Octal math

The people of Delgar use octal math. This is because of the way they count on their fingers, counting 1-4 on the fingers then raising thumb and counting again for 5-8, then using the other hand to count to a total of 16 on both hands (or 64 in the positional style, where the left hand is counted as 8x the shown value).

Number	Thumb	Index	Middle	Ring	Pinky
1	down	up	down	down	down
2	down	up	up	down	down
3	down	up	up	up	down
4	down	up	up	up	up
5	up	up	down	down	down
6	up	up	up	down	down
7	up	up	up	up	down
8 (108)	up	up	up	up	up

This is why Delgar's currencies are divided into multiples of 8 instead of multiples of 10.

What's with that "10₈" you ask? Well, in writing, they write the number 7 with one symbol ("7") but they write the number 8 with two symbols ('10"). If you've ever studied numeric bases for some reason (probably computer science) you probably already understand this, but in case it's confusing, here's the basic idea:

Note: The remainder of this article is primarily about octal itself, which is a real thing. For more information, consult the other wiki.

In decimal (the numbers you know and love) we have 10 different symbols for numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. When counting, after passing 9, we have no individual symbol to write the number 10, so we write it with two symbols: one in the "ten's place" and one in the "one's place", like so:

Tens (101)	Ones (100)	Calculation	Value (Decimal)
1	0	1×101 + 0×100	10

Octal works the same way, but it only has 8 symbols (like an octagon has 8 sides): 0, 1, 2, 3, 4, 5, 6, and 7. After 7, they use two symbols to write the number 8, like so: "10"

Eights (81)	Ones (80)	Calculation	Value (Decimal)
1	0	1×81 + 0×80	8

Okay, but now when I see the number "10" how do I know if it's a ten or an eight? Easy: Unless specified otherwise, it's ten. To do anything else would be very confusing. When a number is octal, it will be indicated with a subscript 8, like so: 10₈ = 8.

Note: For single digit numbers, this distinction is irrelevant. 5₈ = 5₁₀, and an 8 or a 9 has to be base 10 because octal doesn't use those symbols.

Here are some common values in octal and decimal for comparison:

Octal	Decimal
18	1
108	8
118	9
128	10
1008	64
1,0008	512
10,0008	4,096
100,0008	32,768