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− | {{Note|This article is about octal, which is a real thing. For more information, consult [https://en.wikipedia.org/wiki/Octal the other wiki].}}
| + | 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). |
| + | {| class="wikitable" |
| + | |+ |
| + | !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<sub>8</sub>) |
| + | |'''up''' |
| + | |'''up''' |
| + | |'''up''' |
| + | |'''up''' |
| + | |'''up''' |
| + | |} |
| + | This is why Delgar's [[currencies]] are divided into multiples of 8 instead of multiples of 10. |
| | | |
− | The people of Delgar use '''octal math'''. What this means is that 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:
| + | What's with that "10<sub>8</sub>" 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 [https://en.wikipedia.org/wiki/Octal 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: | | 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: |
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| |1 | | |1 |
| |0 | | |0 |
− | |1×10<sup>1</sup> + 1×10<sup>0</sup> | + | |1×10<sup>1</sup> + 0×10<sup>0</sup> |
| |10 | | |10 |
| |} | | |} |
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| |1 | | |1 |
| |0 | | |0 |
− | |1×8<sup>1</sup> + 1×8<sup>0</sup> | + | |1×8<sup>1</sup> + 0×8<sup>0</sup> |
| |8 | | |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<sub>8</sub> = 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<sub>8</sub> = 8. |
− | {{Note|1=For single digit numbers, this distinction is immaterial. 5{8} = 5{10<nowiki>}</nowiki>}} | + | {{Note|1=For single digit numbers, this distinction is irrelevant. 5<sub>8</sub> = 5<sub>10</sub>, 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: |
| + | {| class="wikitable" |
| + | |+ |
| + | !Octal |
| + | !Decimal |
| + | |- |
| + | |1<sub>8</sub> |
| + | |1 |
| + | |- |
| + | |10<sub>8</sub> |
| + | |8 |
| + | |- |
| + | |11<sub>8</sub> |
| + | |9 |
| + | |- |
| + | |12<sub>8</sub> |
| + | |10 |
| + | |- |
| + | |100<sub>8</sub> |
| + | |64 |
| + | |- |
| + | |1,000<sub>8</sub> |
| + | |512 |
| + | |- |
| + | |10,000<sub>8</sub> |
| + | |4,096 |
| + | |- |
| + | |100,000<sub>8</sub> |
| + | |32,768 |
| + | |} |