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.
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