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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 proposed decimal formats, p, emin, and emax have the following values:
| Format
| p
| emin
| emax
|
| binary 32-bit
| 24
| −126
| 127
|
| binary 64-bit
| 53
| −1022
| 1023
|
| binary 128-bit
| 113
| −16382
| 16383
|
| decimal 32-bit
| 7
| −95
| 96
|
| decimal 64-bit
| 16
| −383
| 384
|
| decimal 128-bit
| 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 denormalized numbers or subnormal numbers. Zero is neither normal nor subnormal.
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