What is the IEEE-754 single-precision format?

It is the 32-bit floating-point standard (binary32) used by most languages for the float type. It splits 32 bits into 1 sign bit, 8 exponent bits and 23 mantissa (fraction) bits.

What is the exponent bias?

The 8-bit exponent is stored with a bias of 127, meaning the true exponent equals the stored value minus 127. This lets the field represent both positive and negative exponents without a separate sign.

What is the implicit leading bit?

For normal numbers the mantissa has an implied leading 1 that is not stored, giving 24 bits of precision from only 23 stored bits. Subnormal numbers instead use an implied leading 0.

What are subnormals, infinity and NaN?

When the exponent field is all zeros the value is zero or subnormal; when it is all ones the value is infinity (zero mantissa) or NaN (nonzero mantissa). These special cases let the format represent gradual underflow and undefined results.

Why does my entered value change slightly?

A 32-bit float cannot represent every decimal exactly, so the tool first rounds to the nearest representable value (round-to-nearest-even). The stored value line shows what is actually held in the bits.

IEEE-754 Float32 Inspector

The IEEE-754 single-precision format is how almost every computer stores a 32-bit floating-point number. This inspector takes any decimal you type, rounds it to the nearest representable float, and dissects the exact bits into sign, exponent and mantissa.

How it works

A binary32 value packs 32 bits into three fields. The first bit is the sign: 0 for positive, 1 for negative. The next 8 bits are the exponent, stored with a bias of 127 so the true exponent is the stored field minus 127. The final 23 bits are the mantissa, or fraction.

For a normal number the actual value is (-1)^sign × 1.fraction × 2^(exponent − 127), where the leading 1 before the fraction is implied and not stored. That hidden bit gives 24 bits of significand from only 23 stored. The tool obtains the true bit pattern by writing the value into a 32-bit float and reading the same memory back as a 32-bit unsigned integer, so the result reflects the CPU’s exact round-to-nearest-even conversion.

Special cases

exponent all zeros, mantissa zero      -> ±0
exponent all zeros, mantissa nonzero   -> subnormal (gradual underflow)
exponent all ones,  mantissa zero      -> ±Infinity
exponent all ones,  mantissa nonzero   -> NaN

Example

The value 0.15625 is exactly representable. Its bits are sign 0, exponent 01111100 (124, so unbiased −3), and mantissa 01000000000000000000000. That decodes as 1.25 × 2⁻³ = 0.15625, and the full pattern is 0x3E200000.

Tips and notes

Use this inspector to understand rounding error, to debug binary file formats, or to see why two decimals that look equal compare as different. Because 32-bit floats only hold about 7 significant decimal digits, the stored value line will reveal any rounding the moment you enter a number that cannot be represented exactly. All processing happens locally in your browser.