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

[tggzzz]

Later I consider not to use ternary, but binary using levels 0 and V/2.  I would remove the first ADC, keep the second one and remove the truth table.  According to radiolistener this would now a digtal system because it is purely binary.  Yet radiolistener also contends that digital system does not have ADC but this one does.  The contradiction is evident.

No. You cannot put 3 level signal on two digital input with different level standard, because it will leads to metastability issues. If you want to do what you want, you're needs to use two analog comparators for signal which has 3 discrete levels. Each comparator should be tuned for different analog threshold, then it will works and you can convert your 3-level signal to a digital domain.

1.  You are quoting where I describe a pure binary system.  Nothing 3-level in it.  But then you write nonsense about 3-level on 2 digital input and metastability issues.

2.  Yes you can "put 3 level signal on two digital inputs with different level standard" without issues.

You can.
I can.
All but one person contributing to this thread can.

Some people remain convinced of things that aren't even wrong. The question is why they continue in such beliefs. And then whether it is worth paying any attention to them on that and other subjects.

[TimFox]

Here is a simple digital logic circuit that converts one line of a ternary digital state to two lines of binary digital state, using the conversion table in the figure.

Your circuit uses non digital domain with bipolar voltage source and open voltage threshold of diodes and triggering voltage of relay. These things are not digital, they are analog. So your circuit is mixed signal circuit which uses analog domain and digital domain.

In short, this is simplified ADC which converts analog signal to digital. This is not pure digital circuit.

It will be more easy to understand why this circuit is not pure digital if you add voltage shift +2.5V.
In such way your circuit will works with:
N = +5 V
Z = +2.5 V
P = 0 V
GND = +2.5 V

So, your circuit has digital output from relay. But it has analog circuit which controls relay state.

In order to improve stability of such circuit it will be better to use analog comparators to control relays. So, in such way you will will reduce effect of relay hysteresis and no needs to play with GND offset. But also relays become useless and you can use analog comparators output as digital output directly. And if you overview what happened with circuit, you will notice that it is turned into classic ADC.

The circuit controlling the relays is no more an analog circuit than is a 7404 TTL binary inverter run from a split power supply of +/- 2.5 V.
(In real systems, I have run 4000-series CMOS binary logic from split supplies of +/- 6 V for special purposes.)
The voltage into the 7404 can be varied continuously, but there are only two valid states of the input that give valid states of the output, and the designer must make the transition rapidly to minimize time in the invalid states.
I posted a simple circuit:  obviously, it could be improved.
The ternary levels I quoted are consistent with those suggested in the 1967 thesis for a true ternary system.
Digital systems include those that are not inherently binary, despite your continued baseless claim.

[IanB]

Converting from ternary to binary is of course a digital computation using arithmetic logic. It does not require going through the analog domain. For example:

Suppose we have 1002 in base 3 (a ternary digital value), and we wish to convert it to binary. We can proceed as follows:

Code: [Select]

Ternary logic        Binary digits
1002 - 121 = 111  =>   1
111 - 22 = 12     =>   1
12 - 11 = 1       =>   1
1 - 2 fails       =>   0
1 - 1 = 0         =>   1
As a result, 1002₃ = 11101₂

This is a computation that can be performed by any kind of ternary computing device that supports integer arithmetic.

[TimFox]

That is a good example of a sequential calculation, reminiscent of long division in decimal digital systems.

[tooki]

And it will be crazy to think that he is talking about analog amplifier on sound DAC output which has 16777216 discrete voltage levels...

Not by the time the conversion is done. Then you have a fully analog signal. (Once the bandwidth limit is applied to the output, the steps are gone.)

But of course you’re missing the real point: it’s about how you interpret the signal on the input.

[MK14]

Bold added by me.

Not by the time the conversion is done. Then you have a fully analog signal. (Once the bandwidth limit is applied to the output, the steps are gone.)

But of course you’re missing the real point: it’s about how you interpret the signal on the input.

The following example, is NOT how I think things should be interpreted.  But some other(s), but I won't mention names, **might** think that way.

Example:
A 5 volt (output is precisely 0 volts for logic '0' and precisely 5 volts for logic '1'), all digital logic series, which treats input (threshold) voltages below 2.5 volts as logic '0', and equal to or above 2.5 volts as logic '1'.  Hysteresis, noise thresholds and other practical real life phenomenon, are being disregarded, for this example.

Therefore, it is a 100% analogue device, a non-inverting buffer, is actually a 1 bit, A to D converter.  Which is equivalent (internal circuitry wise) to the inverting input being connected to exactly 2.5 volts, and the non-inverting input, being used as the input.
Much like a comparator, sorry, I mean op-amp, as this is 100% analogue.

In other words.  Yes, a non-binary input/output digital system, **could** be interpreted as being equivalent to an A to D (and DAC, depending on if input or output, etc) converter.  But would still be a 'Digital System', just with more than 2 states, but still a fixed number of defined output (voltage, current, etc) levels.

In the same way a simple wire (or bunch of them, possibly screened or similar), can be used for many different purposes, which would tend to change its name.  E.g. Wire, Cable, Accelerator-Cable, Tie-Wrap, USB lead, Meter Leads, Lighting Cable, Breadboard Leads, Ethernet Patch Cable, etc.

[CatalinaWOW]

I've been thinking about this over the length of the thread, and think that for me the meaning of a digital system is closely tied to reversibility.  Given the outputs can you unambiguously reconstruct the inputs?  Obviously this isn't a formal definition.  You can't reconstruct the input of an or gate from the output, but you do know at least the values that could have been there.  A to D converters illustrate another ambiguity of this definition.  You can certainly reconstruct the inputs from a theoretical D to A, and for a good 8 bit real D to A, but I know of no 32 bit D to A converters that are monotonic and linear enough to allow recovery of the inputs.  In spite of these weaknesses I find this a useful definition.

Edited to correct my bonehead reversal of D to A into A to D, and a spelling error.  Thinking of D to A makes the point I was attempting to make more clear and avoids all the need to discuss thermal noise and the like.  And if someone comes up with a good enough 32 bit converter make it 48 bit.  The points that my definition is not a complete formal definition.  There are counter examples, but it works as an organizing tool for me.  There is no one correct way to sort things.  Others have their preferred bins.

[AndyBeez]

I've been thinking about this over the length of the thread, and think that for me the meaning of a digital system is closely tied to reversibility.  Given the outputs can you unambiguously reconstruct the inputs?  Obviously this isn't a formal definition.  You can't reconstruct the input of an or gate from the output, but you do know at least the values that could have been there.  A to D converters illustrate another ambiguity of this definition.  You can certainly reconstruct the inputs from a theoretical A to D, and for a good 8 bit real A to D, but I know of no 32 bit A to D converters that are mononic and linear enough to allow recovery of the inputs.  In spite of these weaknesses I find this a useful definition.

Totally agreed. A digital system should also be method and time agnostic. That is, a pure digital system will not care how values are derived, stored, transmitted, duplicated or reproduced. Furthermore, it will not care when or even if these events occur. A digital system can comprise of a gate that switches from zero to one in a pico second, yet the bit that is set can stay retained in a data store that is not accessed for another human millennia - in a digital system that has yet to be invented.

[IanB]

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.

[radiolistener]

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 just wonder...  The vinyl record is recorded on material which is discrete and consists of finite number of atoms... The sound waves also quantized with phonons, so it also can be classified as discrete. And according to your classification the number of discrete levels doesn't matter, if it is finite, then it is digital, isn't it? But why did you classify it as analogue? 

[MK14]

I just wonder...  The vinyl record is recorded on material which is discrete and consists of atoms... The sound waves also quantized with phonons, so it also can be classified as discrete. And according to your classification the number of discrete levels doesn't matter, if it is finite, then it is digital, isn't it? But why did you classify it as analogue? 

That does seem to be a valid point!

BUT, there are some counter examples.

Let's say, we had ten identical records.  I.e. They were all pressed (manufactured), from the same master record disc, at the record factory.

In practice, there will be tiny, but significant (minute/tiny) variations, from the master they were pressed from.  When those ten records are, microscopically or using other techniques, compared to each other.

I.e. Noise (variations) between those ten example recordings.

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).

I.e. A digital diff of the ten digital versions of those disks (if they had been recorded digitally, rather than as analogue records), would all agree with each other (assuming no bad data blocks or damage, etc).

[radiolistener]

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.

[MK14]

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 to be able to recover data in case of errors, it is recovered on MCU in CD player.

I agree.  They would (tend to be) different, between the copies of the same CD, if the raw unprocessed (corrected) data, is available.  But, after all error corrections have been implemented (and assuming no actual uncorrectable data errors or damage), the CDs would have the same digital data on them (which could be music).

[TimFox]

Yes, error-correction is vital to audio CDs:  In the compact disc system, cross-interleaved Reed–Solomon code (CIRC) provides error detection and error correction. CIRC adds to every three data bytes one redundant parity byte. [Wikipedia]

Phonons are quantized vibrations of solid lattices, not directly relevant to the encoding surface of the vinyl groove in a phonograph record.
Of course, the surface itself will become discontinuous at the atomic level, which will vary from disc to disc.
The full-scale "wiggle" on an LP is roughly 25 um, and atoms are roughly 10^-4 um in size, so the noise due to atoms is maybe -108 dB from full-scale, well below the electronic noise level.

The only objects that are truly identical are atoms, molecules, elementary particles, and other quantum objects.
Classical physics, when colliding billiard balls, could distinguish them by their color.

[radiolistener]

Phonons are quantized vibrations of solid lattices, not directly relevant to the encoding surface of the vinyl groove in a phonograph record.

But record is made with a needle which is made from solid body and sound waves energy is transferred through needle and is quantized... 

We can walk more deep and remember that mechanical and sound pressure is transferred with electromagnetic interaction between particles (molecules and atoms). And electromagnetic interaction between particles is quantized with discrete energy portions which also known as photons...

So, every thing in our world is discrete. Then there is a question, why you don't classify all things as digital because they all have finite discrete levels?

Of course, the surface itself will become discontinuous at the atomic level, which will vary from disc to disc.
The full-scale "wiggle" on an LP is roughly 25 um, and atoms are roughly 10^-4 um in size, so the noise due to atoms is maybe -108 dB from full-scale, well below the electronic noise level.

Yes, there is noise floor which limits number of pressure levels which can be stable detected, but since number of atoms is finite, there is finite number of configuration for them and finite number of pressure levels which can be recorded on surface. It is very large, but finite

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... 

[TimFox]

A small but macroscopic surface area of the needle is in mechanical contact with a similar small area of the vinyl, and the mechanism responds to either the amplitude or velocity of the needle's displacement (piezo or magnetic, respectively) after passing it through a mechanical system (mass, compliance, etc.).
Phonons are waves propagating through a crystal lattice, which have quantum properties.
(My favorite is "Umklapp", which is like aliasing in sampled time systems, but in three dimensions.)
Phonons in the diamond needle are not relevant to the system response, and are usually up in the GHz range.

[radiolistener]

there is electromagnetic interaction between particles which transfers sound wave as pressure wave from one particle to another.

And the energy of electromagnetic interaction between particles is discrete and quantized with photons. Yes quantum of energy is very small and simple sine sound involves incredible amount of photons to transfer sound wave through vinyl player needle, but energy transfer is discrete, NOT continuous...

So, is vinyl record digital? 

[TimFox]

Is it binary?
All voltage waveforms can be called analog, even at the input of a binary logic gate, but real systems can interpret the waveform as either a discrete (digital) or continuous (analog) code of the important variable (e.g., musical sound).
If the discrete levels that are encoded are closer together than the system noise, then the analog interpretation is normally more relevant.

[radiolistener]

Is it binary?

No it is not binary and therefore not digital but analogue.
But I wonder to know why it is analog from those who thinks that digital means discrete and it don't matter how many discrete levels it has...

[Zero999]

If the discrete levels that are encoded are closer together than the system noise, then the analog interpretation is normally more relevant.

I remember making that point to an audiophool analogue zealot. I tried all sorts of analogies such as a screen consisting of discrete pixels, views through mist, representing noise, but the concept just didn't sink into his thick head. 

[radiolistener]

If the discrete levels that are encoded are closer together than the system noise, then the analog interpretation is normally more relevant.

Noise floor depends on temperature and bandwidth, does it means that classification digital/analog depends on circuit temperature and signal bandwidth?   

[TimFox]

Is it binary?

No it is not binary and therefore not digital but analogue.
But I wonder to know why it is analog from those who thinks that digital means discrete and it don't matter how many discrete levels it has...

Valid logic:  it is not digital, therefore it is analog.
Also:  it is not digital, therefore it is not binary.
The converse of the second is specious.

[TimFox]

If the discrete levels that are encoded are closer together than the system noise, then the analog interpretation is normally more relevant.

Noise floor depends on temperature and bandwidth, does it means that classification digital/analog depends on circuit temperature and signal bandwidth?   

Temperature and bandwidth are valid system parameters.
Other parameters of the system are also needed to estimate the noise floor, such as operating conditions of the amplifiers.
Usually, my statement above can be evaluated without an exact value for the noise floor, in practical situations.

[AndyBeez]

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?

[IanB]

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?

That seems like a good definition, if we qualify it by saying "in the ideal case" or "in principle". Because in practice, there can be unrecoverable errors during transmission or storage, resulting in information loss. An ideal digital system can store or transmit information such that it can be recovered exactly, without loss.