Normalized number

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

\pm d_{0}.d_{1}d_{2}d_{3}\dots \times 10^{n}

where n is an integer, $d_{0},$ $d_{1},$ $d_{2}$ , $d_{3}$ ... are the digits of the number in base 10, and $d_{0}$ is not zero.

As examples, the number $x=918.082$ in normalized form is

9.18082\times 10^{2}

,

while the number −0.00574012 in normalized form is

-5.74012\times 10^{-3}.

Clearly, any non-zero 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

\pm d_{0}.d_{1}d_{2}d_{3}\dots \times b^{n},

where again $d_{0}\not =0,$ and the "digits" $d_{0},$ $d_{1},$ $d_{2}$ , $d_{3}$ ... are integers between $0$ and $b-1$ .

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.

See also