What is a digital system? Is it only binary or decimal, octal as well?

[TimFox]

As integrated circuit technology advances, voltage differences between binary states get smaller and the bandwidth gets larger.
An article I cited many replies ago goes into practical considerations about when thermal noise will cause excessive error rates in binary hardware, swinging the voltage level outside of the noise margin for enough time to register.

[radiolistener]

I did think about a vinyl record which is effectively a linear sound wave. However, even the vinyl record passes the agnostic test in the sense the mastering, whether in analog or digital, cares nothing about the sound reproduction process. The difference is, a digital system can copy without generational loss from the information store. Ad infinitum. Analog systems inherently inject noise into the duplication process. I remember that very well from the early days of editing VHS video tapes. To duplicate vinyl requires a pressing master which, degrades over usage.

So maybe our definition of what IS a digital system needs to state that generation noise is zero. Or the S/N ratio is infinite?

I would not refer it to a property of digital system.  It don't inject new noise, just because it works with math information about wave instead of wave itself. But noise is still injected when you reconstruct wave on digital to analog converter or when you capture wave with analog to digital converter

[Electro Fan]

Totally agreed. A digital system should also be method and time agnostic.

I don't think this is a differentiator for a digital system though. Analog systems can have the same property. For example, a vinyl record. The information it contains can be retrieved by a mechanical stylus, or optically, or by other methods. It is also durable, and probably able to last for millennia if stored carefully.

I did think about a vinyl record which is effectively a linear sound wave. However, even the vinyl record passes the agnostic test in the sense the mastering, whether in analog or digital, cares nothing about the sound reproduction process. The difference is, a digital system can copy without generational loss from the information store. Ad infinitum. Analog systems inherently inject noise into the duplication process. I remember that very well from the early days of editing VHS video tapes. To duplicate vinyl requires a pressing master which, degrades over usage.

So maybe our definition of what IS a digital system needs to state that generation noise is zero. Or the S/N ratio is infinite?

a copy of a copy

[RJSV]

   O.K. now, you can fault me for having obsessions, lots of them.  But observing:
   Started searching through these pages;....OP only here ONCE, starts this thread.  Obsessed would have checked the whole thread, but I gave up at page 7, now assuming OP is maybe, gone now.
Seeing some bikering,...(have fun, folks).
   One argument to be made, is an arithmetic process, say multiplication, where you can just use a PROM, somehow addressed by your two operands.  Then, you simply place each answer, when you make (burn) the PROM tables for multiplying.  That particular ALU type fragment does not need binary - Boolean to do a calculation, as it's all a look-up table.  Now, whether or not the PROM being used is binary based, with internal binary and Boolean functionality, is subject to further argument....(Gosh, I'm my own worst critique, sadly).
But if you can set up some functional approach, say, with UNITARY numbers, then no binary (needed).  I've done that;  the system signals turn out to be 'base 1' or 'un-coded'.
   With a mechanical, chemical, system type you CAN deal with simple, un-coded signals, in the classic sense, where the 'encoding' is maintained by physical channel or line position, and the time encoding is done by the presence of 'signal'.  That is to say; no explicit separate CLOCK signal.  Works with a falling 'pinball' or other moving mechanical signal.
No Boolean operations, you can address and read your PROM storage device, and get the ALU style multiplication result, again in the non-binary 'base 1' format.

Now....Let's argue, about my name/handle....(lol).

[tooki]

BUT, if they had been genuinely digital (E.g. CDs).  They would each (assuming no destructive data errors), after any error correction things used in that digital format.  Be identical (digitally speaking).

each copy of CD disk has it's own errors and it consists a lot of errors, but since records on CD also consists redundant information for recovery purposes, it is recovered on MCU in CD player.

Recovered/corrected: yes. In an MCU: absolutely not. It’s done in dedicated CD decoder chips. They deliver a finished digital audio stream (typically I2S) either directly to a DAC, or first to a DSP for effects. (And often a separate S/PDIF stream to external digital outputs, either coaxial or TOSLINK optical.)

[RJSV]

   In case you are wondering, the particulars of operating a mechanical or chemical PROM, it goes something like this:
   (I didn't want to interrupt or distract from established thread, here.)

   Let's say you've pieced together a decimal system, but using UNITARY or un-coded signalling:
To access your PROM in a row/column fashion, say you have a BUS SWITCH that will direct your BUS.  You need ten variations, of zero thru 9.  Let's say it's a '7', which will enter and operate (position) your multi-pole BUS SWITCH.  If you can get your signal,...I.E. a seven, to reset all ten BUS switches, except the one for ROW7, and have it (the unitary '7' signal) have it also SET the ROW7 switch, then that half of procedure is done.
   Next, you can send the second operand on down the BUS, from the top (gravity fed system), then that is a full decode, to the desired (Row, Column) memory cell.  Example that might be a 'two', if you've set up to multiply '7 X 2'.
Each of the ten signals does this, including 'zero'.  That symbol 'zero' has equal weight as the others, being a symbol, not a numeric value, or at least not directly explicitly.
As a second example, suppose you are multiplying '5 X 3'.  In that example, the incoming '5' is another custom signal, that turns off the switches (0, 1, 2, 3, 4, 6, 7, 8, and 9).  Meanwhile also sets the Row5 BUS switch.  This way the mechanical signal PROM points to the correct ROW.  It's this customized approach, slightly bulky, that gets you the function you want; BUS selection, as per each individual signal.  This all fits in a single X,Y (row, column) access scheme.

   Each such BUS switch has two pivot positions, so you could argue that...

[tooki]

For example, if wee see on the output of modern 32-bit audio DAC's, the weight of its least significant bit is well bellow thermal noise floor, so you cannot detect it even with using high end measurement equipment. The same, as vinyl record... But someone here classified it as digital, just because it has finite number of discrete levels... 

That “somebody” was you if I’m not sorely mistaken.

As I and others have said: part of a DAC is output filtering, and that completely removes the stair steps and restores the original signal.

I’m not aware of any 32-bit ADCs and DACs. You can sorta get 32 bits by oversampling. My understanding is that 32-bit audio formats basically begin as 24-bit sampled audio, and the extra bits are to maintain fidelity during subsequent audio production. Output occurs through whatever DAC the listener is using, after distribution as 16-bit (usually) or 24-bit (“high res”) compressed or uncompressed audio. .

[radiolistener]

I’m not aware of any 32-bit ADCs and DACs.

I'm talking about 32-bit DAC's like AK4493SEQ or PCM1795 or something like that, which is used in modern high-end audio.

[tggzzz]

So maybe our definition of what IS a digital system needs to state that generation noise is zero.

Better to state the necessary and sufficient condition which enables that: discrete levels with a "forbidden zone" between levels.

[tooki]

I’m not aware of any 32-bit ADCs and DACs.

I'm talking about 32-bit DAC's like AK4493SEQ or PCM1795 or something like that, which is used in modern high-end audio.

Without intending to apply a “no true Scotsman” argument, they certainly do accept 32-bit formats, and looks like nice parts, but at a maximum 125dB and 126dB, respectively, SNR (and dynamic range) their true resolution is just under 21 bits. :/

[TimFox]

So maybe our definition of what IS a digital system needs to state that generation noise is zero.

Better to state the necessary and sufficient condition which enables that: discrete levels with a "forbidden zone" between levels.

The "forbidden zone" is a measure of "noise immunity", which is mandatory for binary and other digital systems to be discrete.
Note that the "systems" are digital or analog, the voltage is whatever it is made to be, but the systems' valid states are discrete.

[radiolistener]

Without intending to apply a “no true Scotsman” argument, they certainly do accept 32-bit formats, and looks like nice parts, but at a maximum 125dB and 126dB, respectively, SNR (and dynamic range) their true resolution is just under 21 bits. :/

They have true resolution 32 bit.

SNR shows dynamic range between max amplitude 0 dBFS and noise floor. Ideal 32 bit DAC has quantization noise floor at -194.4 dBFS. But in reality there are a lot of other noise source, so the real noise floor is always worse than quantization noise of ideal DAC. This is why effective number of bits is always less than DAC resolution. For high resolution DAC's this difference is higher. But all 32 bits of these 32 bit DAC are real and used for conversion.

ENOB < resolution bits is due to presence of unwanted noise sources and leakage. Not because they have less significant bits.

It means that you can use all 32 bits, all of them will work and you will find with tests that they all are significant. But if you want to get full 194.4 dB dynamic range from that 32 bit DAC, you will get noise limitation at 123 dB. This is analog circuit limitations... Most of opamp have about 90-100 dB dynamic range or even worse, so 123 dB is very good result.

[RJSV]

   Hi there, OP !
   Doing some more thinking.  Wanting to consider the meaning, when a 2-state device, like any typical pivot lever or sliding thingy gets involved, where the machine itself isn't considered to be in BINARY realm, (such as previous example running as a decimal device and decimal BUS for data transfers.  I think the fuller description has to be something along the lines of 'Binary Coded' numbers.  Otherwise, any device having an obvious physical set of two stable states of position could force folks to admit, perhaps incorrectly, that some system is binary based.
   But that's somewhat imperfect, when a single bit is (often) processed as, yes, 'BINARY'.  So;...round and round we go.
I'd suggest, maybe a more nuanced approach, to 'tiptoe past' the 2-position things as being (sole) proof.  Otherwise every open/closed door, eyelash, birth twins, and other 'things of two's in a set, would trigger a legitimate 'binary System' label.

   Having said that, the OP's question included OCTAL, and DECIMAL based systems.  In those two types, definitely binary, the OCTAL variation uses 3 bits, in binary code, using all eight states, (0 thru 7).
The BCD types simply use just the first 10 states, usually ignoring the (10 thru 15) binary states available, to create a system that has decimal based behavior, and, on lowest function level, binary based hardware.
Another system type is ASCII, for encoding a character set, using 7 of the available bits, (in a system byte), where I believe there are 96 distinct states used for characters, again ignoring states from 97 through 127.  Those, of course, are useful when encoding various punctuation symbols.
So, that language could refer to a 'base 96' system, incorrect language as the 'base' is still base 2, or binary based.

   Somewhat of a matter of language, but I tend to consider a binary coded decimal system as having BOTH types, in a hierarchy,...not definitely correct.  Similarly, if you had a BCD system using two digits (BUS), then I like to refer to
'Base 100', the most correct phrase is 'Modulo 100', as a programmer would think of the BUS and memory formats.  It's more of being 'virtual base100' in those cases.

Twisted language, but once you've used the 'virtual' term....gets dicey but survivable..