A three-integer system?

I've been reading a book on mathematics and have been trying to get a new grasp on numbers. I know math and some algebra and physics, of course, but all that really means is that I know how to drive this car called, "math."

I don't know how to take it apart and put it back together again. I'm an operator, not an architect.

In pursuit of this goal I'm trying to learn a three or six integer system, rather than our ten integer system (1,2,3,4,5,6,7,8,9, 10,11 and so on)

A three integer system would count like this:

1, 2, 10, 11, 12, 20, 21, 22, 100, 101, 102, 110...and so on.

The math would give different results, but, fundamentally, I believe, reduce to the same thing in binary code.

So that's what I'm on to now. Different counting. Has anyone reading this tried that?

- Steve