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:
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—Cathy Rindner Tempelsman (20th century)
“To finish the moment, to find the journey’s end in every step of the road, to live the greatest number of good hours, is wisdom. It is not the part of men, but of fanatics, or of mathematicians, if you will, to say, that, the shortness of life considered, it is not worth caring whether for so short a duration we were sprawling in want, or sitting high. Since our office is with moments, let us husband them.”
—Ralph Waldo Emerson (1803–1882)