Editing Golden ratio base (section)

==Writing golden ratio base numbers in standard form==
In the following example of conversion from non-standard to standard form, the notation <u>1</u> is used to represent the [[signed-digit representation|signed digit]] −1.

211.0<u>1</u><sub>φ</sub> is not a standard base-φ numeral, since it contains a "11" and additionally a "2" and a "<u>1</u>" = −1, which are not "0" or "1".

To put a numeral in standard form, we may use the following substitutions: <math>0\underline{1}0_\phi=\underline{1}01_\phi</math>, <math>1\underline{1}0_\phi=001_\phi</math>, <math>200_\phi=1001_\phi</math>, <math>011_\phi=100_\phi</math>. The substitutions may be applied in any order we like, as the result will be the same. Below, the substitutions applied to the number on the previous line are on the right, the resulting number on the left.

<math>
\begin{align}
211.0\underline{1}0_\phi = 211&.\underline{1}01_\phi &0\underline{1}0\rightarrow\underline{1}01 \\
= 210&.011_\phi &1\underline{1}0\rightarrow001 \\
= 1011&.011_\phi &200\rightarrow1001 \\
= 1100&.100_\phi &011\rightarrow100 \\
= 10000&.1_\phi &011\rightarrow100\\
\end{align}
</math>

Any [[positive number]] with a non-standard terminating base-φ representation can be [[unique (mathematics)|unique]]ly standardized in this manner. If we get to a point where all digits are "0" or "1", except for the first digit being [[negative number|negative]], then the number is negative. (The exception to this is when the first digit is negative one and the next two digits are one, like <u>1</u>111.001=1.001.) This can be converted to the negative of a base-φ representation by [[negation|negating]] every digit, standardizing the result, and then marking it as negative.  For example, use a [[minus sign]], or some other significance to denote negative numbers.