Octal math

From Delgar

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