From: George W Gerrity (g.gerrity@gwg-associates.com.au)
Date: Fri Jun 22 2007 - 21:28:47 CDT
On 2007-06-23, at 02:04, Marnen Laibow-Koser wrote:
> On Jun 22, 2007, at 11:07 AM, George W Gerrity wrote:
> [...]
>>
>> As a retired Computer Scientist who has published on Computer
>> Arithmetic and Computer Design and someone well versed in Number
>> Theory, I can assure you that there is absolutely no future for
>> (human-readable) representations in bases larger than 16, even
>> assuming that future internal representations do not use numbers
>> based on a power of 2 (the smallest computationally-useful Prime
>> Number), but some power of another small Prime Number, such as 3,
>> 5, 7, 11, or even 13.
> [...]
>
> I agree with you that this thread is a bit strange, but I must take
> issue with your statement here. I don't know why you seem to think
> that there's some sort of magic limit at 16, and in fact I have
> seen practical applications of number bases greater than 16.
You miss the point entirely. There is no “magic” about any base
system, including mixed bases such as you mentioned below: indeed, an
number of computational units in modern computers use base 4,
replacing complexity with speed advantage.
The point is that there is ... absolutely no future for (human-
readable) representations in bases larger than 16 ... We are not
interested in how they are represented internally (usually binary,
even when the maths engine uses base 4 or even mixed bases), but how
to represent such numbers for transfer between humans audibly, or
visually on some physical material. Most computer people do finally
get used to manipulating base 16 in their heads (for instance, to
turn it into a decimal number that is meaningful to humans, or to do
some simple addition or subtraction), but base 64? Base 26? How
absurd! of course, a base 64 representation is more compact than
representing the internal computer representation (binary, unless an
entire new technology base takes over), than, say base 16, but who
cares? Who wants to invent (and then have to remember) 64 new
symbols? The times we actually have to write out or say over the
phone a big number are so rare that it simply is absurd to invent an
entire new vocabulary.
> The one that springs most immediately to mind is a hack for use in
> situations of limited memory, which I have seen recommended in at
> least one programming text. The hack takes advantage of the fact
> that 36^3 < 2^16 in order to represent 3-character strings in [0-9A-
> Z] as 16-bit integers in base 36, thus using two bytes per
> pseudostring rather than four (assuming a length byte or terminator).
It's a compression technique, just as the more rudimentary one that
pushes four 6-bit character strings into three 8-bit internal storage
units. The “magic” is done internally at assembler level (or ‘C’, if
a compiler was available), and the humanly-visible code was always (a
subset) of ASCII.
> Also, while this may not be current today, I remember seeing
> base-32 notation (with digits up to V) in active use on the Amiga,
> and I wouldn't be completely surprised if it were resurrected at
> some point. And of course there's base64 encoding, though that's
> certainly not meant to be human-readable...
Exactly!
> Also, it's extremely common in developing for 32-bit architectures
> (particularly Mac OS) to refer to certain 32-bit constants as
> pseudostrings of 4 8-bit ASCII characters, which is effectively
> writing them in base 255. That mmay be a borderline case, however.
Really borderline for the simple reason that the 32-bit word has four
characters, each represented internally as an 8-bit string, packed
into the word. At very low levels, we have to know the order of
packing (big-endian or little-endian), but that concerns the system
programmer, and has nothing to do with human-readable representations.
> I think we are really drifting off the list topic here.
We have been drifting off topic for some time (in the sense of going
from the sublime to the ridiculous), hence my original letter.
George
------
Dr George W Gerrity Ph: +61 2 6386 3431
GWG Associates Fax: +61 2 6386 4431
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