Editing Quater-imaginary base (section)

==Converting from quater-imaginary==
{|class="wikitable" style="width:14em;float:right;margin-left:1em;"
|+ Powers of 2''i''
|-
!''k''
!(2''i'')<sup>''k''</sup>
|-
|align="center"| −5 ||align="center"|  −''i''/32
|-
|align="center"| −4 ||align="center"|  1/16
|-
|align="center"| −3 ||align="center"|  ''i''/8
|-
|align="center"| −2 ||align="center"|  −1/4
|-
|align="center"| −1 ||align="center"|  −''i''/2
|-
|align="center"| 0 ||align="center"|  1
|-
|align="center"| 1 ||align="center"|  2''i''
|-
|align="center"| 2 ||align="center"|  −4
|-
|align="center"| 3 ||align="center"| −8''i''
|-
|align="center"| 4 ||align="center"| 16
|-
|align="center"| 5 ||align="center"| 32''i''
|-
|align="center"| 6 ||align="center"| −64
|-
|align="center"| 7 ||align="center"| −128''i''
|-
|align="center"| 8 ||align="center"| 256
|}

To convert a digit string from the quater-imaginary system to the decimal system, the standard formula for positional number systems can be used. This says that a digit string <math>\ldots d_3d_2d_1d_0</math> in base ''b'' can be converted to a decimal number using the formula
:<math>\cdots + d_3\cdot b^3+d_2\cdot b^2+d_1\cdot b+d_0</math>
For the quater-imaginary system, <math>b = 2i</math>.

Additionally, for a given string <math>d</math> in the form <math>d_{w-1}, d_{w-2},\dots d_0</math>, the formula below can be used for a given string length <math>w</math> in base <math>b</math>
:<math>Q2D_w \vec d \equiv \sum_{k=0}^{w-1} d_k \cdot b^k</math>

===Example===
To convert the string <math>1101_{2i}</math> to a decimal number, fill in the formula above:
:<math>1\cdot(2i)^3 + 1\cdot(2i)^2 + 0\cdot(2i)^1 + 1\cdot(2i)^0 = -8i - 4 + 0 + 1 = -3 - 8i</math>

Another, longer example: <math>1030003_{2i}</math> in base 10 is
:<math>1\cdot(2i)^6 + 3\cdot(2i)^4 + 3\cdot(2i)^0 = -64 + 3\cdot 16 + 3 = -13</math>