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 digits and is related to as:
In the IEEE 754 binary and decimal formats, b, p, , and have the following values: +Smallest and Largest Normal Numbers for common numerical FormatsFormatSmallest Normal NumberLargest Normal Numberbinary16211−1415binary32224−126127binary64253−10221023binary1282113−1638216383decimal32107−9596decimal641016−383384decimal1281034−61436144
For example, in the smallest decimal format in the table (decimal32), 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 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
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