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# Floating-Point Normal Number

For a particular format in the IEEE 754-2008 framework, a normal number is a finite nonzero floating-point number with magnitude greater than or equal to a minimum value where here, is the radix and is the minimum exponent. Normal numbers can use the full precision available in a format.

Finite nonzero floating-point numbers which aren't 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.

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

## References

IEEE Computer Society. "IEEE Standard for Floating-Point Arithmetic: IEEE Std 754-2008 (Revision of IEEE Std 754-1985)." 2008. http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=4610935.

## Cite this as:

Stover, Christopher. "Floating-Point Normal Number." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Floating-PointNormalNumber.html