the correct expression for that class. This gives a reliable result for debugging and documentation.
Precision And Practical Limits
Half precision is compact, not exact for every decimal. Many decimal values become rounded during storage. The decoded decimal may therefore look slightly different from the original value. That is expected. Use the component table to confirm the stored bit pattern. Use the notes field to record device names, test cases, or source data.
Using Results In Workflows
The export buttons help create repeatable records. CSV is useful for spreadsheets. PDF is useful for reports and classroom sheets. The example table gives common reference values. Compare your result with those samples when testing a parser. For deeper checks, decode both the original bytes and the swapped bytes. This often finds endian issues quickly.
Good Input Habits
Paste binary with spaces if needed. The calculator removes simple separators. Hex values may include 0x. Unsigned values must stay from 0 to 65535. Choose the format before calculating. Binary16 is the standard half precision layout. Bfloat16 keeps an eight bit exponent and shorter fraction, which suits some neural processing tasks. These checks make the decimal answer easier to trust when systems compress floats, exchange packets, or load model weights from binary files.
FAQs
What is a 16 bit floating point number?
It is a compact floating value stored in sixteen bits. It usually contains one sign bit, exponent bits, and fraction bits. Binary16 uses five exponent bits and ten fraction bits.
What is Binary16?
Binary16 is the common half precision format. It uses one sign bit, five exponent bits, and ten fraction bits. Its exponent bias is fifteen.
What is Bfloat16?
Bfloat16 is another 16 bit floating layout. It uses one sign bit, eight exponent bits, and seven fraction bits. It has wider range but lower fraction precision.
Why does my decimal result look rounded?
Floating point storage cannot represent every decimal exactly. A stored bit pattern may decode to a nearby decimal. This is normal for compact formats.
What does subnormal mean?
A subnormal value has a zero exponent field and a nonzero fraction. It does not use the implied leading one. It represents tiny values near zero.
When should I swap bytes?
Use byte swapping when the two input bytes are reversed by storage or transmission order. Try both versions when debugging raw binary files.
What does NaN mean?
NaN means not a number. It appears when the exponent field is all ones and the fraction field is not zero.
Can I export the result?
Yes. Use the CSV button for spreadsheets. Use the PDF button for reports, teaching notes, or audit records.