Normal number (computing)

In computing, a normal number is a non-zero number in a floating-point representation which is within the balanced range supported by a given floating-point format: it is a floating point number that can be represented without leading zeros in its significand.

For the mathematical meaning, see normal number.
Floating-point formats
IEEE 754
Other

The magnitude of the smallest normal number in a format is given by bemin, where b is the base (radix) of the format (usually 2 or 10) and emin depends on the size and layout of the format.

Similarly, the magnitude of the largest normal number in a format is given by

bemax × (b − b1−p),

where p is the precision of the format in digits and emax is (−emin)+1.

In the IEEE 754 binary and decimal formats, b, p, emin, and emax have the following values:[1]

Formatbpeminemax
binary16211−1415
binary32224−126127
binary64253−10221023
binary1282113−1638216383
decimal32107−9596
decimal641016−383384
decimal1281034−61436144

For example, in the smallest decimal format, the range of positive normal numbers is 10−95 through 9.999999 × 1096.

Non-zero numbers smaller in magnitude than the smallest normal number are called denormal (or subnormal) numbers. Zero is neither normal nor subnormal.

See also

References
  1. IEEE Standard for Floating-Point Arithmetic, 2008-08-29, doi:10.1109/IEEESTD.2008.4610935, ISBN 978-0-7381-5752-8, retrieved 2015-04-26


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