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

[Manul]

This might upset some purists, but for me the intuitive way of thinking what is digital and what is not digital is simply determinism. Digital system is such a system which maintains the deterministic result while subjected to inherent or external noise (within it's design limits). So in essense, given same input, it has a property of converging into indentical result.

But there do exist digital circuits ("pure" digital, built inside FPGAs) implementing non-deterministic true-random number generators. In some way they exploit "noise in time" to reach this goal.

You are correct, it can be done. That is an interesting category where a digital circuit is intentionally pushed into analog domain. Instead of being insensitive to noise and having converging properties, it is made in such a way that noise is amplified and circuit diverges into uncertain state, a random bit. These random bits usually are not very random, they might correlate strongly with power supply ripple for example. But if these random bits have at least some true randomness in them, then multiple bits can be combined to produce random bits of higher quality. It's like "breeding" where "gene of randomness" is getting stronger every next generation until you get almost fully undeterministic pure random bits, aka true-random. I think bits are usually combined by XORing them. Some extra post processing might be present too. So yeah, the core circuit producing random bits can be seen as analog circuit combined with 1bit ADC and down the stream it's then all digital.

[tggzzz]

This might upset some purists, but for me the intuitive way of thinking what is digital and what is not digital is simply determinism. Digital system is such a system which maintains the deterministic result while subjected to inherent or external noise (within it's design limits). So in essense, given same input, it has a property of converging into indentical result.

But there do exist digital circuits ("pure" digital, built inside FPGAs) implementing non-deterministic true-random number generators. In some way they exploit "noise in time" to reach this goal.

You are correct, it can be done. That is an interesting category where a digital circuit is intentionally pushed into analog domain. Instead of being insensitive to noise and having converging properties, it is made in such a way that noise is amplified and circuit diverges into uncertain state, a random bit. These random bits usually are not very random, they might correlate strongly with power supply ripple for example. But if these random bits have at least some true randomness in them, then multiple bits can be combined to produce random bits of higher quality. It's like "breeding" where "gene of randomness" is getting stronger every next generation until you get almost fully undeterministic pure random bits, aka true-random. I think bits are usually combined by XORing them. Some extra post processing might be present too. So yeah, the core circuit producing random bits can be seen as analog circuit combined with 1bit ADC and down the stream it's then all digital.

Do not conflate "unpredictable" "or "statistical" with "analogue".

Consider a radioactive atom decaying. The decay is a digital event (discrete time, discrete state), and the time at which it occurs is unpredictable. That does not mean it is "pushed into the analogue domain". Similar points can be made about a single photon arriving at a photodetector.

Do not conflate "emergent behaviour" with "analogue".

Consider a digital computer. It will exhibit apparently "random" and "irreversible" behaviour simply because it contains so many states that the output cannot be fully predicted unless you have a "magic" oracle. That does not somehow mean the digital computer has become an "analogue" computer.

[radiolistener]

Consider a radioactive atom decaying. The decay is a digital event

 

[tooki]

This might upset some purists, but for me the intuitive way of thinking what is digital and what is not digital is simply determinism. Digital system is such a system which maintains the deterministic result while subjected to inherent or external noise (within it's design limits). So in essense, given same input, it has a property of converging into indentical result.

But there do exist digital circuits ("pure" digital, built inside FPGAs) implementing non-deterministic true-random number generators. In some way they exploit "noise in time" to reach this goal.

You are correct, it can be done. That is an interesting category where a digital circuit is intentionally pushed into analog domain. Instead of being insensitive to noise and having converging properties, it is made in such a way that noise is amplified and circuit diverges into uncertain state, a random bit. These random bits usually are not very random, they might correlate strongly with power supply ripple for example. But if these random bits have at least some true randomness in them, then multiple bits can be combined to produce random bits of higher quality. It's like "breeding" where "gene of randomness" is getting stronger every next generation until you get almost fully undeterministic pure random bits, aka true-random. I think bits are usually combined by XORing them. Some extra post processing might be present too. So yeah, the core circuit producing random bits can be seen as analog circuit combined with 1bit ADC and down the stream it's then all digital.

Do not conflate "unpredictable" "or "statistical" with "analogue".

Consider a radioactive atom decaying. The decay is a digital event (discrete time, discrete state), and the time at which it occurs is unpredictable. That does not mean it is "pushed into the analogue domain". Similar points can be made about a single photon arriving at a photodetector.

Do not conflate "emergent behaviour" with "analogue".

Consider a digital computer. It will exhibit apparently "random" and "irreversible" behaviour simply because it contains so many states that the output cannot be fully predicted unless you have a "magic" oracle. That does not somehow mean the digital computer has become an "analogue" computer.

OK now that really is a stretch. Yes, it’s discrete, but it’s not information or logic, so it’s irrelevant to the discussion.

[TimFox]

For binary digital systems, there can be errors due to the thermal noise in the system at finite temperature, which becomes important at high speeds and small voltage levels.
For a non-handwaving discussion of this phenomenon, see  https://core.ac.uk/download/pdf/56632959.pdf
Basically, for a binary system sitting at a voltage level consistent with either state 0 or state 1, thermal noise could give an unwanted excursion to the other level, depending on how much time that excursion must last to give an error.

[tggzzz]

This might upset some purists, but for me the intuitive way of thinking what is digital and what is not digital is simply determinism. Digital system is such a system which maintains the deterministic result while subjected to inherent or external noise (within it's design limits). So in essense, given same input, it has a property of converging into indentical result.

But there do exist digital circuits ("pure" digital, built inside FPGAs) implementing non-deterministic true-random number generators. In some way they exploit "noise in time" to reach this goal.

You are correct, it can be done. That is an interesting category where a digital circuit is intentionally pushed into analog domain. Instead of being insensitive to noise and having converging properties, it is made in such a way that noise is amplified and circuit diverges into uncertain state, a random bit. These random bits usually are not very random, they might correlate strongly with power supply ripple for example. But if these random bits have at least some true randomness in them, then multiple bits can be combined to produce random bits of higher quality. It's like "breeding" where "gene of randomness" is getting stronger every next generation until you get almost fully undeterministic pure random bits, aka true-random. I think bits are usually combined by XORing them. Some extra post processing might be present too. So yeah, the core circuit producing random bits can be seen as analog circuit combined with 1bit ADC and down the stream it's then all digital.

Do not conflate "unpredictable" "or "statistical" with "analogue".

Consider a radioactive atom decaying. The decay is a digital event (discrete time, discrete state), and the time at which it occurs is unpredictable. That does not mean it is "pushed into the analogue domain". Similar points can be made about a single photon arriving at a photodetector.

Do not conflate "emergent behaviour" with "analogue".

Consider a digital computer. It will exhibit apparently "random" and "irreversible" behaviour simply because it contains so many states that the output cannot be fully predicted unless you have a "magic" oracle. That does not somehow mean the digital computer has become an "analogue" computer.

OK now that really is a stretch. Yes, it’s discrete, but it’s not information or logic, so it’s irrelevant to the discussion.

The radioactive decay is indeed a stretch in this thread.

A single photon arriving at a detector is digital and does carry information. Example: photon counting OTDRs, which I first looked at >40 years ago when they were a laboratory curiosity. I would have tried to build one myself, but Peltier devices couldn't practically reach the necessary temperatures in field equipment.

The emergent behaviour of a computer is obviously relevant in the context of the point made by Manul.

[Zero999]

Well one could argue that all electronics are digital, since current is quantised as electron flow. . .

Radioactive decay isn't really digital and neither is current flow, because the photons can be emitted at any point in time, which is in not discrete steps i.e. digital.

Is PWM generated by an analogue circuit, such as a 555 timer digital? No, it's not, even though the output can either be high or low, the duty cycle is infinitely variable.

[tggzzz]

Well one could argue that all electronics are digital, since current is quantised as electron flow. . .

For femtoamp circuits that is accurate. For higher currents, it becomes continuous with a statistical component. Much like individual air molecules and air masses.

One of the reasons that transistors can't shrink too much more is that the number of electrons and dopant atoms would become too few.

Radioactive decay isn't really digital and neither is current flow, because the photons can be emitted at any point in time, which is in not discrete steps i.e. digital.

Discrete time is not a required characteristic of digital circuits: consider asynchronous logic. Large circuits are clocked because it is impractical to analyse and design the explosion of transient states in an asynchronous circuit.

The sole required characteristic is that the relevant variable (voltage, current, phase, frequency, etc) has a finite set of discrete values. Practically there fill be forbidden gaps between the discrete states, but that is not strictly necessary.

Is PWM generated by an analogue circuit, such as a 555 timer digital? No, it's not, even though the output can either be high or low, the duty cycle is infinitely variable.

The key point is how the analogue values are interpreted. Consider ASK, FSK and pulse density encoding. Summary: yes, repeat no.

Besides, 555s contain a flip flop that drives the outputs.

[TimFox]

Normal-size current through a metal conductor is a slight tendency of a multitude of electrons to move in one direction: shot noise is not important.
Electron flow through a vacuum diode (or Zener diode) is one at a time hitting the anode, so "shot noise" statistical fluctuations are important.

[Zero999]

Well one could argue that all electronics are digital, since current is quantised as electron flow. . .

For femtoamp circuits that is accurate. For higher currents, it becomes continuous with a statistical component. Much like individual air molecules and air masses.

One of the reasons that transistors can't shrink too much more is that the number of electrons and dopant atoms would become too few.

The current is only one variable. Time is another. Measuring a small current, over a small timescale might seemingly result in a digital output, but it's not really digital, but based on probability. The same is true of air molecules.

Radioactive decay isn't really digital and neither is current flow, because the photons can be emitted at any point in time, which is in not discrete steps i.e. digital.

Discrete time is not a required characteristic of digital circuits: consider asynchronous logic. Large circuits are clocked because it is impractical to analyse and design the explosion of transient states in an asynchronous circuit.

The sole required characteristic is that the relevant variable (voltage, current, phase, frequency, etc) has a finite set of discrete values. Practically there fill be forbidden gaps between the discrete states, but that is not strictly necessary.

Ah yes, that's true of course, it doesn't need a clock.

Is PWM generated by an analogue circuit, such as a 555 timer digital? No, it's not, even though the output can either be high or low, the duty cycle is infinitely variable.

The key point is how the analogue values are interpreted. Consider ASK, FSK and pulse density encoding. Summary: yes, repeat no.

Besides, 555s contain a flip flop that drives the outputs.

The 555 has two comparators and uses an analogue circuit for the timing, so is very much analogue, even though the output is either high or low.

[tggzzz]

Is PWM generated by an analogue circuit, such as a 555 timer digital? No, it's not, even though the output can either be high or low, the duty cycle is infinitely variable.

The key point is how the analogue values are interpreted. Consider ASK, FSK and pulse density encoding. Summary: yes, repeat no.

Besides, 555s contain a flip flop that drives the outputs.

The 555 has two comparators and uses an analogue circuit for the timing, so is very much analogue, even though the output is either high or low.

By one definition a 555 is analogue.

By another definition it is mixed signal: analogue inputs and digital outputs.

By another it is digital - in the same way that a 7414 is digital: an analogue input is interpreted by a Schmitt trigger or comparator, and defined to be either high or low. If you want to think in terms of a 7404, then that too has analogue inputs, and the decision is based on whether the analogue inputs are saturated. (Or ECL where there is no saturation, but it is based on whether one input(s) is higher than the other(s) ).

Philosophy is fun, and it does (or ought to) lead to a deeper understanding of the significant differences and similarities.

[radiolistener]

A signal is considered analog if its interpreted values are continuous (can take any value): an analog signal is valid for any value, regardless of precision, within its extrema. If the interpreted signal cannot take any arbitrary value of any precision, then it’s not analog, and is by definition digital!

Sorry, but your "by definition digital" signal is incompatible with digital electronics, because digital electronics uses classic digital signals which is binary only and is incompatible with your "by definition digital".

So, your unique invention to use any analog signal which has some N discrete levels, where N>2, as digital is broken by definition...
This is not what digital electronics expect for digital signal, it expects binary signals only.

You can invent new reasons and come up with examples, but the fact remains a fact that pure digital electronics expects binary signals only.
So, all your inventions and reasons to name analog signal with discrete levels as digital will be broken by design.

You can cry, laugh, be angry, but you can't change this... 

[TimFox]

In logic, a proposition is equivalent to its contrapositive, but not its converse.
"If a system is binary, then it is digital" is equivalent to "If a system is not digital, then it is not binary."
It is not equivalent to its converse:  "If a system is digital, then it is binary."
We are speaking here of definitions in technical English.
Binary logic is the most common way to do things now with digital systems, but that does not imply that other digital non-binary systems do not exist.
This is getting tiresome.

[edit:  corrected typo on second line for contrapositive statement]

[radiolistener]

Binary logic is the most common way to do things now with digital systems, but that does not imply that other digital non-binary systems do not exist.

Well, you can believe in a mythical digital system which uses non binary signals, but in reality such digital system doesn't exists.

And you're needs to accept the fact that all non binary but discrete signals are treated as analog signals and converted through ADC/DAC in order to process it in digital circuit... That is how it doing in reality 

[madires]

So the tri-state ICs I have don't exist?

[TimFox]

Binary logic is the most common way to do things now with digital systems, but that does not imply that other digital non-binary systems do not exist.

Well, you can believe in a mythical digital system which uses non binary signals, but in reality such digital system doesn't exists.

And you're needs to accept the fact that all non binary but discrete signals are treated as analog signals and converted through ADC/DAC in order to process it in digital circuit... That is how it doing in reality 

As I write this, my left wrist has a standard quartz-type wristwatch, powered from an electrochemical cell.
It contains a 32,768 Hz crystal oscillator, a binary count-down chain to produce a 1 Hz pulse train, and a digital electromechanical system with a stepper motor driving a gear chain.
The result of the gear chain is a system without any binary content whatsoever, displayed using the ancient Mesopotamian sexagesimal system (with pars minuta prima and pars minuta secunda on separate mechanical dials).
The discrete behavior is clearly visible:  typical of a quartz watch, the second hand jumps in 1 second increments;  my mechanical watch shows 1/4 second jumps.
Please take off your blinders:  binary is an important subset of digital, and there is no need for two such words if they were synonymous.
You have ignored not only standard textbook definitions presented here, but practical examples of hardware that are digital but not binary, preaching the heresy that only binary counts.

[IanB]

In logic, a proposition is equivalent to its contrapositive, but not its converse.
"If a system is binary, then it is digital" is equivalent to "If a system is not binary, then it is not digital."
It is not equivalent to its converse:  "If a system is digital, then it is binary."

You have a mistake in your wording here. The correct statement would be this:

"If a system is binary, then it is digital" is equivalent to "If a system is not digital, then it is not binary."

[TimFox]

Oops--I have corrected that typo on my reply above, entered before coffee.

[radiolistener]

So the tri-state ICs I have don't exist?

tri-state signal is binary signal, so this is classic digital.
Third state is not signal value, it just means missing signal (disabled output). It is useful to combine several devices on the same digital bus, so you can select which device put it's output on the bus. But the signal still has two discrete levels 0 and 1.

[TimFox]

Yes, tri-state is a hardware feature used in binary systems.
However, "ternary" is a non-binary digital system using three distinct states.
An early thesis (1967) describing ternary digital systems:  Google "Hu Sung ternary thesis"
(The redactions are signatures on the submitted thesis form.)
The author makes use of PNP and NPN BJTs in some of his circuits, using a ternary system with -V, 0, and +V on each line.
[edit:  sorry, I can't make a citeable link for the Hu Sung thesis.]

From the introduction to the thesis:

"The ternary digital system is one possible form of digital system. Although binary switching theory has
been used in almost every digital system developed so far, this is mainly due to the fact that basic switching
elements in common use are two-state devices and that design techniques for the binary system are
well-developed. However, it is useful to broaden the study of two-leveled logical systems to that of three-leveled
systems."

[madires]

So the tri-state ICs I have don't exist?

tri-state signal is binary signal, so this is classic digital.
Third state is not signal value, it just means missing signal (disabled output). It is useful to combine several devices on the same digital bus, so you can select which device put it's output on the bus. But the signal still has two discrete levels 0 and 1.

Some of those ICs have a tri-state input and all three states are equally important.

[radiolistener]

Some of those ICs have a tri-state input and all three states are equally important.

but input has just two discrete level 0 and 1. Third state just disables output to allow other components to use the same singal. Pull up or pull down modes are used to setup default value when signal is missing. But signal is still binary and can be 0 or 1.

[madires]

Again, the inputs are tri-state, not binary. There's no 'enable/disable output' pin. And the third state (HiZ) doesn't disable any output.

[tooki]

A signal is considered analog if its interpreted values are continuous (can take any value): an analog signal is valid for any value, regardless of precision, within its extrema. If the interpreted signal cannot take any arbitrary value of any precision, then it’s not analog, and is by definition digital!

Sorry, but your "by definition digital" signal is incompatible with digital electronics, because digital electronics uses classic digital signals which is binary only and is incompatible with your "by definition digital".

So, your unique invention to use any analog signal which has some N discrete levels, where N>2, as digital is broken by definition...
This is not what digital electronics expect for digital signal, it expects binary signals only.

You can invent new reasons and come up with examples, but the fact remains a fact that pure digital electronics expects binary signals only.
So, all your inventions and reasons to name analog signal with discrete levels as digital will be broken by design.

You can cry, laugh, be angry, but you can't change this... 

It’s only incompatible with YOUR excessively rigid definition. It’s not incompatible with the actual definition.

We’ve given you numerous examples of non-binary digital signals, systems, and real-world products that employ them.

You’re just either too stubborn or too stupid to recognize why digital ≠ binary.

[AndyBeez]

To me Tri-state either means true, false and don't care, or, there are two stable states of something plus a transitioning metastable state inbetween. Think heads, tails and the edge of the coin. The high Z state on buses is really just a parking brake applied to a GPIO line to keep the noise floor from making up its own states.

However, when you enter the world of quantum qubits, all tri states become a stable state

* Although qubits might just be worked as zeros and ones