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

[oslon]

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?

[xrunner]

Digital fundamentally uses 0 and 1, that's binary. But if you want to group the ones and zeros as groups of three then you have octal like 777 (111 111 111) or 330 (011 011 000), etc, or groups of four for Hex like FFFF (1111 1111 1111 1111). Nevertheless it's still digital at the lowest level.

[EPAIII]

"Digital" is used as the opposite of "Analog". Both are ways of doing calculations or logical decisions in a machine. And both can use various technologies, such as electronic, electric, mechanical, pneumatic, hydraulic, and probably others.

An analog type of system uses a physical representation of a value or state. And this representation can, in theory, have an unlimited level of resolution. So, using a mathematical device, an old fashioned slide rule can be set to any place along it's scale. There is no theoretical limit on where it can be set within it's range. However it's accuracy is limited by real world considerations in setting or reading these values.

A digital system uses numbers to represent a value or state. These numbers can be of any base (10, 2/binary, 8/octal, 16/hexadecimal, etc.)  There are ways to work around this, but in general, a digital system will be limited to a certain number of digits in the number system that it uses. So the accuracy of most digital systems is limited by the number of digits and the number of those digits used in the base that is selected.

Although it may sound like digital would be more limited in accuracy, often it is the better of the two. Analog is usually limited by the ability to either set or read out an analog value while digital allows any number of digits to be easily entered or read out.

But then, it should be remembered that most digital systems rely on conversions from and/or back to analog. Only the calculations or decision making is done in the digital realm.

[themadhippy]

I was taught that digital can only be  1 or 0  and has something to do with a=a²

[TimFox]

"Digital" comes from counting on one's digits:  the steps are discrete.
"Binary" comes from having two choices:  1 or 0.
A "digital voltmeter" normally reads out in base 10, i.e. decimal.
There is more to "digital" than "binary".

[golden_labels]

More or less what EPAIII said. Digital systems work with discrete values. There is no limit to the number of states.

Binary signals are most common, due to simplicity of implementation and highest resilence to noise. But this is not a hard limitation. Negabinary (e.g. UMC-1, UMC-10 computers) and ternary were seen in the past, balanced ternary is used now in experimental solutions due to its compatibility with light-based computing, your flash memory is likely using octal or hexadecimal, wireless commonly uses 256 digits, and there QAM can nowadays go up to 32768 states.

[pdenisowski]

"Digital" comes from counting on one's digits

Or, as Tom Lehrer put it, "Octal is decimal without the thumbs"   

[Siwastaja]

Or decimal, octal, hexa are also digital system?

Yes, by very definition. Digital systems use discrete numbers, "digits". Underlying implementation is irrelevant, although it is often binary. Binary representations are subset of digital representations.

[Dan123456]

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 

[xrunner]

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. 

[golden_labels]

Real men program it directly with 1s and 0s.
Real programmers program it directly with cables.

[tggzzz]

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

Nope. Digital systems are quantised.

Some are ternary, e.g. +1,0,-1. Others have many more levels, e.g. QAM up to 8 bits per symbol https://en.wikipedia.org/wiki/Qam , or flash memory which can store 3 or more bits in each cell https://en.wikipedia.org/wiki/Triple-level_cell

[khs]

Nope. Digital systems are quantised.

Hmmmm: Maybe Mr. Heisenberg would say: All is quantised.

[tggzzz]

Nope. Digital systems are quantised.

Hmmmm: Maybe Mr. Heisenberg would say: All is quantised.

I like to point out that the outputs of digital circuits are analogue waveforms that are interpreted as by an input as a digital signal. Your measuring device (e.g. a scope) might interpret the waveforms differently, especially if there is analogue "noise" around.

The only digital waveforms people are likely to encounter are femtoamp and photon counting circuits

[TimFox]

I have been reading several histories of mathematics, with discussions ranging back to prehistory.
Base 5 and Base 10, using literal digits (fingers), are found in primitive societies, and Aristotle noticed the relationship between decimal notation and human hands.
Before computational aids, such as tally boards, some societies added the gaps between knuckles and other anatomical features to count past 10 or 20 (adding toes).
Sumerians may have been able to count in their Base 60 format (which still persists in time and angle measurement today) before writing numbers in cuneiform.
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.
Late in the first millenium, the Venerable Bede calculated using finger flexing, reaching 0 to 9 with three fingers, and up to 9,999 with two hands.
These early examples are all digital, counting only the "natural numbers" (mathematical term for the positive integers starting with 1).
A recent popular survey of such systems is Chapter 1 of Keith Houston: Empire of the Sum:  The rise and reign of the pocket calculator W W Norton 2023.
Binary means 0 or 1, Quinary means 1 to 5, Decimal means 1 to 10 or 0 to 9, etc.
"Vides ut primos discentes computos digitos tarda agitatione deflicant?"  Firmicus Maternus
(Do you see how awkwardly beginners in computation bend their fingers?)

[TimFox]

Nope. Digital systems are quantised.

Hmmmm: Maybe Mr. Heisenberg would say: All is quantised.

I like to point out that the outputs of digital circuits are analogue waveforms that are interpreted as by an input as a digital signal. Your measuring device (e.g. a scope) might interpret the waveforms differently, especially if there is analogue "noise" around.

The only digital waveforms people are likely to encounter are femtoamp and photon counting circuits

The analog waveforms present at the connector become digital after passing a threshold, like a camel passing through the eye of a needle.

[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?

Since last few years it’s new, trendy terminology “system” the same as “analog system” ...just ignore it
People are being bored and starting to  reinventing the wheel

[alligatorblues]

Most electronic devices are analog and digiital. The parts of the device that interact with the physical world are analog. Meter and scope inputs, digital thermometers, cell phones, or  anything that transforms a real-world reading to a digital readout. Analog components are susceptible to corruption due to various forms of interference and degradation. The beginning of the digital side is sampling. The analog component is sampled at various points. Each sample is assigned a number. In this process, the samples are reduced to binary, or base 2, for use in processing by mcu's, cpu's, and mask roms.

The advantage to digital is error checking. The digital representation will never degrade. Each group of bits is put through a hashsum algorithm when it is transmitted, which appends some bits to the packet.  Those bits are stripped off and stored at the receiving end. The original data is left, and it is hashsummed the same way. The bits stripped off are put back, and if the packets are identical, the receiving end instructs to send the next packet.

Transmitting a digital signal requires about 1/10 the power of an analog signal, and the signal quality is vastly superior. And, if it wasn't for digital electronics, there would be  no digital LCD readouts, only nixie tubes.Practically every electronic device interacts with the real world, so they use both analog and digital. Even computer moniitors process in digital, but convert the image to analog.
 

[Mr.B]

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.

[TimFox]

Most electronic devices are analog and digiital. The parts of the device that interact with the physical world are analog. Meter and scope inputs, digital thermometers, cell phones, or  anything that transforms a real-world reading to a digital readout. Analog components are susceptible to corruption due to various forms of interference and degradation. The beginning of the digital side is sampling. The analog component is sampled at various points. Each sample is assigned a number. In this process, the samples are reduced to binary, or base 2, for use in processing by mcu's, cpu's, and mask roms.

The advantage to digital is error checking. The digital representation will never degrade. Each group of bits is put through a hashsum algorithm when it is transmitted, which appends some bits to the packet.  Those bits are stripped off and stored at the receiving end. The original data is left, and it is hashsummed the same way. The bits stripped off are put back, and if the packets are identical, the receiving end instructs to send the next packet.

Transmitting a digital signal requires about 1/10 the power of an analog signal, and the signal quality is vastly superior. And, if it wasn't for digital electronics, there would be  no digital LCD readouts, only nixie tubes.Practically every electronic device interacts with the real world, so they use both analog and digital. Even computer moniitors process in digital, but convert the image to analog.

Nixie tubes are used in digital systems.  The digital representation of the discrete value is decoded to select one of 10 (or more) discrete electrodes in the Nixie tube for display.
Segmented LED or LCD readouts decode the value into a selection of an appropriate pattern of segments.
This is all done with digital logic circuits.

Perhaps you are confusing Nixie tubes (gas-discharge glow devices) with cathode-ray tubes (that can display continuous waveforms)?

[EPAIII]

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 

[EPAIII]

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. 

[tggzzz]

    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. 

[tggzzz]

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

Nope. Digital systems are quantised.

Some are ternary, e.g. +1,0,-1. Others have many more levels, e.g. QAM up to 8 bits per symbol https://en.wikipedia.org/wiki/Qam , or flash memory which can store 3 or more bits in each cell https://en.wikipedia.org/wiki/Triple-level_cell

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

[TimFox]

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.