Float64 microscope

Why 0.1 + 0.2 ≠ 0.3, at the bit level.

stack

IEEE-754 · Float64Array · BigInt

kind

decoder

status

live

Every JavaScript number is an IEEE-754 binary64: 1 sign bit, 11 exponent bits, 52 mantissa bits. Paste a value, see the bits, step through representable neighbors, and watch why 0.1 + 0.2 lands one ulp past 0.3.

expression

sign

exponent · 11

mantissa · 52

0x3fd3·3333·3333·3334

decoded

value: 0.30000000000000004
category: normal
sign: 0 (+)
raw exp: 1021 / 2047
unbiased: -2
mantissa: 900719925474100
ulp: 5.551e-17

representable neighbors

prev0.3

this0.30000000000000004

next0.3000000000000001

gap = 5.551e-17

memory · eight bytes

The same bits, laid out byte by byte. IEEE logical order reads left-to-right from sign bit to mantissa tail. Your CPU (if x86 or ARM) stores it reversed.

IEEE logical (big-endian)

sign bit first · how the spec is written

off

hex

binary

chr

S/E

E/M

machine RAM (little-endian)

low byte first · how x86 / ARM stores it

off

hex

binary

chr

E/M

S/E

0.1 + 0.2 ≠ 0.3

Both sides round to different binary64 values. The sum of 0.1 and 0.2 overshoots 0.3 by exactly one ulp, which is the minimum possible gap at this magnitude. This is not a bug; it is what "base-2 float" means.

0.1 + 0.2

0.30000000000000004

0x3fd3333333333334

0.3

0x3fd3333333333333

offset: 1 ulp

Decoded with Float64Array + BigUint64Array via a shared ArrayBuffer. Prev/next walk by ±1 on the raw bit integer, which is the IEEE-754 "next representable" operation.

thesis

Paste a float, see sign / exponent / mantissa bits, the nearest representable value, ulp distance, round-trip through decimal. Walk through catastrophic cancellation, subnormals, and NaN payloads.

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