Editing Quater-imaginary base (section)

===Example: Real number===
As an example of an integer number we can try to find the quater-imaginary counterpart of the decimal number 7 (or 7<sub>10</sub> since the [[radix|base]] of the decimal system is 10). Since it is hard to predict exactly how long the digit string will be for a given decimal number, it is safe to assume a fairly large string. In this case, a string of six digits can be chosen. When an initial guess at the size of the string eventually turns out to be insufficient, a larger string can be used.

To find the representation, first write out the general formula, and group terms: 
:<math>
\begin{align}
7_{10}& = d_{0}+d_{1}\cdot b+d_{2}\cdot b^{2}+d_{3}\cdot b^{3}+d_{4}\cdot b^{4}+d_{5}\cdot b^{5} \\
& = d_{0}+2id_{1}-4d_{2}-8id_{3}+16d_{4}+32id_{5} \\
& = d_{0}-4d_{2}+16d_{4}+i(2d_{1}-8d_{3}+32d_{5}) \\
\end{align}
</math>

Since 7 is a real number, it is allowed to conclude that ''d<sub>1</sub>'', ''d<sub>3</sub>'' and ''d<sub>5</sub>'' should be zero. Now the value of the coefficients ''d<sub>0</sub>'', ''d<sub>2</sub>'' and  ''d<sub>4</sub>'', must be found. Because  d<sub>0</sub> − 4 d<sub>2</sub> + 16 d<sub>4</sub>  =  7 and because—by the nature of the quater-imaginary system—the coefficients can only be 0, 1, 2 or 3 the value of the coefficients can be found.  A possible configuration could be:  ''d<sub>0</sub>'' = 3,  ''d<sub>2</sub>'' = 3 and ''d<sub>4</sub>'' = 1. This configuration gives the resulting digit string for 7<sub>10</sub>.

:<math>7_{10} = 010303_{2i} = 10303_{2i}.</math>