How we can write 36 in base 37?

Question

i've been imagining that in the base 16 the number 10 is A and 11 is B so in the base 37, 35 will be Z so how we can write 36 ?

Answer 1

You could use a different symbol. Or you could use commas to separate place values in this base. Something like $5,22,36$ could represent the three-digit base thirty-seven numeral whose value in decimal would be $5\cdot 37^2+22\cdot 37 +36$.

Answer 2

As the comments have said, you have to define a symbol for it. Going to lower case letters is one possibility. A more general approach is to use two decimal digits for each base $37$ digit so your base $37$ digits range from $00$ through $36$. This has the advantage of being extendable to any base.

Answer 3

According to wikipedia and wikiwand this is called Heptatrigesimal, it uses all numbers $0-9$ and all letters of the Spanish alphabet. So people have apparently already thought about this. Here you can also find other clever solutions for all sorts of numeral systems.

This seems to be postponing the problem till we run out of letters so I definitely prefer the other options listed by the others. Though it is fun to find out that other people have at least been naming these systems and enumerating them.

Answer 4

You could represent 36 in base 37 by (36). That could stand for a symbol that means 36. Or if you want to indicate the base with a subscript: $(36)_{37}$. This could be used with all bases no matter how big.

Or you could use an actual (Unicode) symbol that is '36' inside a circle, or inside a square, or rectangle or something like that. Or a tiny '36'. Thus you have an actual symbol (numeral) that means 36 that is 'transparent', by which I mean that what it stands for is obvious from the appearance.

This approach could be good when you want the layperson or absolute beginner to be able to read the numbers. Also if you are experimenting with other bases, or using a very large base.

Answer 5

You can use underscore _ as symbol nr 36 (as the last symbol in your alphabet).

Then you can have nice looking test IDs, if you have unit tests or end-to-end tests, e.g.:

123abczxy_for_widget_a
456uvwxyz_user_b23
456uvwxyz_user_b23_copy

So, your 37 symbols could be: 0...9abc...xyz_.