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: 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 of the format, 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:
FormatSmallest Normal NumberLargest Normal Number
binary16211−1415
binary32224−126127
binary64253−10221023
binary1282113−1638216383
decimal32107−9596
decimal641016−383384
decimal1281034−61436144

For example, in the smallest decimal format in the table, 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'.
Zero is considered neither normal nor subnormal.