How would you count a base $> 36$ system?

Question

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?

Answer 1

You can choose your favorite letter and put an index, e.g. for base $n\in \mathbb{N}$ $$a_1,a_2,a_3,\ldots, a_n.$$

Answer 2

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.

Answer 3

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.

Answer 4

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.

Answer 5

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.

Answer 6

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.

Answer 7

+, -, /, { ,], 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.

Answer 8

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.

• $10^0\pi \mapsto 3$
• $10^1\pi \mapsto 1$
• $10^2\pi \mapsto 4$
• ...

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.