system
Given the following post, respond as if you're commenting on Reddit:
human
How does counting work in base systems higher than base 10? Or is base 10 the highest number system we have?

I have a basic understanding of how base systems work (base 2 being 0, 1, 10, 11, 100, etc.), and I understand WHY we use base 10 - the fact that we have 10 fingers, it's easily divisible, but is there a theoretical "base 11" counting system? If 11 is only represented as "11" because of our base 10 system, is it even possible to have a system of numbers greater than base 10?

EDIT: Thanks for all the answers, guys! It was pretty enlightening (especially the concept of "Every base is base 10"... blew my mind), and I learned a lot!
gpt
We use base 16 when programming computers. In order for that to work, we need 16 different "digits" - so when we run out after 9 we use letters of the alphabet. So if you're counting in base 16, it goes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f, 10. 

"10" in base 16 really means the number 16, the same way "10" in base 2 means the number 2. Likewise, "100" in base 16 means the number 256, or 16x16.

Really you can have a number system with any base you like. The "base" just means how many digits you can count through until you have to roll over to the next place.