calculators

[asto5]

how do calculators work? not the expensive graphic calculators, just an ordinary calculator! how does it work out that the pi(th) root of pi is 1.439619496.

amazing i think, cheers in advance

[Hamish]

All maths problems can be broken down into addition and subtraction - (even finding a sq root). For example 3*5 is also 5+5+5, etc. Doing division is a little more tricky and finding roots harder still. If you want to learn more about this I would read up on basic digital electroics (how to add and subtract in binary) and on anchient methods of calculation (they were working out logs and roots back in the 1650s!). Most of the actual maths is fairly simple, although the methods are complex. I find it even more amazing that when I play a computer game against a 'badie' who behaves like a person, the same simple processes of adding and subtracting are all that is going on and controlling 'his' behaviour! Have fun! Hamish

[Calvesy]

Somehow, minds cleverer than ours have worked out methods of simplifying all mathematical functions into formulae in an infinite series of sums that converge upon the result. Some of these calculations might take you years by hand, and 69! (factorial) or 1x2x3x4......x67x68x69 takes a noticeable amount of time on some calculators. Some cheat with pre-calculated tables of common results and interpolate. Other minds greater than ours have worked out how to wire up millions of transistors that can perform all this logic in binary and etch them on to a piece of grit the size of a gnat's arse.