Normal number (computing) Guide, Meaning , Facts, Information and Description

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 b^emin, 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

b^emax × (b − b^1−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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