Normal number (computing)

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:

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.