#base 8

Base 10 means that the number system goes [ 0 1 2 3 4 5 6 7 8 9 ]. There is no digit smaller than 0 and no digit larger than 9.

Base 8 means that the number system goes [ 0 1 2 3 4 5 6 7 ]. There is still no digit smaller than 0, and there’s no digit larger than 7. 

In Base 10, when you want to make a number bigger than 9, you have to add another digit. 9 + 1 becomes 10. 

In Base 8, when you want to make a number bigger than 7, you have to add another digit as well. 7 + 1 becomes 10 (which would be 8 in base 10). 

Essentially, in Base 10, counting would go like this: [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ]

In Base 8, counting would go like this: [ 1 2 3 4 5 6 7 10 11 12 13 14 15 16 17 20 ]

When you’ve known base 10 all your life, any other base can get confusing. [ 16 17 20 ] in itself looks weird, but it gets even weirder when you realize that this series of numbers only goes up to what we know as 16. 

An easy way to convert from base 8 to base 10 is to multiple the 8′s place (what would be the 10′s place) by 8 and then add the 1’s place. 

ex. 23 in base 8 --> (2 x 8) + 3 --> (16) + 3 --> 19 in base 10

ex. 67 in base 8 --> (6 x 8) + 7 --> (48) + 7 --> 55

In Base 10, 99 is the highest it can go with only two digits; the next number it goes to is 100.

In Base 8, the highest it can go with only two digits is 77; the next number it goes to is 100. 

100 in Base 8 is what we know as 64, or 8^2. 

At this point, it may be self-explanatory, but the numbers go [ 100, 101, 102, 103, 104, 105, 106, 107, 110 ].

To convert a three-digit number from base 8 to base 10, the 64′s place (what would be the 100s place) is multiplied by 64; the 8′s place (what would be the 10′s place) is multiplied by 8, and the 1′s place is multiplied by 1. All three numbers are added together, and that’s your number!

ex. 106 in base 8  --> (1 x 64) + (0 x 8) + (5) --> (64) + (0) + (5) --> 69 

ex. 644 in base 8 --> (6 x 64) + (4 x 8) + (4) --> (384) + (32) + (4) --> 420

And, again, there’s a limit to how far it can go in three digits (777) so then you have to move up to 1000 (what we know as 512, or 8^3). To convert it to base 10, you’d multiple the 512′s place (what we know as the 1000′s place) by 512, and continue the pattern down to the 1′s place. After the 512′s place, it’s the 4096′s place (8^4), then the 32762′s place (8^5), and so on.

This may seem really complicated, and, admittedly, switching between bases can be, but if you’d been taught base 8 since you were born, base 10 would seem just as weird as base 8 seems to someone who’s been raised on base 10. There’s really no reason for us to use base 10 other than the fact that we have 10 fingers to count on, so it would actually be kind of weird for the characters in the Dwampyverse to use base 10 (though they canonically have used numbers that wouldn’t exist in base 8 -- coquet Y8 and hockey Z9 come to mind -- so they must use base 10 which really makes all this speculation useless, even if it’s fun.)