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

[ebastler]

Can't help myself...
What would you call this, then?

https://louis-dr.github.io/index-ternary.html
https://louis-dr.github.io/ternalu3.html

[madires]

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.

The OP's question was mathematics related, just saying.

[MK14]

A digital signal is a signal that represents data as a sequence of discrete values. A digital signal can only take on one value from a finite set of possible values at a given time.

Source: https://www.monolithicpower.com/en/analog-vs-digital-signal

So, according to the supplied source (there seem to be other sources, saying basically the same thing).  It can be binary or any other counting system (i.e. NOT binary), as long as it has a discrete number of states (i.e. is NOT analogue, as in an almost infinite number of states).

This is a very long thread, for something which might have been started either by a 2 post spambot or fly-by user, who just wanted to advertise their link/paper or something like that.

[radiolistener]

Can't help myself...
What would you call this, then?

https://louis-dr.github.io/index-ternary.html
https://louis-dr.github.io/ternalu3.html

This is an example of what is NOT digital system 

[ebastler]

 

[radiolistener]

ebastler, it seems that you don't understand what is the digital logic, digital circuit, digital system.

You can read this article, it will show you what term digital means: https://learn.sparkfun.com/tutorials/digital-logic/all


By the way, just opened your second link and it shows usual digital circuit which emulates ternary logic. This is what I was talking about... There is no signals with 3 disrete levels, it uses binary signals to emulate ternary logic.

So, the answer on your question: this is classic digital circuit with binary signals which emulates ternary logic.

[radiolistener]

https://www.techopedia.com/definition/27425/digital-logic

Digital logic is the underlying logic system that drives electronic circuit board design. Digital logic is the manipulation of binary values through printed circuit board technology that uses circuits and logic gates to construct the implementation of computer operations.

 

I just have no idea where you get misunderstanding that digital circuit may work with non binary signals... Because every dictionary explains that "digital" means binary data, binary signal, boolean logic.... 

[radiolistener]

So, according to the supplied source (there seem to be other sources, saying basically the same thing).  It can be binary or any other counting system (i.e. NOT binary), as long as it has a discrete number of states (i.e. is NOT analogue, as in an almost infinite number of states).

No.

It can be any numbering, any counting, but digital system MUST represent any data with binary signals. This is mandatory requirement for digital system. You can encode any number with binary data. But digital system works with digital signals only which is binary...

You can use any encoding: binary, BCD, one-hot, themperature code, you can invent your own numbering system and invent your own encoding for numbers, etc, but all data must be represented with binary signals.

[MK14]

It can be any numbering, any counting, but digital system MUST represent any data with binary signals. This is mandatory condition for digital system. You can encode any number with binary data. But digital system works with digital signals only which is binary...

You can use any encoding, binary, BCD, one-hot, themperature code, etc, but the data must be represented with binary signals.

So are you saying, that modern high capacity SSD's, are NOT digital devices, because they (typically, for the latest modern ones), use multiple/many states (more than 2), per memory cell element.

https://en.wikipedia.org/wiki/Multi-level_cell

[radiolistener]

So are you saying, that modern high capacity SSD's, are NOT digital devices, because they (typically, for the latest modern ones), use multiple states (more than 2), per memory cell element.

Yes, internally they are not pure digital, they are mixed signal circuit, because they working with analog signal inside. But they expose only digital interface and you don't have access to their internal analog signal. So, you can assume it as digital element, because it's public digital interface works the same as for pure digital device. Analog part is private and not available outside chip, so you can ignore that.

[MK14]

Yes, internally they are not pure digital, they are mixed signal circuit, because they working with analog signal inside. But they expose only digital interface and you don't have access to their internal analog signal. So, you can assume it as digital element, because it's public digital interface works the same as for pure digital device. Analog part is private and not available outside chip, so you can ignore that.

Yes, that sounds right.  But there have been, and perhaps still are, computer systems, calculators and so on, which use systems, that are not binary.

https://en.wikipedia.org/wiki/Ternary_computer

Which describes, various devices, such as computers, which use three different states, in order to work.

[radiolistener]

Yes, that sounds right.  But there have been, and perhaps still are, computer systems, calculators and so on, which use systems, that are not binary.

https://en.wikipedia.org/wiki/Ternary_computer

Which describes, various devices, such as computers, which use three different states, in order to work.

As I know, all ternary computers were implemented on classic digital circuits (with binary signals). It just emulate ternary values with two binary signals and implements ternary logic with usual digital logic elements. This is how ternary computer Setun was implemented.

Some of ternary computers were implemented as software program for usual digital computer. But if there is exists ternary computer which works with 3 level signals, then it will be example of non digital computer, because it don't use digital logic, don't use digital signals and don't use all what is named as digital electronics, but I don't know about such examples.

[Tation]

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

Do you have any reference supporting such claim?

[TimFox]

"digital system MUST represent any data with binary signals. This is mandatory requirement for digital system"
So you keep saying, despite centuries of digital systems using non-binary components and representations, that predate binary systems.
You may have a limited universe of discourse, but there are many examples in the larger picture, brought to your attention by multiple posters, after which you put your fingers in your ears and recite your mantra.

George Boole introduced his system in 1854, following work by Leibnitz.
In the 1930s, Shannon applied binary Boolean algebra to switching circuits, after which "Boolean" came to mean binary.
Boolean algebra is used for symbolic logic that recognizes only "true" or "false" as valid outcomes;  other forms of logic can have further answers in their set of valid outcomes.
Binary arithmetic differs from Boolean algebra, but also uses binary variables.
Modern mathematics recognizes a multiplicity of "Boolean algebras", but that is higher mathematics.

In this forum, there are many opinions legitimately held by individuals that disagree with each other, such as personal preferences for Windows, Linux, Mac, or other operating system.
Different people find different choices better suited to their experience, application, or familiarity.
One of my strongly held opinions is in favor of RPN over "algebraic" notation on pocket calculators.
However, the standard definition of digital (antonym of analog) is that it uses discrete states and representation, instead of continuous.
If someone claims that "there must have been a year zero" in discussing the civil calendar in use in Western countries, that opinion of theirs is wrong, since the civil calendar is otherwise defined to go from 1 BC to AD 1 without a year in between, and a different definition would change the historical date of Caesar's assassination.
(Astronomers do use a different calendar definition, where the year before AD 1 is zero, and years before that are shifted by one from the legal civil calendar, but we don't rewrite the history books.)

[MK14]

But if there is exists ternary computer which works with 3 level signals, then it will be example of non digital computer, because it don't use digital logic, don't use digital signals and don't use all what is named as digital electronics, but I don't know about such examples.

Digital signals having more than two states are occasionally used

So, non-binary signal levels (i.e. more than 2 states), are fine, and still digital (signals), even if rarely used.

Source:  https://en.wikipedia.org/wiki/Digital_signal

[radiolistener]

Do you have any reference supporting such claim?

As I remember, there was shared document with implementation details, it don't covers all details of Setun, but explains some aspects and ternary logic details, it was shared on some forum, but I don't remember where it was exactly. It was many years ago. Probably it was on zx-pk.ru

[TimFox]

I had to edit my reply 244 several pages ago about the 1967 thesis by Sung Chiao Hu at Oregon State University, since there was no http reference copyable.
Looking again at his thesis, he shows practicable ternary logic gates, with -2 V, 0, and +2 V levels on each single line, using NPN and PNP transistors.
He also defines the Boolean-style algebra for ternary variables.
That would have a nuisance with tubes;  he also discusses tunnel diodes as a possible hardware solution.
Google:  "Hu Sung ternary thesis" to download the thesis (pdf of typescript).

[radiolistener]

So you keep saying, despite centuries of digital systems using non-binary components and representations, that predate binary systems.

yes, I keep saying that digital circuit works with binary signals only. And there is no digital system which using non-binary components. All examples which was mentioned in this thread are digital and using binary signals (such as ternary computer and dekatron computer).

Mechanical calculator are analogue systems because it using gears which are continuous devices and is not compatible with digital logic which uses discrete binary values.

However, the standard definition of digital (antonym of analog) is that it uses discrete states and representation, instead of continuous.

There is no such "standard definition" that it uses discrete states instead of continuous.

The standard definition is that digital uses binary digits and digital logic which also known as Boolean logic which is invented for binary signals only.

From that point yes, you can say that digital signal is discrete, because binary is discrete. But you can't say that any discrete signal is digital, this will be incorrect, because it includes non binary signals which are not compatible with digital logic.

[TimFox]

Nonsense:  that is your standard definition.
The actual standard definitions state that binary is an important specific case of "digital".
If you use a Geneva mechanism in the mechanical gear train, the results are as discrete as the output of a TTL logic gate, which does take a finite time to change from one state to another.
https://en.wikipedia.org/wiki/Geneva_drive
My quartz watch shows the second hand jumping discretely in one-second increments, from a gear train driven by a stepper motor.
My old-fashioned 60 Hz synchronous-motor analog wall clock shows the second hand moving continuously.

[radiolistener]

I had to edit my reply 244 several pages ago about the 1967 thesis by Sung Chiao Hu at Oregon State University, since there was no http reference copyable.
Looking again at his thesis, he shows practicable ternary logic gates, with -V, 0, and +V levels on each single line, using NPN and PNP transistors.

Yes, you can implement ternary elements, but will not be digital. Because digital electronics uses digital logic which is designed for binary signals. It won't work for ternary signals. The same digital electronics uses different methods and algorithms designed for binary signals, so it won't work for ternary signals. So your ternary signals will be completely incompatible with digital electronics.

In order to connect your ternary signal to digital circuit you will needs to use analog to digital converter to convert ternary signal from analog to digital.

[TimFox]

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

[radiolistener]

If you use a Geneva mechanism in the mechanical gear train, the results are as discrete as the output of a TTL logic gate, which does take a finite time to change from one state to another.

I can agree here, if you implement mechanical gears that will work with two discrete state and implement boolean logic on such gears, then may be you can name it as digital 

Usually digital system means electronic system, not mechanical. But technically yes, you can implement digital logic with mechanical or pneumatic devices which will work on the same digital principles, but will not use electricity.

[MK14]

Mechanical calculator are analogue systems because it using gears which are continuous devices and is not compatible with digital logic which uses discrete binary values.

Not really.

E.g. A relay, is a sort of very simple, mechanical (or electromechanical device) 'calculator', which can process two digital states, on and off.

[radiolistener]

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.

[TimFox]

If you use a Geneva mechanism in the mechanical gear train, the results are as discrete as the output of a TTL logic gate, which does take a finite time to change from one state to another.

I can agree here, if you implement mechanical gears that will work with two discrete state and implement boolean logic on such gears, then may be you can name it as digital 

Usually digital system means electronic system, not mechanical. But technically yes, you can implement digital logic with mechanical or pneumatic devices which will work on the same digital principles, but will not use electricity.

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.
One of the first was built by Blaise Pascal in the 17th century, and was in limited commercial production for about 10 years, for use in bookkeeping computations.
During the same period, analog computation by devices equivalent to modern sliderules was developed, after the invention of logarithms in mathematics.
The decimal digits appearing on a 20th-century electromechanical calculator jump from one decimal state to another.