The Ternary Calculating Machine of Thomas Fowler

See also Setun &lt;<a href="http://en.wikipedia.org/wiki/Setun&gt;" rel="nofollow">http:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Setun&gt;</a>, a computer from 1958 using the balanced ternary system.

Knuth&#x27;s <i>Art of Computer Programming, vol 2</i> [1], not surprisingly, gives a thorough discussion of the balanced ternary system.<p>The solution for a nice brainteaser can be found quickly once one thinks about balanced trinary, here it is: &quot;Using a balance scale, what is the minimum number of wheights needed to weigh any whole number of grams up to 40g?&quot;<p>[1] <a href="http://www.amazon.com/Art-Computer-Programming-Volume-Seminumerical/dp/0201896842" rel="nofollow">http:&#x2F;&#x2F;www.amazon.com&#x2F;Art-Computer-Programming-Volume-Seminu...</a>

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&#x2F;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?