Why binary is represented by two bits 0 and 1 and not three bits?

[tggzzz]

Analogue computers work by solving differential equations.
Electronic analogue computers use opamps to integrate, add, and multiply.
Mechanical analogue computers use cogs, wheels, motors, wires.

And real programmers use water: https://en.wikipedia.org/wiki/Water_integrator

And real electronic engineers use gas for their logic circuits: https://www.symscape.com/blog/fluidic-logic

I once had a job assessing whether to replace fluidic logic with a microprocessor; I recommended against it.

The logic was on unmanned offshore oil rigs with zero electricity for safety reasons. Adding electricity was possible but had no advantages and many disadvantages.

[tooki]

I think the take-home message here is that often, when people ask "why is x always done like this?" or "why don't we do x [some unusual way]?", they are blithely unaware that all the other ways typically have been tried before, and the reason x became the dominant way is because it has clear advantages.

Ideas aren't nearly as unique and special as people think they are. It's implementations that are difficult!

[konzill]

Looking at the Wikipedia page on trinary logic, it turns out that there isn't even a consensus on how to build a trinary truth table. The page lists half a dozen different trinary logic systems. So yes it goes back to, its rarely done because it adds complexity. 

Even at a basic level having to differentiate three voltage levels, instead of two would make a circuit more suceptable to noise.

[Syntax Error]

@tip.can19 - Binary and it's associated Boolean logic also fits our statefull view of the world; states such as yes-no, up-down, on-off, in-out, high-low, push-pull, mark-space, set-reset, left-right, true-false. Alternate states like whatever, dunno and Brexit, don't work when making decisions as they are not finite states.

Being caught between finite states is being in the noise. A transition between two finite states is the hysteresis. In digital, this is the rate of change of voltage to what is regarded as a stable logic 0 or 1. Real-world, this might involve the thinking time about which shirt to wear on a date; the flowery one or the clean one?

Geek out on Boolean algebra https://en.wikipedia.org/wiki/Boolean_algebra
Geek out on Hysteresis https://en.wikipedia.org/wiki/Hysteresis
Geek out on the Finite State Machine https://en.wikipedia.org/wiki/Finite-state_machine

P.S. Thinking about this, in data analysis, it is possible for an outcome to have three states; an outcome can be none, one or many. I believe this none/one/many concept was created by Australian Aboriginal people tens of thousands of years ago. Clever dudes.

[Vtile]

Why binary not ternary.. I suppose one interesting reason is that all widely used number systems are even based, 2,8,10,16,60.

[Canis Dirus Leidy]

And real programmers use water: https://en.wikipedia.org/wiki/Water_integrator

And real electronic engineers use gas for their logic circuits: https://www.symscape.com/blog/fluidic-logic

Русские физики выбирают Slackware АВК-6!

(The most remarkable thing is that this is a page from an advertising catalog of consumer products).

[tggzzz]

@tip.can19 - Binary and it's associated Boolean logic also fits our statefull view of the world; states such as yes-no, up-down, on-off, in-out, high-low, push-pull, mark-space, set-reset, left-right, true-false. Alternate states like whatever, dunno and Brexit, don't work when making decisions as they are not finite states.

Not true. The value of a state is usually not binary, and in any case is orthogonal to the mechanism used to implement it.

A very simple example might be the state of an electrically opened door with possible states {open, closed, opening, closing, broken}.

I can't be bothered to point out the flaws in your other points.

[paulca]

Almost all information can be recorded as a serious of Yes, No answers to questions.  As long as you keep the questions and the answers that information can be reconstructed.

Although, be careful, when you look at the analogue side of digital circuits they are very often tri-state.  1, 0 and floating.  The later is sometimes a burden, but sometimes can be used to your advantage.  You might have a chip which has a 0 or a 1 (high or low) on it's outputs, but when you pull the "chip enable" low they disconnect the the outputs which gives you a third state which you can pull high or low with a resistor for your purposes.

[tggzzz]

Although, be careful, when you look at the analogue side of digital circuits they are very often tri-state.  1, 0 and floating.  The later is sometimes a burden, but sometimes can be used to your advantage.  You might have a chip which has a 0 or a 1 (high or low) on it's outputs, but when you pull the "chip enable" low they disconnect the the outputs which gives you a third state which you can pull high or low with a resistor for your purposes.

All "digital" circuits are actually analogue; that's most obvious with ECL and derivatives. Some CMOS logic gates can be used as linear amplifiers.

Logic gates interpret input voltages/currents as digital signals. When those inputs are within defined limits, the gate's outputs will (eventually) be within limits that other gates can interpret as a digital signal.

The few digital circuits that you might encounter include photon counting devices and femtoamp circuits.

[Syntax Error]

Not true.
...
I can't be bothered to point out the flaws in your other points.

In binary logic the door has an exclusive true state for IsClosing or IsOpening and then, a true state for IsClosed or IsOpen. And only if HasFailed is false (not true). You might need to know the open angle, but that's not a state, it's a property.

[paulca]

Glider pilot's aphorism: "there is no substitute for span". Retort: "There is a substitute: skill+imagination. But you can buy span".

As a paraglider pilot from a windy country, the bigger the span the more likely you'll be dragged like a rag doll up the hill   Kite surfers tell me they have a 9m2 wing... mine is 29m2 and in a 15mph wind, in it's power zone will pull a family car.

[tggzzz]

Not true.
...
I can't be bothered to point out the flaws in your other points.

In binary logic the door has an exclusive true state for IsClosing or IsOpening and then, a true state for IsClosed or IsOpen. And only if HasFailed is false (not true). You might need to know the open angle, but that's not a state, it's a property.

False, in every respect.

Your FSM might have that and the states might be encoded in that way, and such an FSM might work in your case. But that's all.

You should start by understanding the various at the low-level techniques used to implement the state in an FSM, e.g. https://www.allaboutcircuits.com/technical-articles/encoding-the-states-of-a-finite-state-machine-vhdl/

You should continue by understanding the concepts of how to design and express FSMs in a technology independent way. Clearly FSMs can be implemented in hardware, software or frequently in a combination of the two. Harel's StateCharts have become popular in the last 30 years http://www.inf.ed.ac.uk/teaching/courses/seoc/2005_2006/resources/statecharts.pdf but there are many other formalisms.

[BrianHG]

Why binary not ternary.. I suppose one interesting reason is that all widely used number systems are even based, 2,8,10,16,60.

That's only after the invention of '0'.

[tggzzz]

Glider pilot's aphorism: "there is no substitute for span". Retort: "There is a substitute: skill+imagination. But you can buy span".

As a paraglider pilot from a windy country, the bigger the span the more likely you'll be dragged like a rag doll up the hill   Kite surfers tell me they have a 9m2 wing... mine is 29m2 and in a 15mph wind, in it's power zone will pull a family car.

Yeah, but you can't go at 150kt, nor up to 37k ft (intentionally at least!), and there is the noticable possibility that the oversized handkerchief might collapse. Me biassed? Shurely shome mishtake.

(In the absence of hills, I was towed aloft under a 'chute behind a car on an airfield a couple of times, and have landed in a light aircraft 1/7 of the times I took off in one )

[paulca]

Glider pilot's aphorism: "there is no substitute for span". Retort: "There is a substitute: skill+imagination. But you can buy span".

As a paraglider pilot from a windy country, the bigger the span the more likely you'll be dragged like a rag doll up the hill   Kite surfers tell me they have a 9m2 wing... mine is 29m2 and in a 15mph wind, in it's power zone will pull a family car.

Yeah, but you can't go at 150kt, nor up to 37k ft (intentionally at least!), and there is the noticable possibility that the oversized handkerchief might collapse. Me biassed? Shurely shome mishtake.

(In the absence of hills, I was towed aloft under a 'chute behind a car on an airfield a couple of times, and have landed in a light aircraft 1/7 of the times I took off in one )

LOL.  Unfortunately paraglider pilots have found themselves up there before.  Found unconscious, hypoxic and covered in hail storm bruises, but alive.

I suppose the only advantage I have is that I can carry my glider to the top of the hill and launch and don't need a trailer to get it out of a farmers field   Who needs to go faster than 25knots anyway, it's much easier staying in small thermals when you can orbit inside 10 meters

[tggzzz]

Glider pilot's aphorism: "there is no substitute for span". Retort: "There is a substitute: skill+imagination. But you can buy span".

As a paraglider pilot from a windy country, the bigger the span the more likely you'll be dragged like a rag doll up the hill   Kite surfers tell me they have a 9m2 wing... mine is 29m2 and in a 15mph wind, in it's power zone will pull a family car.

Yeah, but you can't go at 150kt, nor up to 37k ft (intentionally at least!), and there is the noticable possibility that the oversized handkerchief might collapse. Me biassed? Shurely shome mishtake.

(In the absence of hills, I was towed aloft under a 'chute behind a car on an airfield a couple of times, and have landed in a light aircraft 1/7 of the times I took off in one )

LOL.  Unfortunately paraglider pilots have found themselves up there before.  Found unconscious, hypoxic and covered in hail storm bruises, but alive.

Nasty. I suppose the hypothermia partially offset the effects of hypoxia.

I do remember a report of a competition in the Phillipines(?) where about 40 competitors were carried up by a cumulonimbus and turned into corpsicles.

But competitors always push the envelope (ho ho), and long may it remain so. ISTR that about 10% of the top glider pilots have died in competitions.

I suppose the only advantage I have is that I can carry my glider to the top of the hill and launch and don't need a trailer to get it out of a farmers field   Who needs to go faster than 25knots anyway, it's much easier staying in small thermals when you can orbit inside 10 meters

Oooh, picky picky picky

I've flown (just) solo at 29kt, and tandem at about 20kt in an old "barge" trainer. I've also watched the latter loop with a noticeably small radius; must have scared the bejasus out of the woodworm

More entertainingly, I've been in a updraft (can't have been a thermal with unbroken stratus at 3k4ft), at 10kt up, banking at 70degrees, pulling 3G for a minute or so until cloudbase. We kept an eye on the other glider at the same height by looking upwards at the top of his head That was a new experience for an instructor that had been instructing for half a century.

[paulca]

3k4ft), at 10kt up, banking at 70degrees, pulling 3G for a minute or so until cloudbase. We kept an eye on the other glider at the same height by looking upwards at the top of his head That was a new experience for an instructor that had been instructing for half a century.

Only an electronics engineer would report 3400ft as 3k4ft

I'm fairly green and to be honest I haven't been doing it for a few years, but my first experience of a proper thermal under my hanky really freaked me.  The lines stretched, pinged and sung, I was pinned down into the seat, vario screaming faster and higher pitched beeping, I could visibly see the hill in front of me drop away...  then I shot straight through it and the instructor was like "Turn Paul, Turn, you gotta turn in lift."  I was like, "F... that, I'm going back into that beast.", the vario measured 3m/s vertical peak.  Just a little hill side thermal, but a fun ride.

[pwlps]

From yet another perspective: many fast algorithms are based on two-way branching (e.g. binary search) and these can often be implemented more efficiently with binary number arithmetic.  See e.g. https://en.wikipedia.org/wiki/CORDIC  (often used in FPGA implementations).

[TomS_]

I was wondering if digital systems work in binary 0 and 1, why is it so? Why not have 0, 1 and 2 (or some other constant/variable to make it three) and let three numbers represent a digital system?

Is there a specific reason behind this? Just curious.

Thank you,

One way you might be able to understand would be to look at the construction of a binary adder circuit, and then compare it to a circuit that could add various other levels or values of voltages or signals, and compare the complexity.

Its very easy to add and subtract in binary (and in relation to binary only having two states, the key is "bi" which means "two") with minimal circuitry. Once you can add and subtract you can also, with some repetition, multiply and divide quite easily too.

You might also take a look at Ben Eater on YouTube. He has a series where he builds a small "CPU" out of logic chips, of which part is an ALU. He goes in to some detail about how various functions in an ALU work.

Analogue computers were available, and Dave has a video about opamps with some information about how they can be used to do certain functions like add or multiply. But, there is usually always a reason one technology surpasses all others that do the same job - and its usually always lower cost. And you dont normally get lower cost from more complex things.

[TimFox]

Although, be careful, when you look at the analogue side of digital circuits they are very often tri-state.  1, 0 and floating.  The later is sometimes a burden, but sometimes can be used to your advantage.  You might have a chip which has a 0 or a 1 (high or low) on it's outputs, but when you pull the "chip enable" low they disconnect the the outputs which gives you a third state which you can pull high or low with a resistor for your purposes.

All "digital" circuits are actually analogue; that's most obvious with ECL and derivatives. Some CMOS logic gates can be used as linear amplifiers.

Logic gates interpret input voltages/currents as digital signals. When those inputs are within defined limits, the gate's outputs will (eventually) be within limits that other gates can interpret as a digital signal.

The few digital circuits that you might encounter include photon counting devices and femtoamp circuits.

Relay logic uses truly discrete binary signals

[alexanderbrevig]

Trits? Qbits it where it's at 

[Vtile]

Why binary not ternary.. I suppose one interesting reason is that all widely used number systems are even based, 2,8,10,16,60.

That's only after the invention of '0'.

Do you refer zero as logical or numerical operator or both. 

[tggzzz]

Although, be careful, when you look at the analogue side of digital circuits they are very often tri-state.  1, 0 and floating.  The later is sometimes a burden, but sometimes can be used to your advantage.  You might have a chip which has a 0 or a 1 (high or low) on it's outputs, but when you pull the "chip enable" low they disconnect the the outputs which gives you a third state which you can pull high or low with a resistor for your purposes.

All "digital" circuits are actually analogue; that's most obvious with ECL and derivatives. Some CMOS logic gates can be used as linear amplifiers.

Logic gates interpret input voltages/currents as digital signals. When those inputs are within defined limits, the gate's outputs will (eventually) be within limits that other gates can interpret as a digital signal.

The few digital circuits that you might encounter include photon counting devices and femtoamp circuits.

Relay logic uses truly discrete binary signals

No.

You are halfway there but your are conflating/equating digital signals with the analogue variables (voltage/current) used to represent digital signals.

Consider, for example, that if the current is marginally less than the latch in (or hold) currents, the relay will not reliably be in the expected state.

[T3sl4co1l]

Or even worse, what if a relay starts chattering, or a contact starts arcing at a rate faster than subsequent coils can respond?  How could those conditions possibly be expressed purely in relay logic states?

Everything is fundamentally analog, because the flow of charge and electromagnetic fields are continuous and not quantized (at least, not to any degree we care about, and even then, not in nearly the same way).

I'll add this just because it's a common retort -- shot noise proves the electric charge is quantized as electrons, but it doesn't mean charge or current is quantized in bulk.  If I move a charged comb around sufficiently slowly, I will affect the field in its vicinity by less than an electron's worth of charge -- when charges are able to move freely, there is no shot noise (or not as much), and so it is perfectly meaningful to speak of continuum charge.

(I would make similar arguments regarding quantum mechanics as well, but I doubt it would be very productive to do so.)

Tim

[tggzzz]

Or even worse, what if a relay starts chattering, or a contact starts arcing at a rate faster than subsequent coils can respond?  How could those conditions possibly be expressed purely in relay logic states?

Indeed. I considered mentioning that, but thought it an unnecessarily "complex" version of the simpler point.

I also considered mentioning metastability

Everything is fundamentally analog, because the flow of charge and electromagnetic fields are continuous and not quantized (at least, not to any degree we care about, and even then, not in nearly the same way).

Photon counting applications with, say, an APD?

Sure the pulse out of an APD is analogue, but the photon signal is digital.

I'll add this just because it's a common retort -- shot noise proves the electric charge is quantized as electrons, but it doesn't mean charge or current is quantized in bulk.  If I move a charged comb around sufficiently slowly, I will affect the field in its vicinity by less than an electron's worth of charge -- when charges are able to move freely, there is no shot noise (or not as much), and so it is perfectly meaningful to speak of continuum charge.

It looks like you are conflating "electric field" with "charge". Analogy: if I have a 1kg weight on a balanced lever, moving the pivot changes the counterbalancing force by less than (or more than) 1kg.