IEEE 754 Converter
Decimal ↔ float bits: split out the sign, exponent and mantissa to see exactly how a float is stored.
What it does: Split a decimal number into IEEE 754 sign / exponent / mantissa bits, or solve back from hex.
When to use it: When debugging floating-point error, inspecting float values in registers/memory, or working on embedded protocols.
MEANS The sign, exponent and mantissa together make up all the bits of this float; the "actual stored value" is the number that is really saved (which may differ from your input due to floating-point error).
No history yet. Each calculation is automatically saved to this device.
How to use the IEEE 754 converter
Pick a precision; works both ways.
- 01
Pick a precision
Single precision (32-bit float) or double precision (64-bit double).
- 02
Enter a decimal number
Such as
0.15625,-2,3.14, and see it split into sign / exponent / mantissa. - 03
Or enter hex in reverse
Type
3F800000in the hex box to solve back to the float value and see what is actually stored.
Bit-field layout
A floating-point number = sign × 1.mantissa × 2^(exponent − bias).
| Precision | Sign | Exponent | Mantissa | Bias |
|---|---|---|---|---|
| Single (32) | 1 bit | 8 bits | 23 bits | 127 |
| Double (64) | 1 bit | 11 bits | 52 bits | 1023 |
IEEE 754-2019.
Common questions, answered in 3 minutes
Why is 0.1 not stored as exactly 0.1?
0.1 is a repeating fraction in binary, and floating point can only store the nearest representable value, so 0.1 in single precision is actually stored as 0.100000001…. This is the root of floating-point error.
Why subtract a bias from the exponent?
The exponent field is an unsigned "biased" value: single precision stores the true exponent + 127. This represents both positive and negative exponents without a separate exponent sign bit.
What do all-zero and all-one exponents mean?
An all-zero exponent = 0 or a subnormal number; an all-one exponent = infinity (mantissa 0) or NaN (mantissa non-zero). This tool labels the category.
How do I choose between float and double?
float uses half the memory and is fine for everyday use; double has higher precision (about 15–16 decimal digits), so use double for scientific computation or heavy accumulation to reduce error.
Standards and sources referenced by this tool
| Item | Value / Formula | Source |
|---|---|---|
| Floating-point format | sign · exp · mantissa | IEEE 754-2019 |
Bit fields follow IEEE 754; reads exact stored bits via ArrayBuffer, no external API.