What this floating point to decimal converter does
This calculator converts a raw IEEE 754 floating-point bit pattern into its decimal value. That means you can paste a 32-bit or 64-bit binary/hex value exactly as it appears in memory dumps, protocol fields, firmware logs, or debugger output and immediately decode it into human-readable decimal form.
In addition to the final decimal result, this tool breaks the value into sign, exponent, and mantissa (fraction) fields so you can verify how the number is represented internally.
Why floating-point conversion matters
Floating-point numbers are everywhere: spreadsheets, machine learning models, sensor devices, game engines, APIs, and financial systems. If data looks wrong, it is often because the encoded bits were interpreted incorrectly (wrong precision, wrong parsing, or wrong expected format).
- Debug corrupted packets or binary files
- Verify embedded device telemetry values
- Understand rounding behavior in code reviews
- Inspect special values like NaN and Infinity
Quick guide: IEEE 754 layout
Float32 (single precision)
- 1 bit sign
- 8 bits exponent (bias 127)
- 23 bits fraction (mantissa)
Float64 (double precision)
- 1 bit sign
- 11 bits exponent (bias 1023)
- 52 bits fraction (mantissa)
Formula for normal values:
value = (-1)sign × (1.fraction) × 2(exponent - bias)
How to use this calculator
- Select Float32 or Float64.
- Choose input type: Hexadecimal or Binary.
- Enter the exact bit pattern (8/16 hex chars or 32/64 binary bits).
- Click Convert to Decimal.
The output includes decimal value, scientific notation (when applicable), classification (normal/subnormal/zero/infinity/NaN), and full field breakdown.
Common pitfalls and tips
1) Wrong precision selection
A 64-bit value interpreted as float32 will produce a completely different result. Always match the source type.
2) Hex length mismatch
Float32 requires exactly 8 hex digits. Float64 requires exactly 16.
3) Special values are expected sometimes
If exponent is all 1s, you may get Infinity or NaN. This is normal behavior per IEEE 754.
Example values you can test
- 3f800000 (float32 hex) → 1
- bf800000 (float32 hex) → -1
- 400921fb54442d18 (float64 hex) → π
- 7f800000 (float32 hex) → +Infinity
- 7fc00000 (float32 hex) → NaN
Final note
Floating-point representation is precise in structure but approximate in many decimal results. This converter helps you inspect what is actually stored, not what you hoped was stored. Use it as a practical debugging and learning tool anytime you work close to binary data.