From: David Braginsky (daveey@ucla.edu)
Date: Sat May 12 2001 - 13:36:39 MDT
> 1) What can analog do that digital can't.
> Analog can store infinitely complex values in a single unit. The value e
> could be stored in full precision (from what I've read) in a quantum
> computer. Digital systems are always limited by their resources (# of
> flops, how many bits of storage does it have, etc...). Sure, a digital
> computer can get very close to e, but it can never touch the
> value
i think you are missing the major reason why digital is being used as
opposed to analogue. you are right, with a digital system our storage (and
computation) is limited by the number of bits we have to store. so arbitrary
precision requires arbitrary number of "components" (bits of ram for
example). also true, that a single analogue component (say a capacitor, i
know it's not a good analogue component, but it can store a signal in the
electric field) can store an arbitrary precision number(it would have to be
scaled by some value, so we would need two per number). the problem is
twofold. first when you read you 'e' back from the storage, you must have a
very accurate voltmeter. so the precision of the computer now depends
completely on your ability to accurately measure voltage to a very large
number of significant digits. so if you cared about 100 digits of e, you
would need a voltmeter with 100 digit precision. which is a lot harder to
find than 100 flip-flops to represent e in a digital computer. the second
major factor is (always) noise. in a digital computer, an analogue signal
can take on only two values, so it can be distinguished from noise very
easily. if you use analogue components, somewhere along the line, the
precision of the signal you are storing/computing will be drowned out by the
noise of the system. so again, you cannot store a number more precise than
the noise.
both of these problems have a very easy solution. use more "components". if
you need to store 100 digits of e, but your voltmeter is only good at
reading 4, store the number in 25 "components". and if your signal to noise
ratio is to high for you to read those digits, use 50, or 100. as you can
see, its very easy to transform an analogue system into a digital one. in
fact, because you are so limited by noise and instrument precision, you will
have to do it anyway.
so in reality, digital and analogue are equivalent, one requires more bits,
the other, more precise instruments. bits are cheaper, easier to
manufacture, and scale.
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