FM 6-04 Chapter 6 · Numbers and units
IEEE 754 inspector
Float32 and float64 bits: sign, exponent, mantissa, the exact stored value, neighbours and ULP.
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Usable as a step in ChainAccepts 0.1 · -2.5e-3 · Infinity · NaN · 0x1.8p1 · a raw pattern 0x3FB999999999999A
0011111110111001100110011001100110011001100110011001100110011010
Sign Exponent Fraction
- Class
- Positive normal
- Sign
- 0 (+)
- Exponent
- field 1019, unbiased 2^-4 (bias 1023)
- Fraction
- 0x999999999999a, plus the implicit leading 1
- Exact stored value
- 0.1000000000000000055511151231257827021181583404541015625
- Shortest round trip
- 0.1
- Input stored
- rounded to the nearest, ties to even
- Hex pattern
- 0x3FB999999999999A
- Hex float (C99)
- 0x1.999999999999ap-4
- Next up
- 0.10000000000000002 0x3FB999999999999B
- Next down
- 0.09999999999999999 0x3FB9999999999999
- ULP
- 2^-56 ≈ 1.3877787807814457e-17= 0.00000000000000001387778780781445675529539585113525390625
The value is rounded once from the decimal you type to the nearest float64, ties to even, then every digit of what is actually stored is shown. ULP is the gap to the next larger magnitude, as in Java's Math.ulp. Subnormals have exponent field 0 and lose the implicit leading 1. A NaN has an all-ones exponent and a non-zero fraction; the top fraction bit marks it quiet, the rest is the payload. Enter a raw pattern to keep a payload; JavaScript arithmetic may not preserve it.