In article , Jim H
wrote:
Jim Lesurf in uk.rec.audio:


Btw, I mention this because I'm writing a kind of specy/bytecode
converter. The digital/analogue thing gets really interesting when I
copy the sound of speccy tapes to CD, so that they can be more easily
played on my old ZX. One way of thinking of this is as digital in
analogue in digital!

That is a superb example. :-) I'll probably now quote it in my
lectures!

I'm honored, but won't your class be too young to remember computer
programs on audio tape?

Probably. That is one of the reasons it is a nice example as I can explain
that as well to help break down their pre-assumptions. :-)


Yes. You can apply all the same formal Information Theory ideas to
'analogue', but 'digital' systems tend to make these things easier to
explain, quantify, etc. However need to take care here as we've tended
to develop our units, etc, with binary digital in mind. e.g. we now
use 'bit' for quantity of info, but this was not always the case in
early work IIRC.

Interesting, what was considered the lowest possible unit of
information?

My memory is unreliable on this as I only came across references to it many
years ago. Note they weren't regarded as the 'lowest unit' any more than a
metre is the 'lowest unit' in the sense of being indivisible. IIRC one unit
was based upon 'e'. I think these units appear in, for example, some of the
books on the work at Bletchly Park during WW2. Afraid I'd need to find the
books and search through them to see what I could find about this, although
I suppose it may also be "out there" on the web as most things are, these
days!

I sometimes think of 'half bits' as a theoretical thing but know that
half a bit cannot really be transmitted.

Depends upon what you mean. Symbols (and hence symbol patterns) can quite
easily communicate non-integer amounts of information as measured in
'bits'. Indeed, if you do an entropic analysis of English, most letters in
a meassage contribute a non-integer amount of info.

Its interesting that people do tend to think that the 'bit' is somehow a
different kind of unit to a 'metre' or a 'kilo' or a 'degree'. However it
is just a defined amount used as a reference for measurement purposes. Just
happens to have become so much the standard that no-one even thinks of
using an alternative.


I have wondered about building 'digital' CPUs which included a thermal
noise generator to randomise the lowest bit ot two for floating point
computations. This might have an interesting effect upon the
computation of results via very involved methods from large data sets.
"Run until you get the same answer three times in a row!" ;-)

I *think* you could do this without special hardware. I'm not a c++
programmer, but couldn't you override the multiplication operator for
floating point numbers to be off by a pseudo-random value?

Yes, you can do this in software. However you'd still need a source of
'truly random' number sequences [1], and I suspect it would be quicker to
build this into hardware. Just one of my madder thoughts, though... 8-]

I suspect I'll be retired before 'quantum computing' really makes an
impact. This will be useful as I may need the spare time to really
understand it.

Ambitious!


Well, I'm hoping to live long enough... although this may take a while.
;-)

Slainte,

Jim

[1] Can of worms. :-)

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