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:
“In order to move others deeply we must deliberately allow ourselves to be carried away beyond the bounds of our normal sensibility.”
—Joseph Conrad (1857–1924)
“Nothing ever prepares a couple for having a baby, especially the first one. And even baby number two or three, the surprises and challenges, the cosmic curve balls, keep on coming. We can’t believe how much children change everything—the time we rise and the time we go to bed; the way we fight and the way we get along. Even when, and if, we make love.”
—Susan Lapinski (20th century)