In
computing
Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes the study and experimentation of algorithmic processes, and development of both hardware and software. Computing has scientific, ...
, 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
The significand (also mantissa or coefficient, sometimes also argument, or ambiguously fraction or characteristic) is part of a number in scientific notation or in floating-point representation, consisting of its significant digits. Depending on ...
.
The magnitude of the smallest normal number in a format is given by ''b''
''emin'', 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
:''b''
''emax'' × (''b'' − ''b''
1−''p''),
where ''p'' is the precision of the format in
digit
Digit may refer to:
Mathematics and science
* Numerical digit, as used in mathematics or computer science
** Hindu-Arabic numerals, the most common modern representation of numerical digits
* Digit (anatomy), the most distal part of a limb, such ...
s and ''emax'' is (−''emin'')+1.
In the
IEEE 754 binary and decimal formats, ''b'', ''p'', ''emin'', and ''emax'' have the following values:
For example, in the smallest decimal format, the range of positive normal numbers is 10
−95 through 9.999999 × 10
96.
Non-zero numbers smaller in magnitude than the smallest normal number are called
subnormal (or denormal) numbers. Zero is neither normal nor subnormal.
See also
*
Normalized number
References
{{DEFAULTSORT:Normal Number (Computing)
Computer arithmetic