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.

The magnitude of the smallest normal number in a format is given by:

$b^$

where ''b'' is the base (radix) of the format (like common values 2 or 10, for binary and decimal number systems), and ''$E_$'' depends on the size and layout of the format.

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

:$b^\cdot\left(b - b^\right)$

where ''p'' is the precision of the format in digits and ''$E_$'' is related to ''$E_$'' as:

$E_\, \overset\, 1 - E_ = \left(-E_\right) + 1$

In the IEEE 754 binary and decimal formats, ''b'', ''p'', $E_$, and ''$E_$'' have the following values:

For example, in the smallest decimal format in the table (decimal32), 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 subnormal numbers (or ''denormal numbers'').

Zero is considered neither normal nor subnormal.

See also

* Normalized number
* Half-precision floating-point format
* Single-precision floating-point format
* Double-precision floating-point format

References

{{DEFAULTSORT:Normal Number (Computing)
Computer arithmetic