When I am counting in a base greater than ten, I can use the letters of the alphabet. What do I use when I run out of those?
What comes after $z$?:
$0, 1, 2, 3,\ldots, 9, a, b, c, d,\ldots, x, y, z$ (?)
And how would I find it?
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Sign up to join this communityWhen I am counting in a base greater than ten, I can use the letters of the alphabet. What do I use when I run out of those?
What comes after $z$?:
$0, 1, 2, 3,\ldots, 9, a, b, c, d,\ldots, x, y, z$ (?)
And how would I find it?
You can choose your favorite letter and put an index, e.g. for base $n\in \mathbb{N}$ $$a_1,a_2,a_3,\ldots, a_n.$$
00
, 01
, …, 99
. If you do that, then the base-100 representation of, say, 142857, is the three digits 14 28 57
. This kind of system is ubiquitous in computer applications (an example is given by user87690 elsewhere in this thread). The bablyonians used a similar technique for their base-60 system, where the 60 'digits' were effectively 00
, 01
,… 59
, as David K. observed elsewhere in this thread.
$\endgroup$
The Babylonians were able to do math in base $60$. Each digit consisted of $N$ wedge marks in one direction and $M$ in the other direction, and the value of the digit was $10N + M$. They lacked a zero, but that is not hard to provide.
You could also say that time of day is base $60$, so $\mbox{1:23:45} = 1 \cdot 60^2 + 23 \cdot 60 + 45.$ The basic idea of a place-value system is that you can tell what digit is in each place somehow (in this case, by taking the symbols $0$ through $9$ in pairs, and some people insert the symbol ":" beteween pairs as a visual aid). Each digit does not need to be drawn as a single connected region of black paint.
Take for example base $64$, widely used for encoding binary data.
Once it gets to Z
(it starts uppercase) it goes with lowercase letters: WXYZabcd
. The careful observer will note it's still missing two letters, because $10 + 2 \cdot 26 = 62.$
Those two are usually one of /
, +
and -
, but it's more or less implementation dependent.
A base $64$ number looks like this cGxlYXN1cmUu
and you have probably seen it in a URL before.
+/
is the most common pair of highest digits (those are anecdotally the ones used today) and the rest used various combinations of .
, _
, -
, :
, and !
.
$\endgroup$
Jul 2, 2014 at 19:13
-_
and drop the padding, as all three otherwise typically used characters +/=
are not nice to handle in URLs as they all have their special meaning.
$\endgroup$
You can also encode each digit of high-base number system by fixed-width representation of a number in low-base number system. For example, each digit of a number in base $\leq 256$ can be encoded by a pair of hexadecimal digits.
We have tons of symbols available, Take any number of languages which have pairways disjoint letters. Index each of those languages and use the pre-ezisting indexes inside the language and you shall have a lot of letters, just by using the symbols for base $10$ numbers ,Japanese Hiragana, katakana, Arab, Hebrew and Spanish we get $179$ symbols.
This example shows the first 1,600 values from base 40 represented in a particular fashion:
[]
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[1, 0]
[1, 1]
[1, 2]
[1, 3]
[1, 4]
[1, 5]
[1, 6]
[1, 7]
[1, 8]
[1, 9]
[1, 10]
[1, 11]
[1, 12]
[1, 13]
[1, 14]
[1, 15]
[1, 16]
[1, 17]
[1, 18]
[1, 19]
[1, 20]
[1, 21]
[1, 22]
[1, 23]
[1, 24]
[1, 25]
[1, 26]
[1, 27]
[1, 28]
[1, 29]
[1, 30]
[1, 31]
[1, 32]
[1, 33]
[1, 34]
[1, 35]
[1, 36]
[1, 37]
[1, 38]
[1, 39]
[2, 0]
[2, 1]
[2, 2]
[2, 3]
[2, 4]
[2, 5]
[2, 6]
[2, 7]
[2, 8]
[2, 9]
[2, 10]
[2, 11]
[2, 12]
[2, 13]
[2, 14]
[2, 15]
[2, 16]
[2, 17]
[2, 18]
[2, 19]
[2, 20]
[2, 21]
[2, 22]
[2, 23]
[2, 24]
[2, 25]
[2, 26]
[2, 27]
[2, 28]
[2, 29]
[2, 30]
[2, 31]
[2, 32]
[2, 33]
[2, 34]
[2, 35]
[2, 36]
[2, 37]
[2, 38]
[2, 39]
[3, 0]
[3, 1]
[3, 2]
[3, 3]
[3, 4]
[3, 5]
[3, 6]
[3, 7]
[3, 8]
[3, 9]
[3, 10]
[3, 11]
[3, 12]
[3, 13]
[3, 14]
[3, 15]
[3, 16]
[3, 17]
[3, 18]
[3, 19]
[3, 20]
[3, 21]
[3, 22]
[3, 23]
[3, 24]
[3, 25]
[3, 26]
[3, 27]
[3, 28]
[3, 29]
[3, 30]
[3, 31]
[3, 32]
[3, 33]
[3, 34]
[3, 35]
[3, 36]
[3, 37]
[3, 38]
[3, 39]
[4, 0]
[4, 1]
[4, 2]
[4, 3]
[4, 4]
[4, 5]
[4, 6]
[4, 7]
[4, 8]
[4, 9]
[4, 10]
[4, 11]
[4, 12]
[4, 13]
[4, 14]
[4, 15]
[4, 16]
[4, 17]
[4, 18]
[4, 19]
[4, 20]
[4, 21]
[4, 22]
[4, 23]
[4, 24]
[4, 25]
[4, 26]
[4, 27]
[4, 28]
[4, 29]
[4, 30]
[4, 31]
[4, 32]
[4, 33]
[4, 34]
[4, 35]
[4, 36]
[4, 37]
[4, 38]
[4, 39]
[5, 0]
[5, 1]
[5, 2]
[5, 3]
[5, 4]
[5, 5]
[5, 6]
[5, 7]
[5, 8]
[5, 9]
[5, 10]
[5, 11]
[5, 12]
[5, 13]
[5, 14]
[5, 15]
[5, 16]
[5, 17]
[5, 18]
[5, 19]
[5, 20]
[5, 21]
[5, 22]
[5, 23]
[5, 24]
[5, 25]
[5, 26]
[5, 27]
[5, 28]
[5, 29]
[5, 30]
[5, 31]
[5, 32]
[5, 33]
[5, 34]
[5, 35]
[5, 36]
[5, 37]
[5, 38]
[5, 39]
[6, 0]
[6, 1]
[6, 2]
[6, 3]
[6, 4]
[6, 5]
[6, 6]
[6, 7]
[6, 8]
[6, 9]
[6, 10]
[6, 11]
[6, 12]
[6, 13]
[6, 14]
[6, 15]
[6, 16]
[6, 17]
[6, 18]
[6, 19]
[6, 20]
[6, 21]
[6, 22]
[6, 23]
[6, 24]
[6, 25]
[6, 26]
[6, 27]
[6, 28]
[6, 29]
[6, 30]
[6, 31]
[6, 32]
[6, 33]
[6, 34]
[6, 35]
[6, 36]
[6, 37]
[6, 38]
[6, 39]
[7, 0]
[7, 1]
[7, 2]
[7, 3]
[7, 4]
[7, 5]
[7, 6]
[7, 7]
[7, 8]
[7, 9]
[7, 10]
[7, 11]
[7, 12]
[7, 13]
[7, 14]
[7, 15]
[7, 16]
[7, 17]
[7, 18]
[7, 19]
[7, 20]
[7, 21]
[7, 22]
[7, 23]
[7, 24]
[7, 25]
[7, 26]
[7, 27]
[7, 28]
[7, 29]
[7, 30]
[7, 31]
[7, 32]
[7, 33]
[7, 34]
[7, 35]
[7, 36]
[7, 37]
[7, 38]
[7, 39]
[8, 0]
[8, 1]
[8, 2]
[8, 3]
[8, 4]
[8, 5]
[8, 6]
[8, 7]
[8, 8]
[8, 9]
[8, 10]
[8, 11]
[8, 12]
[8, 13]
[8, 14]
[8, 15]
[8, 16]
[8, 17]
[8, 18]
[8, 19]
[8, 20]
[8, 21]
[8, 22]
[8, 23]
[8, 24]
[8, 25]
[8, 26]
[8, 27]
[8, 28]
[8, 29]
[8, 30]
[8, 31]
[8, 32]
[8, 33]
[8, 34]
[8, 35]
[8, 36]
[8, 37]
[8, 38]
[8, 39]
[9, 0]
[9, 1]
[9, 2]
[9, 3]
[9, 4]
[9, 5]
[9, 6]
[9, 7]
[9, 8]
[9, 9]
[9, 10]
[9, 11]
[9, 12]
[9, 13]
[9, 14]
[9, 15]
[9, 16]
[9, 17]
[9, 18]
[9, 19]
[9, 20]
[9, 21]
[9, 22]
[9, 23]
[9, 24]
[9, 25]
[9, 26]
[9, 27]
[9, 28]
[9, 29]
[9, 30]
[9, 31]
[9, 32]
[9, 33]
[9, 34]
[9, 35]
[9, 36]
[9, 37]
[9, 38]
[9, 39]
[10, 0]
[10, 1]
[10, 2]
[10, 3]
[10, 4]
[10, 5]
[10, 6]
[10, 7]
[10, 8]
[10, 9]
[10, 10]
[10, 11]
[10, 12]
[10, 13]
[10, 14]
[10, 15]
[10, 16]
[10, 17]
[10, 18]
[10, 19]
[10, 20]
[10, 21]
[10, 22]
[10, 23]
[10, 24]
[10, 25]
[10, 26]
[10, 27]
[10, 28]
[10, 29]
[10, 30]
[10, 31]
[10, 32]
[10, 33]
[10, 34]
[10, 35]
[10, 36]
[10, 37]
[10, 38]
[10, 39]
[11, 0]
[11, 1]
[11, 2]
[11, 3]
[11, 4]
[11, 5]
[11, 6]
[11, 7]
[11, 8]
[11, 9]
[11, 10]
[11, 11]
[11, 12]
[11, 13]
[11, 14]
[11, 15]
[11, 16]
[11, 17]
[11, 18]
[11, 19]
[11, 20]
[11, 21]
[11, 22]
[11, 23]
[11, 24]
[11, 25]
[11, 26]
[11, 27]
[11, 28]
[11, 29]
[11, 30]
[11, 31]
[11, 32]
[11, 33]
[11, 34]
[11, 35]
[11, 36]
[11, 37]
[11, 38]
[11, 39]
[12, 0]
[12, 1]
[12, 2]
[12, 3]
[12, 4]
[12, 5]
[12, 6]
[12, 7]
[12, 8]
[12, 9]
[12, 10]
[12, 11]
[12, 12]
[12, 13]
[12, 14]
[12, 15]
[12, 16]
[12, 17]
[12, 18]
[12, 19]
[12, 20]
[12, 21]
[12, 22]
[12, 23]
[12, 24]
[12, 25]
[12, 26]
[12, 27]
[12, 28]
[12, 29]
[12, 30]
[12, 31]
[12, 32]
[12, 33]
[12, 34]
[12, 35]
[12, 36]
[12, 37]
[12, 38]
[12, 39]
[13, 0]
[13, 1]
[13, 2]
[13, 3]
[13, 4]
[13, 5]
[13, 6]
[13, 7]
[13, 8]
[13, 9]
[13, 10]
[13, 11]
[13, 12]
[13, 13]
[13, 14]
[13, 15]
[13, 16]
[13, 17]
[13, 18]
[13, 19]
[13, 20]
[13, 21]
[13, 22]
[13, 23]
[13, 24]
[13, 25]
[13, 26]
[13, 27]
[13, 28]
[13, 29]
[13, 30]
[13, 31]
[13, 32]
[13, 33]
[13, 34]
[13, 35]
[13, 36]
[13, 37]
[13, 38]
[13, 39]
[14, 0]
[14, 1]
[14, 2]
[14, 3]
[14, 4]
[14, 5]
[14, 6]
[14, 7]
[14, 8]
[14, 9]
[14, 10]
[14, 11]
[14, 12]
[14, 13]
[14, 14]
[14, 15]
[14, 16]
[14, 17]
[14, 18]
[14, 19]
[14, 20]
[14, 21]
[14, 22]
[14, 23]
[14, 24]
[14, 25]
[14, 26]
[14, 27]
[14, 28]
[14, 29]
[14, 30]
[14, 31]
[14, 32]
[14, 33]
[14, 34]
[14, 35]
[14, 36]
[14, 37]
[14, 38]
[14, 39]
[15, 0]
[15, 1]
[15, 2]
[15, 3]
[15, 4]
[15, 5]
[15, 6]
[15, 7]
[15, 8]
[15, 9]
[15, 10]
[15, 11]
[15, 12]
[15, 13]
[15, 14]
[15, 15]
[15, 16]
[15, 17]
[15, 18]
[15, 19]
[15, 20]
[15, 21]
[15, 22]
[15, 23]
[15, 24]
[15, 25]
[15, 26]
[15, 27]
[15, 28]
[15, 29]
[15, 30]
[15, 31]
[15, 32]
[15, 33]
[15, 34]
[15, 35]
[15, 36]
[15, 37]
[15, 38]
[15, 39]
[16, 0]
[16, 1]
[16, 2]
[16, 3]
[16, 4]
[16, 5]
[16, 6]
[16, 7]
[16, 8]
[16, 9]
[16, 10]
[16, 11]
[16, 12]
[16, 13]
[16, 14]
[16, 15]
[16, 16]
[16, 17]
[16, 18]
[16, 19]
[16, 20]
[16, 21]
[16, 22]
[16, 23]
[16, 24]
[16, 25]
[16, 26]
[16, 27]
[16, 28]
[16, 29]
[16, 30]
[16, 31]
[16, 32]
[16, 33]
[16, 34]
[16, 35]
[16, 36]
[16, 37]
[16, 38]
[16, 39]
[17, 0]
[17, 1]
[17, 2]
[17, 3]
[17, 4]
[17, 5]
[17, 6]
[17, 7]
[17, 8]
[17, 9]
[17, 10]
[17, 11]
[17, 12]
[17, 13]
[17, 14]
[17, 15]
[17, 16]
[17, 17]
[17, 18]
[17, 19]
[17, 20]
[17, 21]
[17, 22]
[17, 23]
[17, 24]
[17, 25]
[17, 26]
[17, 27]
[17, 28]
[17, 29]
[17, 30]
[17, 31]
[17, 32]
[17, 33]
[17, 34]
[17, 35]
[17, 36]
[17, 37]
[17, 38]
[17, 39]
[18, 0]
[18, 1]
[18, 2]
[18, 3]
[18, 4]
[18, 5]
[18, 6]
[18, 7]
[18, 8]
[18, 9]
[18, 10]
[18, 11]
[18, 12]
[18, 13]
[18, 14]
[18, 15]
[18, 16]
[18, 17]
[18, 18]
[18, 19]
[18, 20]
[18, 21]
[18, 22]
[18, 23]
[18, 24]
[18, 25]
[18, 26]
[18, 27]
[18, 28]
[18, 29]
[18, 30]
[18, 31]
[18, 32]
[18, 33]
[18, 34]
[18, 35]
[18, 36]
[18, 37]
[18, 38]
[18, 39]
[19, 0]
[19, 1]
[19, 2]
[19, 3]
[19, 4]
[19, 5]
[19, 6]
[19, 7]
[19, 8]
[19, 9]
[19, 10]
[19, 11]
[19, 12]
[19, 13]
[19, 14]
[19, 15]
[19, 16]
[19, 17]
[19, 18]
[19, 19]
[19, 20]
[19, 21]
[19, 22]
[19, 23]
[19, 24]
[19, 25]
[19, 26]
[19, 27]
[19, 28]
[19, 29]
[19, 30]
[19, 31]
[19, 32]
[19, 33]
[19, 34]
[19, 35]
[19, 36]
[19, 37]
[19, 38]
[19, 39]
[20, 0]
[20, 1]
[20, 2]
[20, 3]
[20, 4]
[20, 5]
[20, 6]
[20, 7]
[20, 8]
[20, 9]
[20, 10]
[20, 11]
[20, 12]
[20, 13]
[20, 14]
[20, 15]
[20, 16]
[20, 17]
[20, 18]
[20, 19]
[20, 20]
[20, 21]
[20, 22]
[20, 23]
[20, 24]
[20, 25]
[20, 26]
[20, 27]
[20, 28]
[20, 29]
[20, 30]
[20, 31]
[20, 32]
[20, 33]
[20, 34]
[20, 35]
[20, 36]
[20, 37]
[20, 38]
[20, 39]
[21, 0]
[21, 1]
[21, 2]
[21, 3]
[21, 4]
[21, 5]
[21, 6]
[21, 7]
[21, 8]
[21, 9]
[21, 10]
[21, 11]
[21, 12]
[21, 13]
[21, 14]
[21, 15]
[21, 16]
[21, 17]
[21, 18]
[21, 19]
[21, 20]
[21, 21]
[21, 22]
[21, 23]
[21, 24]
[21, 25]
[21, 26]
[21, 27]
[21, 28]
[21, 29]
[21, 30]
[21, 31]
[21, 32]
[21, 33]
[21, 34]
[21, 35]
[21, 36]
[21, 37]
[21, 38]
[21, 39]
[22, 0]
[22, 1]
[22, 2]
[22, 3]
[22, 4]
[22, 5]
[22, 6]
[22, 7]
[22, 8]
[22, 9]
[22, 10]
[22, 11]
[22, 12]
[22, 13]
[22, 14]
[22, 15]
[22, 16]
[22, 17]
[22, 18]
[22, 19]
[22, 20]
[22, 21]
[22, 22]
[22, 23]
[22, 24]
[22, 25]
[22, 26]
[22, 27]
[22, 28]
[22, 29]
[22, 30]
[22, 31]
[22, 32]
[22, 33]
[22, 34]
[22, 35]
[22, 36]
[22, 37]
[22, 38]
[22, 39]
[23, 0]
[23, 1]
[23, 2]
[23, 3]
[23, 4]
[23, 5]
[23, 6]
[23, 7]
[23, 8]
[23, 9]
[23, 10]
[23, 11]
[23, 12]
[23, 13]
[23, 14]
[23, 15]
[23, 16]
[23, 17]
[23, 18]
[23, 19]
[23, 20]
[23, 21]
[23, 22]
[23, 23]
[23, 24]
[23, 25]
[23, 26]
[23, 27]
[23, 28]
[23, 29]
[23, 30]
[23, 31]
[23, 32]
[23, 33]
[23, 34]
[23, 35]
[23, 36]
[23, 37]
[23, 38]
[23, 39]
[24, 0]
[24, 1]
[24, 2]
[24, 3]
[24, 4]
[24, 5]
[24, 6]
[24, 7]
[24, 8]
[24, 9]
[24, 10]
[24, 11]
[24, 12]
[24, 13]
[24, 14]
[24, 15]
[24, 16]
[24, 17]
[24, 18]
[24, 19]
[24, 20]
[24, 21]
[24, 22]
[24, 23]
[24, 24]
[24, 25]
[24, 26]
[24, 27]
[24, 28]
[24, 29]
[24, 30]
[24, 31]
[24, 32]
[24, 33]
[24, 34]
[24, 35]
[24, 36]
[24, 37]
[24, 38]
[24, 39]
[25, 0]
[25, 1]
[25, 2]
[25, 3]
[25, 4]
[25, 5]
[25, 6]
[25, 7]
[25, 8]
[25, 9]
[25, 10]
[25, 11]
[25, 12]
[25, 13]
[25, 14]
[25, 15]
[25, 16]
[25, 17]
[25, 18]
[25, 19]
[25, 20]
[25, 21]
[25, 22]
[25, 23]
[25, 24]
[25, 25]
[25, 26]
[25, 27]
[25, 28]
[25, 29]
[25, 30]
[25, 31]
[25, 32]
[25, 33]
[25, 34]
[25, 35]
[25, 36]
[25, 37]
[25, 38]
[25, 39]
[26, 0]
[26, 1]
[26, 2]
[26, 3]
[26, 4]
[26, 5]
[26, 6]
[26, 7]
[26, 8]
[26, 9]
[26, 10]
[26, 11]
[26, 12]
[26, 13]
[26, 14]
[26, 15]
[26, 16]
[26, 17]
[26, 18]
[26, 19]
[26, 20]
[26, 21]
[26, 22]
[26, 23]
[26, 24]
[26, 25]
[26, 26]
[26, 27]
[26, 28]
[26, 29]
[26, 30]
[26, 31]
[26, 32]
[26, 33]
[26, 34]
[26, 35]
[26, 36]
[26, 37]
[26, 38]
[26, 39]
[27, 0]
[27, 1]
[27, 2]
[27, 3]
[27, 4]
[27, 5]
[27, 6]
[27, 7]
[27, 8]
[27, 9]
[27, 10]
[27, 11]
[27, 12]
[27, 13]
[27, 14]
[27, 15]
[27, 16]
[27, 17]
[27, 18]
[27, 19]
[27, 20]
[27, 21]
[27, 22]
[27, 23]
[27, 24]
[27, 25]
[27, 26]
[27, 27]
[27, 28]
[27, 29]
[27, 30]
[27, 31]
[27, 32]
[27, 33]
[27, 34]
[27, 35]
[27, 36]
[27, 37]
[27, 38]
[27, 39]
[28, 0]
[28, 1]
[28, 2]
[28, 3]
[28, 4]
[28, 5]
[28, 6]
[28, 7]
[28, 8]
[28, 9]
[28, 10]
[28, 11]
[28, 12]
[28, 13]
[28, 14]
[28, 15]
[28, 16]
[28, 17]
[28, 18]
[28, 19]
[28, 20]
[28, 21]
[28, 22]
[28, 23]
[28, 24]
[28, 25]
[28, 26]
[28, 27]
[28, 28]
[28, 29]
[28, 30]
[28, 31]
[28, 32]
[28, 33]
[28, 34]
[28, 35]
[28, 36]
[28, 37]
[28, 38]
[28, 39]
[29, 0]
[29, 1]
[29, 2]
[29, 3]
[29, 4]
[29, 5]
[29, 6]
[29, 7]
[29, 8]
[29, 9]
[29, 10]
[29, 11]
[29, 12]
[29, 13]
[29, 14]
[29, 15]
[29, 16]
[29, 17]
[29, 18]
[29, 19]
[29, 20]
[29, 21]
[29, 22]
[29, 23]
[29, 24]
[29, 25]
[29, 26]
[29, 27]
[29, 28]
[29, 29]
[29, 30]
[29, 31]
[29, 32]
[29, 33]
[29, 34]
[29, 35]
[29, 36]
[29, 37]
[29, 38]
[29, 39]
[30, 0]
[30, 1]
[30, 2]
[30, 3]
[30, 4]
[30, 5]
[30, 6]
[30, 7]
[30, 8]
[30, 9]
[30, 10]
[30, 11]
[30, 12]
[30, 13]
[30, 14]
[30, 15]
[30, 16]
[30, 17]
[30, 18]
[30, 19]
[30, 20]
[30, 21]
[30, 22]
[30, 23]
[30, 24]
[30, 25]
[30, 26]
[30, 27]
[30, 28]
[30, 29]
[30, 30]
[30, 31]
[30, 32]
[30, 33]
[30, 34]
[30, 35]
[30, 36]
[30, 37]
[30, 38]
[30, 39]
[31, 0]
[31, 1]
[31, 2]
[31, 3]
[31, 4]
[31, 5]
[31, 6]
[31, 7]
[31, 8]
[31, 9]
[31, 10]
[31, 11]
[31, 12]
[31, 13]
[31, 14]
[31, 15]
[31, 16]
[31, 17]
[31, 18]
[31, 19]
[31, 20]
[31, 21]
[31, 22]
[31, 23]
[31, 24]
[31, 25]
[31, 26]
[31, 27]
[31, 28]
[31, 29]
[31, 30]
[31, 31]
[31, 32]
[31, 33]
[31, 34]
[31, 35]
[31, 36]
[31, 37]
[31, 38]
[31, 39]
[32, 0]
[32, 1]
[32, 2]
[32, 3]
[32, 4]
[32, 5]
[32, 6]
[32, 7]
[32, 8]
[32, 9]
[32, 10]
[32, 11]
[32, 12]
[32, 13]
[32, 14]
[32, 15]
[32, 16]
[32, 17]
[32, 18]
[32, 19]
[32, 20]
[32, 21]
[32, 22]
[32, 23]
[32, 24]
[32, 25]
[32, 26]
[32, 27]
[32, 28]
[32, 29]
[32, 30]
[32, 31]
[32, 32]
[32, 33]
[32, 34]
[32, 35]
[32, 36]
[32, 37]
[32, 38]
[32, 39]
[33, 0]
[33, 1]
[33, 2]
[33, 3]
[33, 4]
[33, 5]
[33, 6]
[33, 7]
[33, 8]
[33, 9]
[33, 10]
[33, 11]
[33, 12]
[33, 13]
[33, 14]
[33, 15]
[33, 16]
[33, 17]
[33, 18]
[33, 19]
[33, 20]
[33, 21]
[33, 22]
[33, 23]
[33, 24]
[33, 25]
[33, 26]
[33, 27]
[33, 28]
[33, 29]
[33, 30]
[33, 31]
[33, 32]
[33, 33]
[33, 34]
[33, 35]
[33, 36]
[33, 37]
[33, 38]
[33, 39]
[34, 0]
[34, 1]
[34, 2]
[34, 3]
[34, 4]
[34, 5]
[34, 6]
[34, 7]
[34, 8]
[34, 9]
[34, 10]
[34, 11]
[34, 12]
[34, 13]
[34, 14]
[34, 15]
[34, 16]
[34, 17]
[34, 18]
[34, 19]
[34, 20]
[34, 21]
[34, 22]
[34, 23]
[34, 24]
[34, 25]
[34, 26]
[34, 27]
[34, 28]
[34, 29]
[34, 30]
[34, 31]
[34, 32]
[34, 33]
[34, 34]
[34, 35]
[34, 36]
[34, 37]
[34, 38]
[34, 39]
[35, 0]
[35, 1]
[35, 2]
[35, 3]
[35, 4]
[35, 5]
[35, 6]
[35, 7]
[35, 8]
[35, 9]
[35, 10]
[35, 11]
[35, 12]
[35, 13]
[35, 14]
[35, 15]
[35, 16]
[35, 17]
[35, 18]
[35, 19]
[35, 20]
[35, 21]
[35, 22]
[35, 23]
[35, 24]
[35, 25]
[35, 26]
[35, 27]
[35, 28]
[35, 29]
[35, 30]
[35, 31]
[35, 32]
[35, 33]
[35, 34]
[35, 35]
[35, 36]
[35, 37]
[35, 38]
[35, 39]
[36, 0]
[36, 1]
[36, 2]
[36, 3]
[36, 4]
[36, 5]
[36, 6]
[36, 7]
[36, 8]
[36, 9]
[36, 10]
[36, 11]
[36, 12]
[36, 13]
[36, 14]
[36, 15]
[36, 16]
[36, 17]
[36, 18]
[36, 19]
[36, 20]
[36, 21]
[36, 22]
[36, 23]
[36, 24]
[36, 25]
[36, 26]
[36, 27]
[36, 28]
[36, 29]
[36, 30]
[36, 31]
[36, 32]
[36, 33]
[36, 34]
[36, 35]
[36, 36]
[36, 37]
[36, 38]
[36, 39]
[37, 0]
[37, 1]
[37, 2]
[37, 3]
[37, 4]
[37, 5]
[37, 6]
[37, 7]
[37, 8]
[37, 9]
[37, 10]
[37, 11]
[37, 12]
[37, 13]
[37, 14]
[37, 15]
[37, 16]
[37, 17]
[37, 18]
[37, 19]
[37, 20]
[37, 21]
[37, 22]
[37, 23]
[37, 24]
[37, 25]
[37, 26]
[37, 27]
[37, 28]
[37, 29]
[37, 30]
[37, 31]
[37, 32]
[37, 33]
[37, 34]
[37, 35]
[37, 36]
[37, 37]
[37, 38]
[37, 39]
[38, 0]
[38, 1]
[38, 2]
[38, 3]
[38, 4]
[38, 5]
[38, 6]
[38, 7]
[38, 8]
[38, 9]
[38, 10]
[38, 11]
[38, 12]
[38, 13]
[38, 14]
[38, 15]
[38, 16]
[38, 17]
[38, 18]
[38, 19]
[38, 20]
[38, 21]
[38, 22]
[38, 23]
[38, 24]
[38, 25]
[38, 26]
[38, 27]
[38, 28]
[38, 29]
[38, 30]
[38, 31]
[38, 32]
[38, 33]
[38, 34]
[38, 35]
[38, 36]
[38, 37]
[38, 38]
[38, 39]
[39, 0]
[39, 1]
[39, 2]
[39, 3]
[39, 4]
[39, 5]
[39, 6]
[39, 7]
[39, 8]
[39, 9]
[39, 10]
[39, 11]
[39, 12]
[39, 13]
[39, 14]
[39, 15]
[39, 16]
[39, 17]
[39, 18]
[39, 19]
[39, 20]
[39, 21]
[39, 22]
[39, 23]
[39, 24]
[39, 25]
[39, 26]
[39, 27]
[39, 28]
[39, 29]
[39, 30]
[39, 31]
[39, 32]
[39, 33]
[39, 34]
[39, 35]
[39, 36]
[39, 37]
[39, 38]
[39, 39]
[1, 0, 0]
You can invent any way you want to represent a number.
+, -, /, { ,], ä, ö, ü, ß, ă, î, ț, ﺞ, 덖, 哶, ...
There are millions of characters you could use. There are standards mostly used for base $64$ or base $32$ but I'd say that it's mostly up to you what you choose.
I don't mean to be silly, but why not use base 6? If you want join the gitis in groups of two bits
1234123051
can be understood as a 5-digit number:
12 34 12 30 51
In the decimal system multiplying by ten $T: x\mapsto 10x$ plays a very special role.
If we want to learn about a number $\alpha$ we could take the integer part (e.g. $\lfloor 3.5\rfloor = 3$), then multiply by 10, take the integer part again. Doing this over and over would give our decimal system.
In your case, using 36 instead of 10. Or just use two base-6 digits. This is also related to channel coding from information theory.