Normalized number

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

$\pm d_0.d_1d_2d_3\dots\times 10^n$

where n is an integer, d₀, d₁, d₂, d₃... are the digits of the number in base 10, and d₀ is not zero.

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

$9.18082\times10^2$,

while the number −0.00574012 in normalized form is

$-5.74012\times 10^{-3}.$

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

$\pm d_0.d_1d_2d_3\dots\times b^n,$

where again $d_0\not=0,$ and the "digits" d₀, d₁, d₂, d₃... 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