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

[golden_labels]

Forgot the most important 4-level digital system, where the symbols are C, A, G, T.

DNA uses base-64, not quaternary. Each single symbol consists of three bases, giving 4³ = 64 possible values.

[tggzzz]

Perhaps Tim Fox put it well and succinctly: "'Digital' comes from counting on one's digits:  the steps are discrete." Discrete steps are the essence of digital. And digital may have come from counting on one's fingers, but digital systems are not limited to ten digits. Hexadecimal, which adds six additional digits (usually A - F are used) to the ten decimal digits for a total of sixteen. Some cultures have used as many as 60 digits.

And again he says that, "'Binary' comes from having two choices:  1 or 0." So binary is just one of many digital systems.

Binary is so popular as a digital system because it is a lot easier to implement just two states in electronic systems. Things like mechanical adding machines and calculators were made using base ten, our common counting system which was derived from our ten fingers. They were true digital devices, but not binary based. there were ten buttons in each of the "place" columns. Eighty, ninety, or even a hundred or more keys was not unusual. A mechanical wheel with ten divisions on it was used to display each digit. But mechanical computational devices were both expensive and hard to keep running without routine maintenance or repairs. Electronic devices were more reliable with almost zero maintenance. But when things were to be made with electrical and electronic devices, it became a lot harder to have ten separate states. Yes, you could represent ten values with 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 Volts. But then, consider how expensive circuits that can distinguish those ten values would be. With electric and electronic devices it is a lot easier and less expensive to use only two values: ON and OFF, HI and LOW, Current and No Current, etc. Also logic circuits could be implemented with devices that have only two possible states because traditional logic has only two values: True and False. Thus binary was used when electronic devices were developed. And it is all due to economics that we now have the world where digital is almost synonymous with binary. Electronic circuits are a lot cheaper than mechanical devices and binary circuits are a lot cheaper than those that would use other numeric bases.

So binary and digital are not the same. Binary is a sub-set of digital. Binary is digital. But digital is not always binary.

And the person who said, "Follow the money." is oh so right.

I always thought all digital systems are fundamentally binary as they are looking for an on or off.

In my mind Hex, Oct, Decimal etc. are still looking for an on or off but just over a range.

i.e. an IC says “do I have exactly 1V, 2V, 3v, etc.” Therefore it is still looking for a on or off aka a 1 or a 0.

That said, maybe my understanding is flawed 

With respect to mechanical calculators and cash registers:
Again, this is discussed in that book about pocket calculators.
With non-decimal monetary systems, such as pounds-shillings-pence, the mechanical dials could be designed to count decimal (for pounds) and  base 12 or 20 for the other two denominations.

... and halfpenny (pronounced ha'penny) and farthing 1/4d, so you also needed 0.25d. I remember, and still have halfpennies in circulation, but not farthings. Thrup'ny bits, tanners, bobs, florins, half-crowns and crowns (3d, 6d, 1s, 2s,  2/6d and 5s respectively) didn't require any special accomodation

It used to be fun to fun to find that your change contained pennies that had been in circulation for a century.
It wasn't fun doing manual arithmetic in all the strange bases, but we were taught some tricks.

[TimFox]

The origin of the old British system goes back to the Romans:  among many variations, they had the libra, solidus, and denarius, whence pound (L), shilling (s), and pence (d).
Etymologically, denarii live on in the Arabic dinars.
At some point, the British decided they needed to add the "guinea" to confuse things, ending with 21 shillings after changes in gold prices.
The American copper one-cent coin is often called a "penny", which it isn't, but the ten-cent coin is, legally, a "dime", as stamped on the reverse of the coin.
The five-cent coin, called a "nickel", is actually 5 g of cupronickel (75 Ag, 25 Ni), and the raw material costs more than $0.05.

[TimFox]

A tribe in Papua New Guinea was documented in 1994 using lots of body parts, including the naughty bits, to reach 33, counting by anatomy.

And Women could count to 34... 

Sorry, I couldn't miss that opportunity.

Actually, the Papuan system included both nipples, which males have as well as females.

[JustMeHere]

Any set that has a fixed universe of values.  The null value may not fit in that set though.  Probably not.

[TimFox]

Genesis 15.5
"Look now toward heaven, and tell the stars, if thou be able to number them"

[radiolistener]

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

Term "Digital" is used for a digital circuit where the signal must be one of two discrete levels. Each level is interpreted as one of two different states (for example, on/off, 0/1, true/false).

If you combine 3 or 4 digital signals (with binary level) it still Digital, because uses digital signals.

But if signal has more than 2 levels (is not binary) it is not "Digital". Technically you can name it as "Analog".

For example, the signal which have 3 possible levels can be processed with ternary logic elements, but ternary logic is different from digital logic which uses binary signal representation. Ternary logic has different rules and different math, and such ternary logic is not common, so you can't name it as digital, because digital logic works with signals represented with binary levels.

Also note that there is third type of circuit - Mixed Signal circuit. It used on boundary between Analog and Digital signals. For example ADC, DAC, etc.

You can simulate ternary logic with digital logic, such circuit will have digital part which works with binary signal levels and usual digital logic elements, and mixed signal part that converts from ternary analog signal to binary digital signal and vice versa.

This way was used for ternary computing experiments such as ternary computer "Сетунь" which was built in 1958 in the Soviet Union and was used to research ternary logic math.


First Nixie tubes had 10 digits and each digit was controlled by separate signal which had two possible levels - on and off (1 and 0). In such way one binary signal was used to control one digit. This is why binary signals get name "Digital"... 

[EPAIII]

Well, here I go, "top posting" again. You may not believe me, but I actually agree that it is annoying.

Years ago I was first introduced to e-mail at the company where I worked. They used it extensively. And I had to use it to answer messages that were sent to me. So I LOGICALLY placed my answers BELOW the text of the message, keeping things in proper order.

Well, they would have none of it. I was promptly scolded by multiple persons for being such an independent and logical thinker. I tried for a week or two, but when the e-mails had multiple levels of responses and the others were "top posted" it only confused things for me to add my response at the bottom.

You can't fight the world and, for better or worse, the world "top posts".

Or is there some rule on this board about this? I don't recall reading any.

    A: Because it messes up the order in which people normally read text.

    Q: Why is top-posting such a bad thing?

    A: Top-posting.

    Q: What is the most annoying thing in e-mail posted responses?

Been there! Done that!

Yes, I actually wrote programs and input them that way.

It isn't fun. Slow process so you have a very large incentive to minimize your code. But it did work. The machine in your photo is a lot nicer than the one I programmed. Mine had simple toggle switches and not near as many. That one looks like a dream by comparison.

Oh, and I didn't get the tee shirt. Wish I had.

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

Back in the day you could fiddle with the the computer's physical binary switches right in front of you, and be a real man - program it directly 1's and 0's. 

[jonpaul]

Hexeary logic:

The Top secret 1942 SIGSALY speech scrambler digitized Vovcoder analog parameters into one of 6 logarithmic levels. These were added MOD 6 with  a six level true random key, Vernam type code.

https://media.defense.gov/2021/Jul/13/2002761542/-1/-1/0/SIGSALY.PDF

My 2019 IEEE Spectrum articles

https://spectrum.ieee.org/rebuilding-a-piece-of-the-first-digital-voice-scrambler
https://spectrum.ieee.org/sigsaly-analogtodigital-converter-construction-and-debugging

Enjoy!
\ Jon

[tggzzz]

Top posts can work for fast single-point responses between two people. If there are interleaved conversations and/or multiple people, top-posting becomes a nightmare.

Well, here I go, "top posting" again. You may not believe me, but I actually agree that it is annoying.

So, you choose to do something annoying (your description). Why?

Years ago I was first introduced to e-mail at the company where I worked. They used it extensively. And I had to use it to answer messages that were sent to me. So I LOGICALLY placed my answers BELOW the text of the message, keeping things in proper order.

Well, they would have none of it. I was promptly scolded by multiple persons for being such an independent and logical thinker. I tried for a week or two, but when the e-mails had multiple levels of responses and the others were "top posted" it only confused things for me to add my response at the bottom.

Why did you continue to work there? That would have been a red flag to me!

You can't fight the world and, for better or worse, the world "top posts".

This forum is not the world, oddly enough. See next point.

Or is there some rule on this board about this? I don't recall reading any.

As for a formal rule, no - and there shouldn't be. But that's unimportant. What's important is to observe the way people in the "society" interact, because that's an important part of why the society works.

Or doesn't work, see edaboard and stackexchange which, while fine for boring "which button do I press to floggle the widget" questions, are useless for interesting subtle conversations.

    A: Because it messes up the order in which people normally read text.

    Q: Why is top-posting such a bad thing?

    A: Top-posting.

    Q: What is the most annoying thing in e-mail posted responses?

Been there! Done that!

Yes, I actually wrote programs and input them that way.

It isn't fun. Slow process so you have a very large incentive to minimize your code. But it did work. The machine in your photo is a lot nicer than the one I programmed. Mine had simple toggle switches and not near as many. That one looks like a dream by comparison.

Oh, and I didn't get the tee shirt. Wish I had.

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

Back in the day you could fiddle with the the computer's physical binary switches right in front of you, and be a real man - program it directly 1's and 0's. 

[TimFox]

Back to the original question, here is a practical example of the distinction.
Imagine a weighing scale, with a digital readout.
It can be made using an analog sensor, such as a strain gauge, that requires an analog circuit to measure the strain (force) and convert it to a continuous voltage.
That analog signal then goes into an ADC  (analog-to-digital converter), which puts out a series of digital values (discrete multiple-binary-bit words).
That digital signal train then goes into appropriate digital circuitry, including a digital processor, to compute desired values (in grams, ounces, taels, etc.) that go to the driver circuits to produce decimal patterns on Nixie tubes, LEDs, or a screen.
Both signal types have their origins and uses.

[BeBuLamar]

For the question in the tittle. They are all digital whether it's binary or decimal, hex, octal etc... The term digital doesn't mean binary.

[radiolistener]

For the question in the tittle. They are all digital whether it's binary or decimal, hex, octal etc...

No! This is typical mistake that non binary signal is digital, you can name it Discrete if it has discrete N levels, but if N is not 2, then you cannot name it as Digital. As said above term digital is used for circuit which works with signals that have binary state representing 0 or 1. Because Digital means that it works in binary system with binary math and binary logic. If signal is not binary, it cannot be processed with binary math and such signal is NOT digital.

In theory you can create math and logic for any N-level discrete signals, but in practice such math will be complicated and needs research to understand it's properties. Binary logic and math is well known and analyzed, it already has a lot of components, so in practice only binary logic and math is used and such circuits are named Digital.

Non digital but discrete signals are often used in modern communications, for example gigabit ethernet uses PAM-5 modulation, this is discrete signal, but not digital. In order to process it with digital processing circuit it needs to be converted from analog to digital form. It can be done with ADC and DAC. And when its converted to digital signals (represented with binary levels) PHY chip can do further processing in digital domain with usual circuit elements which working with digital signals.

The term digital doesn't mean binary.

NO. The term digital means binary, this is synonym for binary and cannot be used for system which works with non binary signals.

[radiolistener]

Just for your information:

Merriam-Webster's Dictionary:

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

Oxford Learners Dictionaries:

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

Tech Terms Dictionary:

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.

[TimFox]

If digital be synonymous with binary, there is no need for both terms.
Binary is a subset of digital.
Normal arithmetic is done with 10 digits.
A general definition from Wikipedia, which includes but is not limited to a single wire with a binary choice of states.
"A digital signal is a signal that represents data as a sequence of discrete values; at any given time it can only take on, at most, one of a finite number of values. This contrasts with an analog signal, which represents continuous values; at any given time it represents a real number within a continuous range of values."

[CatalinaWOW]

If digital is only binary, which is in turn a sequence of ones and zeros, then the output of a parallel out A-D converter is not digital because the output is not a sequence of ones and zeros.  It can only bet interpreted as a group of simultaneous sequences.

The interpretation I have just given is solely to illustrate the silliness of the how many angels can dance on the head of a pin argument going on here.

If for some reason it is important for your application to make a distinction between a binary and octal system, then more words are necessary to explain why that distinction is important and what that difference is.  Trying to load all of the possible minor differences that might require such a distinction is too much to load on a single word.

[radiolistener]

If digital be synonymous with binary, there is no need for both terms.

Actually Digital it is alias for Binary. Since many peoples are not familiar with term Binary, they don't know math and don't want to know about discrete math and other stuff, it's more easy for them to use term Digital. But if you're dealing with math, you can be happy with term binary.

For example the math for binary logic and for ternary logic is different and have different properties and different laws. Binary logic is usual logic that we know with it's own math rules. But ternary logic is different thing, it has it's own rules, different math and laws that many peoples don't know at all and even don't know that it is exists. The term digital is applied to circuit that working with well known binary logic. Don't confuse it with logic and math for other numbering systems.

[radiolistener]

If digital is only binary, which is in turn a sequence of ones and zeros, then the output of a parallel out A-D converter is not digital because the output is not a sequence of ones and zeros.  It can only bet interpreted as a group of simultaneous sequences.

AD converter is not digital, but not because it has group of digital lines, but because it works with both domains - Analog and Digital. Actually AD converter is Mixed Signal device.

The parallel bus part of AD converter is of course Digital, because it uses digital signals represented with two levels 1 and 0.

And analog input/output of AD converter is of course Analog, because it uses analog signal represented with more than two levels. For example if you use 2-bit DAC, it has analog output with 4 levels, 3-bit DAC has 8 levels, etc.

For DAC this analog signal is Discrete, but NOT Digital, because represented with non binary state.

Digital signal needs to be represented with binary state - 1 or 0. If it is represented with not binary state, then this is not digital signal. And all things known as Digital cannot be applied to such signal, because digital circuit works with binary state only.

If you see some circuit that works with non binary state signals, then this is NOT Digital circuit.

[CatalinaWOW]

If digital is only binary, which is in turn a sequence of ones and zeros, then the output of a parallel out A-D converter is not digital because the output is not a sequence of ones and zeros.  It can only bet interpreted as a group of simultaneous sequences.

AD converter is not digital, but not because it has group of digital lines, but because it works with both domains - Analog and Digital. Actually AD converter is Mixed Signal device.

The parallel bus part of AD converter is of course Digital, because it uses digital signals represented with two levels 1 and 0.

And analog input/output of AD converter is of course Analog, because it uses analog signal represented with more than two levels. For example if you use 2-bit DAC, it has analog output with 4 levels, 3-bit DAC has 8 levels, etc.

For DAC this analog signal is Discrete, but NOT Digital, because represented with non binary state.

Digital signal needs to be represented with binary state - 1 or 0. If it is represented with not binary state, then this is not digital signal. And all things known as Digital cannot be applied to such signal, because digital circuit works with binary state only.

If you see some circuit that works with non binary state signals, then this is NOT Digital circuit.

So in your opinion circuitry that works on four discrete voltage levels (some memories did this) are not digital, and hence analog?

[radiolistener]

So in your opinion circuitry that works on four discrete voltage levels (some memories did this) are not digital, and hence analog?

This is not my opinion, this is official meaning of word digital. 

Yes, part of memory circuit which works with four discrete levels is not digital, but analog.
Since memory chip also has digital controller which process that data, such memory chip is Mixed Signal circuit.
And since all these analog things are encapsulated and there is no analog input/output with 4 levels from that memory chip, you can assume it as digital, just because all input/output signals of the chip are digital. But internally it is Mixed Signal circuit, because part of it's circuit works with analog discrete signal which has 4 levels. 

[kjpye]

Merriam-Webster's Dictionary:

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

Note that word before the part you emphasised. "Especially" most definitely does not mean "only".

I suspect the other options you give are simplified for beginners.

Given the origins of the word digital, if it is restricted to only a single number base, then that must be decimal.

Calling all non-binary discrete systems analog makes the term analog useless,

[golden_labels]

radiolistener:
This is complete bullshit, contrary to actual usage, supported by a comically failed attempt in appeal to authority. You could at least read the backlog, where people working in the industry for decades share their experience or give actual examples.

This is an invalid argument, but since you considered it ok and it may be worth waking you up from your denial of reality, here is what your own sources say about word “analog”: Merriam-Webster, Oxford Learner’s Dictionaries, TechTerms, also Wiktionary. Now look at what you claim to be “analog” and stop making fool of yourself.

[radiolistener]

radiolistener:
This is complete bullshit, contrary to actual usage, supported by a comically failed attempt in appeal to authority. You could at least read the backlog, where people working in the industry for decades share their experience or give actual examples.

"This is complete bullshit" - this is what you will hear when you try to provide some signal which has 4 levels on digital GPIO pin of some controller and ask firmware developer to handle all 4 levels because this is "digital" signal...  And I will agree with him, because this is really complete bullshit.

If you're talking that the signal is digital, it should have two possible state 1 or 0.

And when you're talking that analog discrete signal with possible 4 levels is "digital", this is complete bullshit. Because there is no digital logic circuit that supports signal with 4 possible states.

You can name digital signal as analog and analog as digital for yourself, but if you're want so other people can understand you, you should use term digital for signals with 2 possible levels 1 and 0. And use analog term for signals which can have more than 2 possible levels.

This is an invalid argument[/b], but since you considered it ok and it may be worth waking you up from your denial of reality, here is what your own sources say about word “analog”

I don't needs to walk. Analog signal means that signal IS NOT DIGITAL. So, any signal which has more than 2 possible levels is analog. This is pretty easy...

In order to process analog signal in digital domain you're needs to convert it from analog domain to digital domain. And in order to generate analog signal from digital domain you're needs to convert from digital domain to analog domain. There is no way to process analog signal in digital domain without converting. And you're needs to learn the difference between analog domain and digital domain to avoid confusing them.

This is very simple:
- Digital signal has two possible states: 1 and 0.
- Analog signal has more than two possible states.

Grouping of several signals don't change their type. If you have 8 lines and all are digital, then this is digital bus, not analog. The same if you use 8 lines and all are analog, then this is analog bus, not digital.

[tggzzz]

Radiolistener, I don't know about the meanings in Ukranian (as per your country flag).

But in English and general engineering, you are wrong. Full stop.

If you want to try arguing by "appeals to authority", consider this definition... "In digital electronics, a digital signal is a pulse train (a pulse amplitude modulated signal), i.e. a sequence of fixed-width square wave electrical pulses or light pulses, each occupying one of a discrete number of levels of amplitude.[6][7] A special case is a logic signal or a binary signal, which varies between a low and a high signal level."
https://en.wikipedia.org/wiki/Digital_signal#In_digital_electronics

The other definitions on that page are also useful.

Having pointed that out, it is also worth pointing out that digital values are implemented as analogue waveforms where the receiver interprets the analogue waveform as a digital value.

[radiolistener]

Given the origins of the word digital, if it is restricted to only a single number base, then that must be decimal.

Origin of word digital is a binary signal which controls correspond digit on Nixie tube.

For there is 10 signals, each can have state 0 or 1, so we have:
0000000001 = decimal digit 0
0000000010 = decimal digit 1
0000000100 = decimal digit 2
0000001000 = decimal digit 3
...
1000000000 = decimal digit 9

As you can see these signals controls decimal digits on Nixie tube, each signal = digit, so they called "digital".

This is how it happened historically, so now you cannot name non binary signal as "digital", just because you want. It will leads to confusion.

It just happened that term digital is used for binary signals in electronics and you're needs to accept it as is.

Calling all non-binary discrete systems analog makes the term analog useless,

There is nothing useless, any non-binary discrete signal is analog, just because it is not digital.

For example discrete signal with 16777216 possible levels is analog signal.
The same discrete signal with 4 possible levels is also analog signal.

But discrete signal with 2 possible levels is digital.

Digital signals are used in digital domain. Digital domain uses digital components which work is based on Boolean logic and math.
Analog signals are used in analog domain. Analog domain uses analog circuits, but can be processed in digital domain with conversion.
All pretty clear and easy.