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From: mwm@cuuxb.UUCP (Marc W. Mengel)
Newsgroups: sci.electronics
Subject: Re: Analog/Digital
Message-ID: <894@cuuxb.UUCP>
Date: Sun, 2-Nov-86 20:24:17 EST
Article-I.D.: cuuxb.894
Posted: Sun Nov  2 20:24:17 1986
Date-Received: Tue, 4-Nov-86 07:51:30 EST
References: <1111@dicome.UUCP>
Reply-To: mwm@cuuxb.UUCP (Marc W. Mengel)
Organization: AT&T-IS, Software Support, Lisle IL
Lines: 63
Summary: Yes, but what about precision?

* sacrifice to the Great Line Eater God *

In article <1111@dicome.UUCP> plate@dicome.UUCP (Douglas B. Plate) writes:
...
>The goal of DIGITAL then would be to
>represent things 100% accurately.  
...
>I would
>risk to say that the smallest element of ANALOG have not been 
>measured yet if they do ideed exist.
>The thing is, Analog has the "natural" advantage.  The universe is
>made of it and what is only theory to DIGITAL is reality to
>ANALOG.  The intrinsic goal of DIGITAL is to become like
>ANALOG.  Why?  Because DIGITAL "represents" and until it
>becomes like ANALOG in it's finity/infinity, all of it's
>representions can only be approximation.
>DIGITAL will forever be striving to attain what ANALOG 
>was "born with".  In theory, DIGITAL is just as continuously
>inifinite as ANALOG, because an infinite number of bits could
>be used to represent an infinite number of things with 100%
>accurancy.  In practice, ANALOG already has this "infinity"
>factor built into it and DIGITAL, like a dog chasing it's own
>tail, will be trying to catch up on into infinity.

Anything measurable can only so be by a process known as "measurement".

Measurements have a given (that is, finite) precision.

=> Any measured quanity has a finite precision.  

Digital systems can represent exactly, and compute exactly, to a
given, finite, precision.

Analog computations cannot be more accurate than the measurements
used to generate the values used for computation, and therefore
cannont be any more precise than a digitally computed result carrying
the precision of the original measurements.

So, in practice, both analog and digital are limited by the precision
of the measurements used to get the quantities with which computation
is being performed.

For example, I can write a program that will spew out (correct) values
for pi as arbitrarily precise as I want on a digital computer, yet
an analog system such as a compass and ruler is only as precise as
my ruler.  I can theoretically build an arbitrarily precise ruler,
but in practice this is not true. (Not to mention the fact that I
cannot build a perfect compass, if it's radius varies at all during
the inscription of the circle, I lose accuracy as well).

Analog's true advantage is that for special purpose applications, such as
simple device control, an analog circuit to perform a job is often much
simpler than a corresponding digital device.  A classic example is the
volume knob, which can be built with a simple potentiometer, or with
an analog/digital converter, a numeric volume input of some sort, a
division circuit, and a digital/analog converter... A potentiometer is
considerably simpler than a division circuit.
-- 
 Marc Mengel			"All that is gold does not glitter
 ...!ihnp4!cuuxb!mwm		 Not all who wander are lost
				 The old that is strong does not whither
				 Deep roots are not touched by the frost"
				  -- J.R.R Tolkein