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

[TimFox]

No, if the ternary system is used consistently within the mechanism, it will compute without any binary representation.

yes, exactly. But this will be ternary mechanism, not digital mechanism.

At the end of the ternary computation, it is straightforward to convert the result to binary to connect with your conventional system, but that's a conversion from one digital system to another, which does not require ADCs.

No. There is no way to convert analog signal (ternary) to digital without analog to digital conversion. For digital system ternary signal is analog signal.

You are totally wrong.  Using ternary logic gates with only three states, it is a straightforward digital design problem to produce the discrete binary equivalent of a discrete ternary value.
Of course, a ternary value cannot be connected directly to a binary gate, since that would result in an incorrect result where the binary gate could not discriminate between, say, -2 V and 0 V.
In principle, that is no harder than designing a circuit using only binary logic gates to directly (no recursion or successive steps) convert a hexadecimal binary word to the same value in BCD or grey code.

[radiolistener]

One feature of mechanical and electromechanical digital systems is that they are not limited to binary, and usually worked directly in decimal (or pounds-shillings-pence) digits.

if it works with decimal values directly (without binary signals), then it cannot use digital logic and so, cannot be named as digital.

[TimFox]

Once again, you argue that a digital system must be binary, because only binary systems are digital, ignoring the fact that binary is but one of a countably-infinite types of digital representations.
Your opinion that "digital" and "binary" are synonymous is contrary to technical definition, and confuses two related but separate concepts.

[CatalinaWOW]

No, if the ternary system is used consistently within the mechanism, it will compute without any binary representation.

yes, exactly. But this will be ternary mechanism, not digital mechanism.

At the end of the ternary computation, it is straightforward to convert the result to binary to connect with your conventional system, but that's a conversion from one digital system to another, which does not require ADCs.

No. There is no way to convert analog signal (ternary) to digital without analog to digital conversion. For digital system ternary signal is analog signal.

Minor logical correction.  Connection of a ternary system to a binary system requires a ternary to binary converter.  You will not agree with this correction because the subtle point here is at the heart of your view of the world.

I am not trying to correct your view of the world.  You find this view both useful and sufficient.  I am curious why you feel so strongly about trying to change others views, views which those others find useful?  I agree with you that Boolean logic only works in binary systems.  Just as Euclidean geometry only works in Euclidean spaces.   But I don't deny the existence of non Boolean logics any more than I reject the existence of non Euclidean geometries.

[radiolistener]

Once again, you argue that a digital system must be binary, because only binary systems are digital, ignoring the fact that binary is but one of a countably-infinite types of digital representations.
Your opinion that "digital" and "binary" are synonymous is contrary to technical definition, and confuses two related but separate concepts.

No. Digital and binary are not synonymous. And digital system must be binary not because only binary systems are digital.

The reason why digital system must be binary is because entire digital domain is designed for binary signals only. Digital logic works with binary signals only, digital methods and algorithms are designed for binary signals only. That's the reason why digital circuit must use binary signals.

If you want to use non binary signal in digital circuit, you're needs to treat it as analog and use ADC.

[radiolistener]

Minor logical correction.  Connection of a ternary system to a binary system requires a ternary to binary converter.  You will not agree with this correction because the subtle point here is at the heart of your view of the world.

Yes, it requires ternary to binary converter. But for digital domain ternary to binary converter is nothing else as analog to digital converter.

I agree with you that Boolean logic only works in binary systems.  Just as Euclidean geometry only works in Euclidean spaces.   But I don't deny the existence of non Boolean logics any more than I reject the existence of non Euclidean geometries.

I also don't deny existence of non Boolean logic, on the contrary I already said that you can develop non digital system and it will include logic, math and algorithms.

But you can't name Minkowski space as Euclidean space. The same you can't name a system designed for ternary signals as digital system, just because digital system is designed for binary signals.

[ebastler]

Gentlemen, I think it is time to conclude that radiolistener is trolling you. If you enjoy the exchange, feel free to keep going of course. But don't expect any breakthroughs...

[TimFox]

The ternary to binary converter can stay in the realm of discrete states, for example using relays, and never venture into the realm of analog signals.

You need to look up "petitio principii", the logical fallacy ("begging the question") when an argument's premises assume the truth of the conclusion, roughly synonymous with circular reasoning.

[wasedadoc]

No, if the ternary system is used consistently within the mechanism, it will compute without any binary representation.

yes, exactly. But this will be ternary mechanism, not digital mechanism.

At the end of the ternary computation, it is straightforward to convert the result to binary to connect with your conventional system, but that's a conversion from one digital system to another, which does not require ADCs.

No. There is no way to convert analog signal (ternary) to digital without analog to digital conversion.

Let's say I have a ternary system and it transmits the "messages" 0, 1 or 2 using the three levels -V, 0 and +V.  At the receiver I convert the messages to binary. I have a 2-bit ADC with quantising levels at -V/2, 0 and +V/2. I use a truth table to convert the 2-bit output to binary.

Later I realise I could substitute the 2-bit ADC with two 1-bit ADCs. One with threshold at -V/2 and another 1-bit ADC with threshold at +V/2.  Again I use a truth table slightly modified from the above one, to convert the two 1-bit outputs to binary.  Input below -V/2, input above -V/2 and below +V/2, input above V/2.  I'm converting ternary to binary using two ADCs. According to radiolistener this system is not digital.

Later I consider not to use ternary, but binary using levels 0 and V/2+V.  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.

Edited to correct "V/2" to "+V" in the first sentence of the third paragraph.  The concept is not affected.

[tggzzz]

That’s not a definition, it’s a circular argument: “binary means digital because digital means binary”. We’ve given you multiple proven definitions of digital that your “definition” violates.

You still aren’t getting it, but it’s obvious you’re not even attempting to understand what people have explained to you multiple times.

Has anybody else made the observation that radiolistener  in an inappropriate moniker?

[MK14]

Has anybody else made the observation that radiolistener  in an inappropriate moniker?

I noticed, and was tempted to mention it.

[IanB]

Has anybody else made the observation that radiolistener  is an inappropriate moniker?

I guess it is because nobody has accepted his premise that modern digital electronics works in binary. Which is true, but it is too limiting. The title asks "What is a digital system?" It doesn't limit the discussion to electronic digital logic circuits, which are, conventionally, binary in operation.

[tggzzz]

Has anybody else made the observation that radiolistener  is an inappropriate moniker?

I guess it is because nobody has accepted his premise that modern digital electronics works in binary. Which is true, but it is too limiting. The title asks "What is a digital system?" It doesn't limit the discussion to electronic digital logic circuits, which are, conventionally, binary in operation.

The problem is that radiolistener doesn't listen to all the other people.

There are numerous commercially important electronic digital logic circuits that aren't binary. I have some in my pocket: a USB flash disc.

[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.
The circuit is purely "combinational", not "sequential" logic.
Normal DC-coil relays are used since they are agnostic about the polarity of the coil current.
This example of diode-relay logic is no more an ADC than is a 7404 TTL inverter gate section.
For completeness, the drawing defines the conversion table between the three input states that I have named "N", "Z", and "P" and the two-bit binary code at the output.
The logic levels are also defined, although obviously the discrete input levels are not precisely defined as shown, just as TTL levels are not precise but given as ranges.
The ternary source will deliver only three possible states, each of which is near the voltage shown, but does not vary continuously between states, but jump between the three states in the same manner as binary TTL hardware jumps between two states.

[Electro Fan]

Ok, so it seems that "ternary" is "exhibit A" and the poster child example of why digital is not the same as binary.

The claim is that +5V, 0V, and -5V are discreet levels, ie they are digital and not continuously variable; however it is noted in this example that these 3 levels are not really exact discreet levels but ranges.  ("The logic levels are also defined, although obviously the discrete input levels are not precisely defined as shown, just as TTL levels are not precise but given as ranges.").

Presumably in this argument we don't want to call the ranges "analog" because they are not "continuously variable"’; rather they are values within "ranges."  Seems like skating on some random ambiguity as many analog signals are not infinitely variable but rather fall within "ranges."  Nonetheless, we will proceed on the premise that these 3 ranges are not "analog" but rather they are "digital" values.  Fair?

Next, after all of that ^, we proceed to show how these three values (each representing some range) are designated as 1s and 0s (binary digits):  00, 01, and 10.  So in the end, we have taken some value that we insist is not "analog" but digital and we represent the value with binary digits.

It seems that in terms of the output, ie the representation of non-binary digital values in this digital system, the example shows the output to be binary.  So, if this is our poster child example, we can't argue with the fact that the output of a digital system is binary because this example shows that the output is binary.

All that is left then is to make the case that the input of this digital system is not binary - which is based on the premise that this digital system has 3 possible states (some range in the vicinity of +5V, some range in the vicinity of 0V, and some range in the vicinity of -5V).  This then, is the basis for the argument that digital systems are not necessarily binary.

If this is a fair restatement of the discussion, then we can say that the input of a digital system might be something other than binary (ie, something with more than 2 states), but the output (at least in this poster child example) is still binary.

Now, before going too far into the rabbit hole, someone might say "but the output isn't really binary either, it isn’t two states because the values (as shown) are 00, 01, and 00.  So according to this logic there are three states.  Personally, I would say "tilt" on such an argument because as has been said over and over throughout this thread, the notion of binary is that two states (0 and 1) can be used to code many other values subject only to the number of bits within a "Byte".  So, I think we have to agree that the output of a digital system is binary (unless it gets converted to something else, such as analog).

So unless someone wants to argue otherwise (and I’m guessing someone will), it seems that the “ternary” example is consistent with a digital system in which the output is “binary.”

This leaves us with whether the input of a digital system is binary, or if in fact the input of a digital system can have more than 2 states.  Again, in our poster child example the input has 3 states, and even though the poster child example clarifies that these 3 states are not limited to 3 discreet values but are in fact values that fall within 3 ranges, we choose to refer to these 3 ranges as "ternary."  Whether "ternary" means exactly 3 values (which it doesn't in the poster child example) or whether it means roughly 3 values (which it does in the poster child example), we can all agree that the input has more than 2 values.  However, if we accept that these three values are not discreet, but are in fact ranges, then we have to acknowledge that the values could be many values more than 3.  For example, approximately +5V could be 5.000000V or 5.0000001V or 4.999999V or pretty much any number of values if we are willing to move the decimal point.  Nonetheless, in this poster child example we say it's "ternary" and we use the ternary example to defeat the idea of digital as meaning binary and we insist that because there are (at least) 3 values in the input, it is therefore an example of a "digital" system and therefore "digital" cannot be synonymous with "binary".  Or so the argument goes.

If it ended this discussion on a consensus, I'd be inclined to say "ok, if we can accept that the output of a digital system is binary, ie 1s and 0s, ie, binary digits then sure, good enough for discussion sake if not an exact definition."  But I have a hunch this thread might have a bunch more posts to go, so what the heck, let's keep going.

So, next, beyond the output side of a digital system being binary, let's revisit the idea that "ternary" is a special case that has 3 states.  As we've seen above, the 3 states are not discreet, they are ranges, and the ranges could represent a huge number of actual values depending on where the decimal point resides.  But let's give the poster child example the benefit of the doubt; let's call it 3 states and say "ah ha, it is 3 values and 3 is greater than (and definitely different than) the 2 states of binary – so therefore digital can’t mean just binary.”  This then raises the question of "who cares"?  Because darn near everything we input to a digital system (all the alphas, all the numerics, all the special characters, all the pixels, and pretty much all the everything) has more than 2 states.  But you know what?  When we get done coding all the darn near everything (including in the poster child ternary example that we insist is "not binary") what the digital system does is it converts the 3 states (or n states), or ranges (with an infinite number of possible values) to 1s and 0s, ie to 2 states we call "binary."  Again, how many 1s and 0s we use to encode something else is just a function of how many values we want to represent with binary digits as we string the bits together into Bytes according to various coding conventions.

If we zoom out and look at the huge amount of information inputted, processed, and outputted with computers and embedded devices and all the information collected and distributed with networks the vast vast vast majority of it gets reduced to 1s and 0s.  The argument that digital and binary are not synonymous might be more academically interesting than useful.

(edit for typos and clarification)

[CatalinaWOW]

Read the Wikipedia article on ternary logic.  The discussion there has nothing to do with electrical circuits.   After reading that I realized that my comment about a ternary to binary converter was naive and wrong.  There is no way to directly convert a three state system to two states.  It is possible to emulate a ternary system using two bits to hold the three symbols.  And it is possible to create circuits which implement the (complex) logic tables of ternary logic.  But I find it very strained to call such circuitry analog.  In a sense it is analog, but it is analog in exactly the same sense as binary circuitry which uses voltage levels to represent the states.

[radiolistener]

The ternary to binary converter can stay in the realm of discrete states, for example using relays, and never venture into the realm of analog signals.

Any ADC staying in the realm of discrete states, but this is device which get analog signal on the input and produce digital signals on the output. But ADC input is still analog input, it is not digital.

[radiolistener]

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.

You're needs to understand, that digital signal doesn't allows valid level between 0 and 1. This is why digital signals are not compatible with analog one. If you put such analog signal with 3 discrete level on digital input it will leads to metastability issues and your digital circuit won't works as expected.

Analog comparator is analog component and if you're using it, your circuit is not pure digital. It is mixed signal, because it works with both kind of signals - analog and digital.


You can create analog circuit using digital and analog components. This is how ADC and DAC are implemented. But it don't means that you can assume discrete 3 level signal as digital and process it on digital logic such as AND/OR/XOR/NOT elements.

It just means that when you build some circuit which works with analog and digital signals, such circuit is not pure digital. It is mixed signal circuit. It means that is uses both domains - digital and analog.

There are only two domain: digital and analog. And any circuit which is not digital (based on non binary signals) is fall to analog category. It can be discrete, but still fall to analog category, because incompatible with digital.

There is no ternary domain, so if you invent ternary signal and ternary logic elements, your circuit automatically falls into analog catergory. Because it is not compatible with digital logic.

[JeremyC]

https://www.uobabylon.edu.iq/eprints/publication_12_1733_6174.pdf
I'm here.

I'm wondering what is a digital system? Is it only binary? Or decimal, octal, hexa are also digital system?

@oslon, you just opened a can of worms 

[radiolistener]

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.

[radiolistener]

The problem is that radiolistener doesn't listen to all the other people.

I cannot listen to all peoples, this is just impossible, because there is more than 8 billion peoples on the Earth
But I listen to peoples in this thread, which of course cannot represent all peoples.
And I am not obliged to accept someone else's opinion with which I do not agree, even if it is shared by several people.

As we already discussed before, most part of peoples are stupid, smart peoples are rare.
So accepting opinion just because it is shared by many peoples is a stupid idea.
You're needs to have your own head and not rely on mass opinion.

There are numerous commercially important electronic digital logic circuits that aren't binary.

This is your mistake. There is no electronic digital logic circuits that aren't binary. This is technically impossible and even sounds absurdly.

I have some in my pocket: a USB flash disc.

USB flash drive is mixed signal device, it includes analogue voltage regulators and other analogue stuff inside. For example it can store data as analog signals, etc.

But it has digital interface and don't expose it's analog signals outside. So you can categorize it as digital, just because nothing will be changed if you replace it with pure digital device - it will have the same digital interface and will works the same.

So you shouldn't care if there are analog signals inside the device if you don't have access to those analog signals. Since you have only digital interface, you can assume that device is digital.

[radiolistener]

When someone talking about digital circuit, it is pretty clear that he is talking about circuit that works with binary signals and uses digital logic elements such as AND/XOR/OR/NOT.

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

[tooki]

Has anybody else made the observation that radiolistener  is an inappropriate moniker?

I guess it is because nobody has accepted his premise that modern digital electronics works in binary. Which is true, but it is too limiting. The title asks "What is a digital system?" It doesn't limit the discussion to electronic digital logic circuits, which are, conventionally, binary in operation.

What do you mean? Multiple people, including myself, have agreed that practically all digital electronics, save for some types of memory and many types of communications, are strictly binary. But he’s too stubborn or too stupid to even recognize that.

[Zero999]

When someone talking about digital circuit, it is pretty clear that he is talking about circuit that works with binary signals and uses digital logic elements such as AND/XOR/OR/NOT.

Not necessarily.

A quote from the programmable gain amplifier IC, I mentioned earlier.

PROGRAMMABLE GAIN LOGIC
The ISL2853x and ISL2863x feature a three-state logic interface for digital programming of the amplifier gain. This allows the PGIA’s gain to be changed without an external gain setting resistors, improving the gain accuracy and reducing component count. The three-state logic pins have voltage levels for recognizing valid logic states to set the gain of the amplifier (see Figure 75). With three logic states per input, this allows nine gain settings with just two digital input pins (see Table 3).

https://docs.rs-online.com/81e5/0900766b814ecfcf.pdf

[wasedadoc]

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.