On Tue, 18 Jan 2005 15:59:50 -0800 (PST), Globe Trotter <itsme_410@xxxxxxxxx> wrote: > Hi, thanks, to you and everybody! > > My question is: how does a computer actually do it? When we are dividing a > number by a multiple of two, for example 5 = 101 divided by 2 = 10, then all we > do is shift the bit by the number of digits after the leading 1 in 2. So, 101 > divided by 10 means drop the last 1 in the 101 so we get 10. > > What happens if we divide 5= 101 by 3= 11? Anything similar? Oh, so you're more interested in the "algorithm", and not the actual hardware (transistors and stuff). The hardware implementation (which is how the computer *really* does it) is covered by the subject known as "computer architecture". But you can discuss the algorithms without the hardware, in which case it's then either computer science or just plain mathematics. In general, division by any power of your *base* is extremely easy. In everyday base 10 (decimal) everyone knows that to divide by 10 you just drop the rightmost digit. Some computers actually work in base 10 (mostly older mainframes using what's called "packed decimal"), and so for them division by 10 is trivial. Most modern computers primarily work with base 2 (binary). And as you discovered, division by 2 in binary is likewise just dropping the rightmost digit (a right bit-shift operation). It works the same for any base (>=2). The difficulty is when you're not dividing by the base (or a power of the base). Then it's hard, and the most straightforward solutions usually involve things like carrys, iteration, etc. It's really too involved to discuss here; but it's really not that much different from how go about doing long division on paper (although there are more complex optimizations out there too). You may of course realize that division by any number is extremely easy if you just convert your numbers into the correct base beforehand. But, not surprisingly, the algorithms to convert from one base to another in fact depend upon the division operation. If you really want to understand these kinds of things in depth, perhaps the best book you can get is Volume 1 of Donald Knuth's series The Art of Computer Programming. It's really the *bible* of these sorts of things. See http://en.wikipedia.org/wiki/The_Art_of_Computer_Programming -- Deron Meranda
