Are there two widely accepted meanings for digital?

Question

Countable number of states (modes) such as on/off etc.
- Suitable for "things which aren't defined as signals"
Discrete in both time and in value
- Suitable for "things which are defined as signals"

Update

This question shouldn't be marked as a duplicate of this question because the other question is not about if there are two extremely common (macro and micro) definitions for digital, or not.

@AlexTP I'm not convinced- perhaps you mean "countable"? The real numbers between +/-5 are finite and continuous so wouldn't consider that digital. — Dan Boschen, Mar 19 '22 at 13:15
@DanBoschen No, I mean really "finite", not "countable". For example, countably infinite sets cannot be processed with digital techniques we (at least I) know. I don't understand what you mean by "the real numbers between $\pm 5$ are finite and continuous". If you are referring to the number of real numbers between $\pm 5$, it is infinite. — AlexTP, Mar 19 '22 at 13:21
@AlexTP ok I see, I am referring to the magnitude as being finite while you are referring to the number of items as being finite. — Dan Boschen, Mar 19 '22 at 13:23
@DanBoschen I see. To be more precise, I am referring to the definition of "digitalness" in the context of information processing: whether we can represent a data set by a finite number of states. — AlexTP, Mar 19 '22 at 13:30
@AlexTP You should add below, sounds like a (good) precise answer. (and better than my answer at the linked post) — Dan Boschen, Mar 19 '22 at 13:35
@MarcusMüller With all respect to O&H (and you!) I would argue (and did in the linked post) that a definition that excluded discrete in time would be a valid description of something that is still digital. My thoughts are influenced by continuous time S/H circuits, whose value we could represent with digital values if we quantized magnitude only. Would/could such a continuous time output still be considered digital as long as we (only) quantized the magnitude? — Dan Boschen, Mar 19 '22 at 14:21
@DanBoschen hey :) this is a super interesting topic and I'm scribbling on a lot of paper here and finding things that contradict things I've assumed for years. I'd argue something that is continuous in time really isn't a digital signal (it might be composed of digital values, if you will). Well, when it comes to definitions, all we can do is appeal to authority – Oppenheim/Schafer say digital signal means discrete in time and value – and it inuitively fits what I'd use "digital" for (and which your answer also implies): We can represent things in a number of samples that have a number of — Marcus Müller, Mar 19 '22 at 14:29
@MarcusMüller yes I'm in the same boat, although I love to question authority ;) — Dan Boschen, Mar 19 '22 at 14:31
digits in some number system. Without the discreteness in time, I don't see how we can describe things in a number of samples! (but now, the thing with AlexTP's stronger requirement for the amplitudes not only being countably many, but even finite, is, that it is sufficient for finite-digit representation of every single sample. It's not necessary – there's infinite discrete distributions with finite entropy!) — Marcus Müller, Mar 19 '22 at 14:31
@MarcusMüller I may have to modify / change my other answer-- in thinking it through this is exactly how I would distinguish the sides of an A/D and D/A converter, consistent with our buddies and authoritarians O&H — Dan Boschen, Mar 19 '22 at 14:34
So, here I'm stuck between Authority (with a capital "A") saying something that I myself find insufficient (because discrete amplitude also allows for infinite discrete distributions where each sample might need infinite digits for representation) and @AlexTP's definition that I find overly restrictive (because many distributions, and in fact, those that we'll find useful, I guess, can be discrete-infinite support, finite entropy), but kind of — practical, I guess? I can look at a system and say "oh, it outputs this set of values at this set of times, that's digital", I can't see the P(X). — Marcus Müller, Mar 19 '22 at 14:34
@MarcusMüller We learn every day. I added your O&H insights and AlexTP's insights to my other answer and like it better now with both considerations. It does seem Alex's is a catch all since both magnitude and time can be a finite set..but here's the catch- we CAN have an infinite time duration and still be (in my opinion) "digital" even though it isn't realizable (in our lifetime) - I will stop chatting here before Peter gets alerted to scold us. — Dan Boschen, Mar 19 '22 at 14:44
@MarcusMüller "there's infinite discrete distributions with finite entropy" it's true. But, what we are interested in is the finite entropy, not the discrete-infinite supports. Like a physical waveform is continuous, but if it is used to transmit binary data of finite states, that is a digital signal. — AlexTP, Mar 19 '22 at 15:24
@AlexTP so, my signal consists of values $\in \mathbb N \sim \text{Pois}(\lambda=1)$. (that's, by the way, not an implausible signal model – might be for example the number of photons hitting a detector in a sample period.) That source has entropy errrr something around 0.3 bit. Is that a digital signal? — Marcus Müller, Mar 19 '22 at 17:48
@MarcusMüller if you can find a source coding technique to represent that source of information in a way that is "acceptable" for you, the generated code is a digital signal (that represents your source of information in the aforementioned acceptable way). If you cannot, there is no digital signal: for example, you can use a countably infinite set $0, 1, ..., \infty$ why not, but what do you do next with that set? IMHO, a source of information and the signal that represents it are different. — AlexTP, Mar 19 '22 at 18:23
I've reopened. Feel free to add an answer... perhaps a wiki one, because of all the different contributors in the comments. Leaving comments alone for now, but will move to chat if they generate a decent consensus answer (it'll be easier to make such an answer with the comments here than in a a chat elsewhere). — Peter K., Mar 20 '22 at 17:47

score 1 · Answer 1 · answered Mar 22 '22 at 11:58

Digital Waveform: Discrete in time (or other dependent variable such as Frequency) and discrete in magnitude.

Digital Data: Information represented by discrete symbols selected from a finite alphabet (such as digits).

Other digital "items" with regards to electronics and signal processing are items that consist of or have to do with digital waveforms or more generally digital data.

score 0 · Answer 2 · answered Mar 19 '22 at 13:24

0

Would it be correct to say that there are two common, distinct, meanings for "digital"?

No.

Digital has multiple meanings but none of them is commonly used as "countable number of states". If you want to know what a specific term means, it's generally a good idea to look it up.

answered Mar 19 '22 at 13:24

Hilmar

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I'd argue that the broad comment discussion in my question post proves that it's not a simple matter of an opener passage in Wikipedia (which I already searched long before the post). If for anything we define "discrete" we define "two or more possible states", I'd assume that it is plausible to say that a digital system is a system with countable or "finite" (digital) number of states. – yaraklis Mar 19 '22 at 20:22
You can define digital for yourself anyway you like, but as long as you are the only one using the word in this way, any communication with other people will be challenging. By your definition a simple mechanical light switch is "digital". If you call this a "digital light switch" you'll end up a with a lot of confusion. Look, language just is this way: Terms get defined more by common use and habit then by logistical consistency. While there are a lot of discussion in the comments, none of them include your specific definition – Hilmar Mar 21 '22 at 11:28

Are there two widely accepted meanings for digital?

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