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Float Visualizer - Free Online IEEE 754 Tool | IconVault

Explore IEEE 754 floats bit by bit: click sign, exponent and mantissa bits of doubles and floats. Includes the 0.1 + 0.2 demo. Free.

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Float Visualizer

Click IEEE 754 bits and see the exact decimal value

5 of 5 free uses left

Bit explorer: click any bit to flip it

0x3fb999999999999a

sign

exponent

mantissa

Sign

0 = positive

Exponent

01111111011

raw 1019, unbiased -4, factor 2^-4

Mantissa

1001100110011001100110011001100110011001100110011010

value = (-1)^0 x 2^-4 x 1.10011001...

The 0.1 + 0.2 demo (binary64)

Step 1 of 4: 0.1 cannot be stored exactly

0.1 in binary is 0.0001100110011... repeating forever. A double keeps the closest 53 significant bits, which is very slightly more than 0.1. This is the exact value actually stored:

sign

exponent

mantissa

0.1000000000000000055511151231257827021181583404541015625

Decoded value

0.1

Exact decimal value

0.1000000000000000055511151231257827021181583404541015625

Neighbors:

- 0.09999999999999999

+ 0.10000000000000002

Anything between two neighbors rounds to one of them. That rounding is where 0.1 + 0.2 comes from.

5 of 5 free copies left. Flipping bits and stepping the demo are always free.

About this model

Bit layouts, rounding and exact values match IEEE 754 binary64 and binary32 precisely. Typing a decimal converts it exactly the way JavaScript's Number() does. Denormals, signed zero, infinities and NaN are all explorable: flip the exponent bits to all 1s and watch Infinity appear.

About this tool

IconVault's Float Visualizer opens up IEEE 754 floating point at the bit level: click any sign, exponent, or mantissa bit of a binary64 (double) or binary32 (float) and instantly see the exact decimal value, the neighboring values, and the unbiased exponent. Switch between hex, binary, and decimal views.

It ships with the famous 0.1 + 0.2 demo so you can see exactly which bits make the sum not quite 0.3. Built for students, game developers, and anyone burned by rounding errors. Free and runs fully in your browser.

Frequently asked questions

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