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: it is a floating point number that can be represented without leading zeros in its significand.

The magnitude of the smallest normal number in a format is given by:

where b is the base (radix) of the format (like common values 2 or 10, for binary and decimal number systems), and depends on the size and layout of the format.

Similarly, the magnitude of the largest normal number in a format is given by

where p is the precision of the format in digitss and is related to as:

In the IEEE 754 binary and decimal formats, b, p, and have the following values:For example, in the smallest decimal format in the table (decimal32), the range of positive normal numbers is 1095 through 9.999999 × 1096.

Non-zero numbers smaller in magnitude than the smallest normal number are called subnormal numbers (or denormal numbers).

Zero is considered neither normal nor subnormal.

See also

• Normalized number

• Half-precision floating-point format

• Single-precision floating-point format

• Double-precision floating-point format

References