Hex to Float Converter
Convert an 8-digit hexadecimal value into an IEEE 754 32-bit single-precision floating-point number. Decode the sign bit, biased exponent, unbiased exponent, fraction field, significand, binary pattern and final decimal float with big-endian and little-endian byte input support.
(−1)^sign × (1.fraction) × 2^(exponent−127).
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Hex to Float Converter
The Hex to Float Converter decodes a 32-bit hexadecimal bit pattern as an IEEE 754 single-precision floating-point number. It is designed for raw four-byte values found in memory dumps, embedded systems, network messages, PLC registers, binary files, debugger output and protocol documentation.
Unlike ordinary hexadecimal-to-decimal conversion, a floating-point hex value is not treated as a simple unsigned integer. The same 32 bits are divided into a sign field, exponent field and fraction field according to the IEEE 754 binary32 format.
How to Convert Hex to Float
Enter eight hexadecimal digits representing four bytes. For the common human-readable IEEE 754 form, leave the byte order set to Big Endian / Normal Hex. If you copied bytes directly from little-endian memory, select Little Endian Byte Sequence.
Click Convert Hex to Float. The tool reorganizes the bytes if required and extracts all 32 IEEE 754 bits before calculating the floating-point value.
Hex:
3F800000
Binary:
00111111100000000000000000000000
Sign:
0
Exponent:
01111111 = 127
Fraction:
00000000000000000000000
Result:
1IEEE 754 32-Bit Float Format
IEEE 754 single precision contains exactly 32 bits. The first bit controls the sign, the next eight bits encode the exponent and the final twenty-three bits store the fractional part of the significand.
| Field | Bits | Purpose |
|---|---|---|
| Sign | 1 | Positive or negative |
| Exponent | 8 | Biased power of two |
| Fraction | 23 | Fractional significand bits |
| Total | 32 | 4 bytes |
Example: Convert 3F800000 to Float
The hexadecimal bit pattern 3F800000 is the standard IEEE 754 representation of positive 1.0.
Hex:
3F800000
Binary:
0 01111111 00000000000000000000000
Sign bit:
0 → positive
Stored exponent:
127
Exponent bias:
127
Actual exponent:
127 − 127 = 0
Significand:
1.0
Value:
(+1) × 1.0 × 2^0
= 1.0Example: Negative IEEE 754 Float
The sign bit changes the sign of the complete floating-point value. For example, C0200000 represents −2.5.
Hex:
C0200000
Binary:
1 10000000 01000000000000000000000
Sign:
Negative
Stored exponent:
128
Unbiased exponent:
1
Significand:
1.25
Value:
−1 × 1.25 × 2^1
= −2.5IEEE 754 Exponent Bias
For normal binary32 values, the eight-bit stored exponent is biased by 127. This allows both positive and negative powers of two to be represented without requiring a separate exponent sign bit.
Stored exponent:
130
Bias:
127
Actual exponent:
130 − 127
= 3Exponent values 0 and 255 are special and are not interpreted using the ordinary normal-value formula.
Fraction and Mantissa Bits
The final 23 bits are commonly called the mantissa or fraction field. For a normal IEEE 754 number, an implicit leading binary 1 is assumed before those fraction bits.
Fraction bits:
01000000000000000000000
Normal significand:
1.01000000000000000000000₂
= 1 + 2^-2
= 1.25Normal, Subnormal, Zero, Infinity and NaN
Not every 32-bit float is a normal finite number. IEEE 754 reserves exponent patterns for zero, subnormal numbers, infinities and NaN values.
| Exponent | Fraction | Classification |
|---|---|---|
| 0 | 0 | Signed zero |
| 0 | Non-zero | Subnormal |
| 1–254 | Any | Normal finite value |
| 255 | 0 | Infinity |
| 255 | Non-zero | NaN |
Hex Values for Common Float Numbers
| Float | IEEE 754 Hex |
|---|---|
| 0.0 | 00000000 |
| 1.0 | 3F800000 |
| -1.0 | BF800000 |
| 2.0 | 40000000 |
| 2.5 | 40200000 |
| -2.5 | C0200000 |
| +Infinity | 7F800000 |
Hex Float Endianness
Endianness changes the order in which bytes are stored or transmitted. It does not change the internal IEEE 754 definition after the bytes have been placed in their correct significance order.
Float:
1.0
Canonical / big-endian hex:
3F 80 00 00
Little-endian memory bytes:
00 00 80 3F
Both represent the same IEEE 754 value:
1.0If a four-byte dump reads 00 00 80 3F, choose Little Endian Byte Sequence so the converter reverses the byte order before interpreting the IEEE 754 fields.
Hex Float vs Hex Integer
It is important to distinguish interpreting a bit pattern as an integer from interpreting the same bits as a floating-point value.
Hex:
3F800000
As unsigned integer:
1065353216
As IEEE 754 binary32:
1.0The bits have not changed. Only the interpretation of those bits is different.
Where Hex to Float Conversion Is Used
Hex-to-float decoding is commonly required in embedded systems, PLC communications, Modbus registers, CAN data, firmware debugging, memory dumps, sensor messages, binary files and network protocols. Technical specifications often describe floating-point values as raw hexadecimal bytes because hex maps cleanly onto binary data.
This tool is especially useful when you need more than the final decimal answer because it exposes the sign, exponent and fraction fields used to produce that value.