The Ternary Calculating Machine of Thomas Fowler (opens in new tab)

See also Setun <http://en.wikipedia.org/wiki/Setun>, a computer from 1958 using the balanced ternary system.

Knuth's Art of Computer Programming, vol 2 [1], not surprisingly, gives a thorough discussion of the balanced ternary system.

The solution for a nice brainteaser can be found quickly once one thinks about balanced trinary, here it is: "Using a balance scale, what is the minimum number of wheights needed to weigh any whole number of grams up to 40g?"

[1] http://www.amazon.com/Art-Computer-Programming-Volume-Seminu...

I often wonder if there is some notion of a basis of computation in mathematics. You can do stuff in binary, trinary, what about further out systems? What about working with functions/mappings which take more than two inputs. What can be said about the expressive power of these different ways of computing? Any one know where I should be looking for this kind of stuff?