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 (10_{8}) | 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 "10_{8}" 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 (10^{1}) | Ones (10^{0}) | Calculation | Value (Decimal) |
---|---|---|---|
1 | 0 | 1×10^{1} + 0×10^{0} | 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 (8^{1}) | Ones (8^{0}) | Calculation | Value (Decimal) |
---|---|---|---|
1 | 0 | 1×8^{1} + 0×8^{0} | 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: 10_{8} = 8.
Note: For single digit numbers, this distinction is irrelevant. 5_{8} = 5_{10}, 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 |
---|---|
1_{8} | 1 |
10_{8} | 8 |
11_{8} | 9 |
12_{8} | 10 |
100_{8} | 64 |
1,000_{8} | 512 |
10,000_{8} | 4,096 |
100,000_{8} | 32,768 |