Editing Senary (section)

==Base 36 as senary compression==
{{Redirect|Base 36|the encoding scheme used to represent binary data as text|Base36}}
For some purposes, senary might be too small a base for convenience. This can be worked around by using its square, base 36 (hexatrigesimal), as then conversion is facilitated by simply making the following replacements:

{| class="wikitable"
|- align="right"
! Decimal
| 0 || 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 || 10 || 11 || 12 || 13 || 14 || 15 || 16 || 17
|- align="right"
! Base 6
| 0 || 1 || 2 || 3 || 4 || 5 || 10 || 11 || 12 || 13 || 14 || 15 || 20 || 21 || 22 || 23 || 24 || 25
|- align="right"
! Base 36 
| <code>0</code> || <code>1</code> || <code>2</code> || <code>3</code> || <code>4</code> || <code>5</code> || <code>6</code> || <code>7</code> || <code>8</code> || <code>9</code> || <code>A</code> || <code>B</code> || <code>C</code> || <code>D</code> || <code>E</code> || <code>F</code> || <code>G</code> || <code>H</code>
|- 
| style="font: 0.5em/0.5em serif;" colspan="19" | &nbsp;
|- align="right"
! Decimal
| 18 || 19 || 20 || 21 || 22 || 23 || 24 || 25 || 26 || 27 || 28 || 29 || 30 || 31 || 32 || 33 || 34 || 35
|- align="right"
! Base 6
| 30 || 31 || 32 || 33 || 34 || 35 || 40 || 41 || 42 || 43 || 44 || 45 || 50 || 51 || 52 || 53 || 54 || 55
|- align="right"
! Base 36 
| <code>I</code> || <code>J</code> || <code>K</code> || <code>L</code> || <code>M</code> || <code>N</code> || <code>O</code> || <code>P</code> || <code>Q</code> || <code>R</code> || <code>S</code> || <code>T</code> || <code>U</code> || <code>V</code> || <code>W</code> || <code>X</code> || <code>Y</code> || <code>Z</code>
|}

Thus, the base-36 number WIKI<sub>36</sub> is equal to the senary number 52303230<sub>6</sub>. In decimal, it is 1,517,058.

The choice of 36 as a [[radix]] is convenient in that the digits can be represented using the [[Hindu–Arabic numerals|Arabic numerals]] 0–9 and the [[Latin alphabet|Latin letters]] A–Z; this choice is the basis of the [[base36]] encoding scheme. The compression effect of 36 being the square of 6 causes a lot of patterns and representations to be shorter in base 36:

:{{sfrac|1|9<sub>10</sub>}} = 0.04<sub>6</sub> = 0.4<sub>36</sub>

:{{sfrac|1|16<sub>10</sub>}} = 0.0213<sub>6</sub> = 0.29<sub>36</sub>

:{{sfrac|1|5<sub>10</sub>}} = 0.{{overline|1}}<sub>6</sub> = 0.{{overline|7}}<sub>36</sub>

:{{sfrac|1|7<sub>10</sub>}} = 0.{{overline|05}}<sub>6</sub> = 0.{{overline|5}}<sub>36</sub>