If a digital system has two or more modes (states), does a continuous system have just one mode (state)?
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Please add detail. Do you mean to end that with "does _the equivalent_ continuous-time system have just one mode?" – TimWescott Oct 18 '21 at 02:48
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@TimWescott I don't understand your clarification question, please consider to rephrase it. – Alkalix Oct 18 '21 at 03:59
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@Alkalix we're missing context here. Basically, what Tim (and I) are asking is "um, this question is very strange; the wording itself doesn't make much sense on its own. Now, you introduce another, analog and hence different system, and ask about that. Is the analog system somehow related to the digital system, or are they simply completely different things?" – Marcus Müller Oct 18 '21 at 07:49
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@MarcusMüller I don't know what is the analog system you mean to, so I just need to try to read your answer; my main aim here is just to under what continuous is --- not in mathematics but in Physics / Electrical Engineering /Signal processing. – Alkalix Oct 18 '21 at 12:23
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@MarcusMüller I think that in "digital signal" I actually meant "discrete signal" ; discrete signal can indeed have two or more modes, nut not just one (for example a water vending machine is a signal that can have at least two states, off or on, right?). If so, what would be an analogue signal? – Alkalix Oct 18 '21 at 13:35
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@Alkalix continuous in engineering is the same as in math: the mathematical definition 100% applies and it's really the simplest one that applies. An analog signal is any signal that is *not* digital. It's as simple as that! – Marcus Müller Oct 18 '21 at 13:48
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@Alkalix: There's some word collision going on here, which you must clarify before we can answer (or you must reword your question if it's the wording that's giving you trouble). In the sense of the word "state" for a continuous-valued system, the state of the "ON" switch can *take* two values -- but the on-state is just one state. Computer scientists and set theorists will want to say "two states" -- but that's a *different meaning of the word "state"* than, say, a battery voltage, which can be any real number in some range. Ditto "mode", but I'm running out of space here. – TimWescott Oct 18 '21 at 15:19
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@TimWescott I understand from Marcus's answer that I had a mistake in the question. I didn't define digital correctly. – Alkalix Oct 19 '21 at 08:51
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Your first statement
a digital system has two or more modes (states)
is a bit confusing or misleading; it misses the point!
The point is that a digital system can only be in one of a countable set of possible states (and that these are acquired in a countable set of times). The state space of an analog system can be uncountable.
Now the problem with your statement is that
two or more
doesn't say much about the countability of states of digital systems. Uncountably many states, as an analog system might have, is always more than countably many.
does a continuous system have just one mode (state)?
um, no, only a constant system (a very boring system) would have one state. Such as system could be both analog or digital. (so, your definition "two or more" is actually wrong...)
In generally, as mentioned above, an analog system can take one of a uncountable infinite set of states, whereas a digital system can only take one of a countable infinite or finite number of states.
That's the usual definition of the difference between digital and analog, together with the time-discreteness of digital systems.
Marcus Müller
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Thanks Marcus. The main thing I understand from your answer is that I had a mistake defining digital ; a digital system can have any (by-definition) countable set of possible states (1 or 2 or more, the main thing is that it has to be countable) and an analogue system doesn't, i.e. (by definition) the set of possible states of an analogue system is non-countable. – Alkalix Oct 19 '21 at 08:54