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The numbers game, as applied to IT

Sunday 14th February 2010

Be prepared - there are some very large numbers coming along in the not-too-distant future

Manufacturers' marketing departments always like to parade numbers in front of would-be customers.  It may be a boast that their new laptop is "only" 20mm thick or that its battery lasts for 6 hours.  Sometimes, they will claim to have the largest/smallest/fastest/slowest/etc "whatsit" and wheel on a few numbers to justify the claim.  For really large numbers, however, 64-bit operating systems take some beating.

The universally-popular search engine Google derives its name from a rather bad pun on "Googolhedron", a 3-dimensional mathematical shape (or polyhedron) with 10^100 facets.  Were it possible to make such an object, it would look like a sphere with an apparently smooth surface, because each facet would be so small.

Although the googolhedron is the clear winner in the numbers game, a 64-bit operating system can at least finish a distant second.  The maximum amount of memory any operating system can address directly is govderned by the number of bits of data it can manipulate concurrently.  In the case of MS-DOS, this was 2^16, or about 640KB.  Developers, of course, used various tricks to overcome this limit, with varying degrees of success.  When 32-bit operating systems came along, the limit became 2^32, or about 4GB, roughly 4 x 10^9 bits.  This is for many current situations, but with the rise in popularity of virtualisation, as well as the ever-increasing demands of new applications, it is gradually becoming as restrictive as the old 640KB limit was in its day.

Fortunately, 64-bit computing has come to the rescue.  A full-64-bit operating system, running on 64-bit hardware, can address about 16 Exabits or 16 x 10^18 bits of memory.  At present, it seems inconceivable that any computer could possibly use such a vast amount of memory, or even that it could be manufactured in a realistic timescale.  However, it is pertinent to remember Bill Gates' famous assertion during the 1980's that "640K should be enough for anyone".