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.
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, p, emin, and emax have the following values:
| Format | p | emin | emax |
|---|---|---|---|
| binary16 | 11 | −14 | 15 |
| binary32 | 24 | −126 | 127 |
| binary64 | 53 | −1022 | 1023 |
| binary128 | 113 | −16382 | 16383 |
| decimal32 | 7 | −95 | 96 |
| decimal64 | 16 | −383 | 384 |
| decimal128 | 34 | −6143 | 6144 |
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.
Famous quotes containing the words normal and/or number:
“The obese is ... in a total delirium. For he is not only large, of a size opposed to normal morphology: he is larger than large. He no longer makes sense in some distinctive opposition, but in his excess, his redundancy.”
—Jean Baudrillard (b. 1929)
“[The] elderly and timid single gentleman in Paris ... never drove down the Champs Elysees without expecting an accident, and commonly witnessing one; or found himself in the neighborhood of an official without calculating the chances of a bomb. So long as the rates of progress held good, these bombs would double in force and number every ten years.”
—Henry Brooks Adams (1838–1918)