Normalized Number

A real number is called normalized, if it is in the form:

where n is an integer, ... are the digits of the number in base 10, and is not zero.

As examples, the number in normalized form is

,

while the number −0.00574012 in normalized form is

Clearly, any non-zero real number can be normalized.

The same definition holds if the number is represented in another radix (that is, base of enumeration), rather than base 10. In base b a normalized number will have the form

where again and the "digits", ... are integers between and .

Converting a number to base 2 and normalizing it are the first steps in storing a real number as a floating-point number in a computer.