Normalized number: Difference between revisions

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

• scientific notation
• floating-point number