A floating-point normal number in a particular format of the IEEE 754-2008 framework is a finite nonzero floating-point
number with absolute value greater than or
equal to a minimum value radix and minimum exponent .
Normal numbers can use the full precision available
in a format.
Finite nonzero floating-point
numbers which are not normal are said to be subnormal .
The given definition of normal number shouldn't be confused with the definition of normal number from number
theory . In that instance, a number is said to be normal
if it is irrational and if any finite pattern
of numbers occurs with the expected limiting frequency
in the expansion relative to a given base .
See also Arithmetic ,
Biased Exponent ,
Floating-Point Algebra ,
Floating-Point Arithmetic ,
Floating-Point
Exponent ,
Floating-Point Number ,
Floating-Point Preferred Exponent ,
Floating-Point Quantum ,
Floating-Point
Representation ,
IEEE 754-2008 ,
Interval
Arithmetic ,
NaN ,
Quiet NaN ,
Signaling NaN ,
Significand ,
Subnormal Number
This entry contributed by Christopher
Stover
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References IEEE Computer Society. "IEEE Standard for Floating-Point Arithmetic: IEEE Std 754-2008 (Revision of IEEE Std 754-1985)." 2008. https://doi.org/10.1109/IEEESTD.2008.4610935 . Referenced
on Wolfram|Alpha Floating-Point Normal Number
Cite this as:
Weisstein, Eric W. , with contributions by Christopher Stover . "Floating-Point Normal Number." From MathWorld https://mathworld.wolfram.com/Floating-PointNormalNumber.html
Subject classifications
where here, 
is the radix and 
is the minimum exponent.
Normal numbers can use the full precision available
in a format.
