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

[TimFox]

You can make a truth table for a logic gate that works with tri-state gates, but you have to have three outcomes, just as a normal binary gate has two outcomes.

[Zero999]

Tri-state output can be used to get three logic levels.  The programmable instrumentation amplifiers, ISL28533, ISL28534, ISL28535, ISL28633, ISL28634 and ISL28635, use two pins to select between 9 different gains, with a microcontroller with tri-state outputs.

https://www.renesas.com/eu/en/document/dst/isl28533-isl28534-isl28535-isl28633-isl28634-isl28635-datasheet?r=493621

[Electro Fan]

Not sure what the debate is really about any more in this thread.

While digital could mean various things depending on the context, it generally refers to a technique for coding and processing information which at the foundation is binary (ie, a 1 or 0, the presence or absence of electricity) subject to some agreed upon thresholds and conventions.

Of course, digital might refer to digits as in human fingers and toes, or it might refer to a digital readout such as the output of a clock, and it could probably mean a lot of things to a lot of people but the vast majority of the Information Technology humans use to create Information Systems that are used to manage information (including in the form of data, text, audio, image, and video) gets foundationally managed as bits (binary digits), ie, 1s and 0s.  The 1s and 0s can be coded according to popular standards such as ASCII, or Hex, etc, or using proprietary, or special purpose, or obscure techniques, but digital at it's foundation is more often than not (there are exceptions for nearly everything) binary, ie 1s and 0s.

Sometimes when trying to determine if something is on or off we might come up with can't discern/don't know or maybe even don't care.  No doubt we can point to three states or conditions, or potentially n number of states and conditions.  In fact we can do a lot of things a lot of different ways, but while we could do a lot of things it turns out that with just 1s and 0s we can do a huge number of things, and the simplicity, consistency, and elegance of binary has made the concept of binary the foundation of the biggest revolution in human history - so maybe instead of obscuring the reality with what are interesting if not edge cases at best, we ought to acknowledge that digital is fundamentally, at it's core, binary.  I think we might be blurring bits with states and logic and codes.  The distinctions are meaningful but we might be losing sight of the forest while examining the trees. 

Using 1s and 0s we can represent virtually anything but given that our systems generally need to provide some practical utility the 1s and 0s get truncated into Bytes or other finite sets of bits which then in some cases come up short of analog's "continuously variable".  And of course, humans are becoming very clever at developing "mixed-use" techniques which use A2D and D2A.  We live in an analog and physical world that we are learning to increasingly impact through the application of digital technology - which generally, at it's foundation, is binary, ie, 1s and 0s.

Net, net:  I think we can give it to radiolistener that for most people most of the time "binary" and "digital" are highly and very commonly related even if the two terms are not completely synonymous and not fully interchangeable.
 

[TimFox]

I will not give to Radiolistener his emphatic statement that all digital systems are binary, just because most of them are, and that inherently decimal digital systems do not exist, by his idiosyncratic definition.

[TimFox]

Tri-state output can be used to get three logic levels.  The programmable instrumentation amplifiers, ISL28533, ISL28534, ISL28535, ISL28633, ISL28634 and ISL28635, use two pins to select between 9 different gains, with a microcontroller with tri-state outputs.

https://4donline.ihs.com/images/VipMasterIC/IC/RNCC/RNCC-S-A0010774787/RNCC-S-A0011027418-1.pdf

That use of tri-state hardware would then be a ternary digital system, where each pin has three possible levels.

[radiolistener]

Tri-state output can be used to get three logic levels. 

you can use N digital signals to get 2^N discrete levels, this is how digital-to-analog converter works, but digital signals on input of DAC is still digital and uses 2 discrete levels.

It just means that circuit which converts digital binary signal with third state to analog discrete signal with 3 levels is digital-to-analog converter.

[radiolistener]

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.

it is incompatible not with my "excessively rigid definition", it is incompatible with all existing digital electronics. You can't connect your analog N-level discrete signal, where N>2 to a digital electronics component, because all of them expecting signals with only 2 discrete level.

You can fantasize and invent mythical digital circuits that support discrete analog signals, but in reality they don't exists and you will have to use analog-to-digital conversion if you want to use such a discrete signal in a digital circuit. There is no other way.

I'm sorry to ruin your myths, but this is the reality, all existing digital electronics works with binary signals and uses math, logic and algorithms which expecting binary signals only 

If you want to use N-level discrete signal where N>2 in digital electronics, you're needs to convert that signal from analog to digital with ADC.

If you want to generate N-level discrete signal where N>2 in digital electronics, you're needs to convert digital binary signals to analog with DAC.

Sorry, but there is no way to process N-level discrete signals where N>2 directly in digital circuit.

Yes, in theory you can invent ternary signals, develop math and logic for it and implement components that works with ternary signals directly without classic digital electronics that uses binary signals. But such ternary signals and components will be incompatible with all existing digital electronics, so you cannot name it as digital and cannot use digital methodology and digital algorithms for such ternary signals, you're needs to invent some new name, otherwise it will leads to confusion.

But there is no such ternary components, this is dead branch of electronics, and any ternary signals (or other discrete signals with N>2) are treated as analog and processed with classic digital electronics (using binary signals) with help of DAC and ADC converters, so there is no sense to even talking about it...

[tggzzz]

Not sure what the debate is really about any more in this thread.

While digital could mean various things depending on the context, it generally refers to a technique for coding and processing information which at the foundation is binary (ie, a 1 or 0, the presence or absence of electricity) subject to some agreed upon thresholds and conventions.

Thresholds are a necessary characteristic, often with a forbidden zone.

Binary is a sufficient characteristic, but not a necessary characteristic.

There are technically and commercially important non-binary digital circuits and systems. See previous posts for examples.

[radiolistener]

There are technically and commercially important non-binary digital circuits and systems. See previous posts for examples.

non binary but digital circuit doesn't exists and cannot exists, because digital circuit needs to use binary signals by convention. If it doesn't use binary signals, then it is not digital and needs to be treated as analog signals.

The circuit can use both kind of signals analog and digital (binary), this kind of circuit is named as mixed signal. It has two interfaces - digital and analog.

Some people may mistakenly name such mixed signal circuit as digital, because it has digital interface. But to be clear it is not digital, but mixed signal circuit because has both digital and analog interfaces.

The example of such mixed signal circuit is programmable gain amplifiers, they have analog input and output and digital (binary) signals to control the gain.

Another example of mixed signal component is DAC (Digital to Analog Converter). It has digital (binary) signals on the input and analog signal on the output.

By convention digital (binary) signals are marked as Dxx, where xx is the meaning of signal. And analog signals are marked as Axx, where xx is the meaning of signal.

For example DAC inputs are digital (binary) signals and marked as D0...D15.
DAC output is analog signal and marked as AVOUT.
DAC reference input is analog signal and marked as AREF.

Analog ground is usually marked as AGND and digital ground is marked as GND or DGND.

[tooki]

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.

[radiolistener]

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.

I understand it very well you're name all circuits as digital, just because you want.
I'm name digital things that is a part of digital electronics and is compatible with digital interfaces.
That's the difference

[tooki]

It’s not because “I want” it, but because that’s the formal definition.

Everyone has acknowledged that non-binary digital logic isn’t used. But multilevel signaling does get used (we provided examples) to interface with the outside world. And because digital vs. analog deals with how the signal is interpreted (not how it’s generated, and not how the interpretation is physically implemented, and not how the signal is further used once inside), those signals are still digital, because they’re encoding digital information. (Multiple bits encoded into a single symbol are still digital.)

[radiolistener]

But multilevel signaling does get used (we provided examples) to interface with the outside world.

yes, it is used but with help of analog-to-digital and digital-to-analog converters.
Multilevel signals first converted form analog to digital then processed in digital circuit as binary signals and then converted back to analog signal.

Digital signals don't needs to be converted from analog to digital... 

[tooki]

But multilevel signaling does get used (we provided examples) to interface with the outside world.

yes, it is used but with help of analog-to-digital and digital-to-analog converters.
Multilevel signals first converted form analog to digital then processed in digital circuit as binary signals and then converted back to analog signal.

Digital signals don't needs to be converted from analog to digital... 

Yes, they do. As we’ve told you already: every signal is “analog” at the physical level. The bilevel digital inputs of a typical logic device do convert voltages to logic states. As someone already said: you could consider such inputs to be 1-bit ADCs. Sure, it’s a spectacularly simple circuit. But it does convert the dirty analogness of the physical signal to digital. It is the very fact that the circuit interprets the voltage levels as ones and zeros that makes it digital; the same signal going into, for example, an op-amp could be interpreted differently by an analog circuit.

[ebastler]

non binary but digital circuit doesn't exists and cannot exists, because digital circuit needs to use binary signals by convention. If it doesn't use binary signals, then it is not digital and needs to be treated as analog signals.

The circuit can use both kind of signals analog and digital (binary), this kind of circuit is named as mixed signal. It has two interfaces - digital and analog.

Some people may mistakenly name such mixed signal circuit as digital, because it has digital interface. But to be clear it is not digital, but mixed signal circuit because has both digital and analog interfaces.

You are really arguing yourself into a corner here. Nobody, over these many pages of discussion, has tought of mixed-signal systems when they argued that "digital" is not the same as "binary". Rather, everyone except you seems to be thinking of systems which use a small, discrete number of states to represent mathematical digits (!) and perform operations on them.

Historically, digital computers using the base-10 system have existed -- using both, mechanical and electronic implementations. The mechanical implementations make it most obvious that there is no underlying binary representation: The gear and counter wheels can indeed take 10 different positions. Nevertheless, they have always been considered "digital" computers, and still are.

A bit more recently, ternary logic has been used in computers -- not very commonly, sure. But there's no doubt that it uses digital, non-binary logic. https://en.wikipedia.org/wiki/Ternary_computer

I happily agree that pretty much all "digital logic" ICs you can buy today are binary. But that does not mean that "digital" is the same as "binary".

[TimFox]

Logic again:
To disprove the statement "all digital systems are binary", it is only necessary to show one digital system that is not binary (e.g., ternary or decimal or sexagesimal).
That has been done many times in this thread.
The statement "almost all digital systems now in use are inherently binary" is different.

[radiolistener]

Historically, digital computers using the base-10 system have existed -- using both, mechanical and electronic implementations. The mechanical implementations make it most obvious that there is no underlying binary representation: The gear and counter wheels can indeed take 10 different positions. Nevertheless, they have always been considered "digital" computers, and still are.

A bit more recently, ternary logic has been used in computers -- not very commonly, sure. But there's no doubt that it uses digital, non-binary logic. https://en.wikipedia.org/wiki/Ternary_computer

As explained before, these  computers with base-10 was used binary signals to represent base-10 digits. 10 binary signals represent decimal value in one-hot encoding or 4 binary signals represent decimal value in BCD encoding. But they all used binary signals.

This encoding:
00000000001 = 0
00000000010 = 1
00000000100 = 2
00000001000 = 3
...
still uses binary signals 

The same with ternary computer, it uses two binary signals to represent 1 ternary value.

They all used classic digital signals (binary), this is why it was digital.

[TimFox]

Historically, digital computers using the base-10 system have existed -- using both, mechanical and electronic implementations. The mechanical implementations make it most obvious that there is no underlying binary representation: The gear and counter wheels can indeed take 10 different positions. Nevertheless, they have always been considered "digital" computers, and still are.

A bit more recently, ternary logic has been used in computers -- not very commonly, sure. But there's no doubt that it uses digital, non-binary logic. https://en.wikipedia.org/wiki/Ternary_computer

As explained before, these  computers with base-10 was used binary signals to represent base-10 digits. 10 binary signals represent decimal value in one-hot encoding or 4 binary signals represent decimal value in BCD encoding. But they all used binary signals.

The same with ternary computer, it was used two binary signals to represent 1 ternary value.

Wrong:  a true ternary computer system uses three possible levels on one wire to represent one ternary value, typically -V, 0, and +V, where V is a discrete voltage value.
Just because they are not common does not mean they don't exist or have never existed.
A decimal computation device (most of which are mechanical or electromechanical) has ten states on a dial (or similar) to represent one decimal digit, with no binary component whatsoever!
You are defying common technical English definitions of terms to fight a useless battle to impose your narrow view of digital systems by excluding those you don't like.
Have you ever used an electromechanical calculator?

[ebastler]

As explained before, these  computers with base-10 was used binary signals to represent base-10 digits.

I had specifically mentioned the mechanical base-10 digital computers/calculators as an obvious counter-example.

The same with ternary computer, it uses two binary signals to represent 1 ternary value.

Why would you think so?? 

[radiolistener]

Wrong:  a true ternary computer system uses three possible levels on one wire to represent one ternary value, typically -V, 0, and +V, where

No, they all used binary signals. Ternary logic was emulated on digital circuit which uses classic digital signals (binary). They don't use 3 discrete levels for physical signal representation.

For example ternary computer Сетунь (Setun) was used the following encoding for ternary values:

binary signals = ternary value
00 = 0
01 = 1
10 = 2
11 = not used state

In such way ternary logic was implemented with classic digital logic elements AND/OR/XOR/NOT which working with binary signals and Boolean algebra.

And some of them was emulated on a usual computer as software implementation.

[radiolistener]

I had specifically mentioned the mechanical base-10 digital computers/calculators as an obvious counter-example.

Mechanical computers with base 10 are decimal computers, not digital. It doesn't have any relation to digital electronics at all.

Why would you think so?? 

Some time ago I was talked with people who worked on ternary computer Сетунь and he explained how it was implemented.

[radiolistener]

You are defying common technical English definitions of terms to fight a useless battle to impose your narrow view of digital systems by excluding those you don't like.

As already mentioned here. According to English dictionary, digital means:

digital adjective: composed of data in the form of especially binary digits

digital adjective: using a system of receiving and sending information as a series of the numbers one and zero, showing that an electronic signal is there or is not there

Digital information is stored using a series of ones and zeros. Computers are digital machines because they can only read information as on or off -- 1 or 0. This method of computation, also known as the binary system, may seem rather simplistic, but can be used to represent incredible amounts of data.

As you can see, this is you are defying common technical English definitions of terms... 

[ebastler]

Mechanical computers with base 10 are decimal computers, not digital. It doesn't have any relation to digital electronics at all.

I'm reluctant to even call that circular reasoning, because there is no rhyme or reason to it. "Decimal" and "binary" are both special cases of "digital". And why you suddenly want to limit the discussion to "electronics" is beyond me; please see the thread title.

I waited for a long time before I joined this discussion. I'll be much quicker to leave it again. Cheers!

[radiolistener]

"Decimal" and "binary" are both special cases of "digital".

No. Decimal and binary are names of numbering system with different base.
Digital electronics works with binary signals only, but can store information about decimal (or any other) values as a set of binary signals.

And why you suddenly want to limit the discussion to "electronics" is beyond me; please see the thread title.

Because thread title is about "digital system" and term "digital system" is used as category of electronic system which is implemented with digital electronics.

[radiolistener]

mechanical base-10 digital computers/calculators

digital computer, any of a class of devices capable of solving problems by processing information in discrete form. It operates on data, including magnitudes, letters, and symbols, that are expressed in binary code—i.e., using only the two digits 0 and 1.

digital computer, Computer capable of solving problems by processing information expressed in discrete form. By manipulating combinations of binary digits (see binary code), it can perform mathematical calculations, organize and analyze data, control industrial and other processes, and simulate dynamic systems such as global weather patterns. See also analog computer.