How is a double-precision float laid out?

A 64-bit IEEE-754 double uses 1 sign bit, 11 exponent bits and 52 mantissa bits. The exponent is biased by 1023, and normalized numbers carry an implicit leading 1 in the mantissa.

What is the exponent bias?

The 11-bit exponent field stores a biased value: the true exponent equals the stored value minus 1023. This lets the field represent exponents from -1022 to +1023 without a separate sign bit.

Why does 0.1 not have a clean bit pattern?

0.1 has no exact binary fraction, so it is rounded to the nearest representable double. The inspector shows the actual stored bits, which is why 0.1 + 0.2 famously does not equal exactly 0.3.

What are subnormal numbers?

When the exponent field is all zeros but the mantissa is non-zero, the number is subnormal (denormalized). These represent values smaller than the smallest normalized double, with reduced precision.

Is my input sent anywhere?

No. The bit extraction uses a DataView in your browser and nothing is transmitted. The tool is fully client-side and privacy-first.

IEEE-754 Float64 Inspector

The IEEE-754 double-precision format (also called binary64) is how almost every programming language stores double and JavaScript number values. This inspector takes any decimal you enter and reveals the exact 64-bit pattern the processor holds for it, broken into its three fields.

How it works

A 64-bit double is divided into three parts, reading from the most significant bit:

Sign (1 bit) — 0 for positive, 1 for negative.
Biased exponent (11 bits) — the true exponent plus a bias of 1023. So a stored value of 1024 means an actual exponent of +1.
Mantissa / fraction (52 bits) — the significant digits. For normalized numbers an implicit leading 1. is assumed, giving an effective 53 bits of precision.

The reconstructed value is (-1)^sign × 1.mantissa × 2^(exponent − 1023). The tool reads the raw bits with a DataView, so what you see is the genuine stored pattern, not an approximation.

Special cases

Zero: exponent and mantissa both all-zero (the sign bit distinguishes +0 from -0).
Subnormal: exponent all-zero, mantissa non-zero — values too small to normalize.
Infinity: exponent all-ones, mantissa all-zero.
NaN: exponent all-ones, mantissa non-zero.

Example

Try 0.1. You will see it is not exact: the mantissa is a repeating pattern rounded to 52 bits. This is the root cause of floating-point surprises like 0.1 + 0.2 === 0.30000000000000004. Inspecting the bits makes the rounding visible and explains why money should never be stored as a float.