metric vs. hexadecimal [was: Re: [oclug] KWeather]

[Richard Guy Briggs]

On Sun, Mar 20, 2005 at 09:36:57PM -0500, GR Gaudreau wrote:
> <snip>
> > > [GR]  But why does it make sense to count in hexadecimal?
> >
> > Repeatedly multiplying or dividing by two keeps the same number of
> > significant digits.
> 
> [GR]   And what does that mean in plain English? :-)

Well, multiplying repeatedly by 2 gives the series:

1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 ...

where the number of significant digits goes from 1 to 5 as we increase
to maintain the exact values.  For division, we get

1 0.5 0.25 0.125 0.0625 0.03125 0.015625 0.0078125 0.0039063 0.0019531 ...

where the number of significant digits goes from 1 to 5 as we decrease
to maintain exact values.

2 is the most often used division or multiplication factor for rough
work.

If we work in hexadecimal, ignoring whether or not you understand it at
this point, we get:

0x1 0x2 0x4 0x8 0x10 0x20 0x40 0x80 0x100 0x200 0x400 0x800 0x1000
0x2000 0x4000 0x8000 0x10000 0x20000 ...

where we have one significant digit from start to finish.  Similarly,
for division, we get:

0x1 0x0.8 0x0.4 0x0.2 0x0.1 0x0.08 0x0.04 0x0.02 0x0.01 0x0.008 0x0.004
0x0.002 0x0.001 0x0.0008 ...

where we have one significant digit from start to finish.  (I'm not sure
of the notation for fractional hexadecimal representation...)

The reason for this is that 10 factors out to 2 x 5 whereas 16 factors
out to 2 x 2 x 2 x 2.

If we had hands with 2 fingers and a thumb, we may have ended up
counting in base six (sextal?).  Decimal doesn't make any more sense
than that.  It is all just convention by this point...  (Hexadecimal by
name is actually mixing two ancient languages in one word...  :-/  )

> GR Gaudreau <grgaud at gmail.com>

	slainte mhath, RGB
	GPC Listmaster

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