Slashdot Mirror
Ternary Computing Revisited
Black Acid writes: "American Scientist's Third Base was a nice introduction to the advantages base 3 but didn't really explain ternary computing. Since 1995, Steve Grubb has maintained trinary.cc which covers many aspects of computing with base 3. Not only are the basic unary and binary gates enumerated, which I independently verified as being basic building blocks, but real-world circuits are described also. Half and full adders, multiplexers and demultiplexers, counters, shift registers, and even the legendary flip-flap-flop are all covered with ternary algebra equations and schematics. Steve Grubb touches on problems of of interfacing to binary computers elegantly, although no schematics are given. Perhaps most impressive are the Transistor Models - schematics of the basic gates which can be built from cheap parts available at your local electronic component store."
does ternary processing mean you will be using on, off, and some third state of electricity? "dim"?
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fight global cooling
If a Bit is short for Binary Digit...
Does that mean that a Ternary digit is a 'Tart'? Do 8 Tarts make a 'Tight'?
We could be having MegaTights of Ram, and GigaTights (or even TeraTights) of disk!
Tony
Just wondering.
However, in stodgy old binary, the levels are typically something like 0 Volts (i.e. "off") and 5 Volts (or 3.5 Volts). A "typical" ternary system would add a negative voltage, like -5V (or -3.5V), since that's easier to detect reliably than an intermediate positive voltage value.
So to answer your question, yes a "third state of electricity" is used, one which was previously being ignored in binary circuits. Instead of on, off, and dim, think of positive, off, and negative.
This is all nice, but if we have to go to all the effort to reinvent the wheel , why not go all the way, I mean if we have to come up with all new components and software why no go the Analog route ?
Digital computing gained popularity for many reasons, cost effective to build, easy to program, with the state of current electronics this is no longer neccesarly the case but we there ,
Analog copmuting has many advantages over digital computing, especially in the AI arena, Since there can never be a digital concept of infinity
Rockets in the beggining were put into orbit using ANALOG computers, there is a reason, accuracy to the nth factor.
I played around with analog computing in the 70-early 80's cool stuff if more would have been available, fact wsas everyone was happy with their 8 bit pc.
Trinary computing sounds a little like taking something that was settled on in the first place and resettling again
I mean come on isnt the goal of computing to have a supercomputer take control of our national defense grid when it becomes sentient ?
Sig went tro...aahemmm.....fishing........
To be honest I say "who cares" if I'm running on a base 2, base 3, base 98 or Analogue computer. The vast majority of applications are written in languages that are then compiled to the wire. So use the most efficient deployment machine but it doesn't effect your day to day job. There appears in general to be too much in computing about the next whiz bang feature from marketing rather than developing from the building blocks we already have.
Sure this sort of thing is "interesting", but what is the actual benefit of writing applications in HLL that are then compiled down to this instruction set or that ? If it runs faster and is more reliable then fair enough but most of this is redundant as in reality a slower processor that has had more development time in its compiler will probably function better than a faster processor with a poor compiler.
This obsession with the quirky and the new is indicative of marketing and the hacking culture of computing as it now stands, M$ are probably the worst proponents of this approach but no other really make a stand against it.
This isn't "Stuff that matters" its "irrelevant stuff to pass sometime"
When was the last time anyone read an article _anywhere_ that talks about building on the current technology base rather than re-inventing the wheel. Linux has succeeded by building on the past. M$ have succeeded by continually re-inventing it. This is yet another example of the desire for "new or different" over getting hands dirty and improving what is there
An Eye for an Eye will make the whole world blind - Gandhi
One of the engineering problems w.r.t. trenary computing is how to have a crypto algoritm for trenary computing, since all of the modern crypto schemes assume binary computing.
One of the nice things about the Rijndael crypto algorithm is that, becuase of its "wide trail strategy" design, it is easy to adopt to different environments, including trenary computing.
I am sure that a variant of Rijndael which does everyting in "trits" instead of "bits" would have the same security features as the current Rijndael algorithm. The only thing that would have to be re-invented is the sbox. The rest (changing the galois field to a 3-base instead of a 2-base galois field, and chainging the MDS matrix used) could be simply adopted.
- Sam
The secret to enjoying Slashdot is to realize that it should not be taken too seriously.
i guess every average geek can now make it to 3rd base with their girl. all they need to do is to visit radioshack and purchase their on-and-off switches and gates - sounds like someone's semi-automatic gun's fully loaded already! ;-)
my blog
A very similar story was posted less than three weeks ago. Many of the replies were lame jokes about Tits and Yes|No|Maybe logic - please don't make us suffer them again.
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Reverse outsourcing: it's the future
Easy answer: Signal to Noise ratio renders ternary logic useless. Either it comes at a slower speed than binary logic or at higher power consumption.
In addition - the site design doesnt make it look very credible..
Actually, as the previous article (Third Base) pointed out, it really is -1, 0, and 1. this system works even better than 0, 1, 2 since it it symmetrically balanced. That article used a symbol similar to a 1 with a hyphen through it, for which I'll use the "t" key.
The example given is 19, which in 0, 1, 2 is expressed as 201 [ (2* 3^2) + (0* 3^1) + (1* 3^0) ] = 18 + 0 + 1 = 19.
In -1, 0, 1 this is represented as 1t01 [ (1* 3^3) + (-1* 3^2) + (0* 3^1) + (1* 3^0) ] = 27 - 9 + 0 + 1 = 19.
Although it does often take more digits to represent the number via the second method, the balanced system does have many advantages. Without getting to deeply involved, the important one is that you have one system fo both positive and negative number, thus eliminating the need for the actual sign.
I hope this basic summary of that previous article helps.
"Omnia quia sunt, umbra sunt."
The whois record for trinary.cc says the registration date was 2000-04-14. Did Steve Grubb maintain the content elsewhere, and then move it over to the trinary.cc domain upon registration?
was always half the fun!
Okay god that was bad
The ultimate network admin tool needs HELP!
One thing I've wondered about is the "closed world" logic problem - rather than binary logic true/false, how about true/false/don't-know ? I would have thought balanced ternary computers would be better equipped to handle such "real world" problems - e.g. -1, 0 , +1 == false, dunno, true.
"Dude, check this out. So I'm reading this news site for nerds, right, and I see this article on computers that work on some "base 3" kinda deal. So I'm like Damn! Those PCs can get to third base! I wonder if I can learn some tips from em?"
"So I call one up and we agree to meet out at Woody's on 4th. And this PC never shows up. So I just keep drinking, waiting for it. I musta had too many because all I know is that I woke up in this apartment on 84th with these three midgets screaming at me in portugeuse."
"Damn unreliable computers."
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Let me give you the lowdown
Err how would that be broken exactly by a move to base3. Guess what you can represent base 2 directly in base 3. In the same way as working in base 10 doesn't break on a base 2 machine. The definition of & etc are within the specification of the language, to take advantage of the base 3 processor you'd need base 3 operators and base 3 syntax for those operators (if x, else y, else). It would not break anything that currently exists.
I'd ask for a refund on that college education if I were you.
An Eye for an Eye will make the whole world blind - Gandhi
Naturally, such systems get enhanced so they can send more data at the cost of a little harmonic purity. For expample, they could get 50% more data through by using pairs of trits to send 3 binary bits. The 9th state would be used to prevent leaving the line at one voltage level too long. The real encodings are better behaved in the analog domain, and therefore more complex, but lookup tables for the trit to binary conversions take very little silicon.
For those who haven't memorized powers of three, if trinary logic, memory or signalling works better in some situation, 1 trit holds 1 bit, 2 trits hold 3 bits, 12 trits hold 19 bits, 31 trits hold 49 bits, etc...
Going the reverse is also very simple. If you have an algorithm that works better in trinary, store 1 trit in 2 bits, 3 trits in 5 bits, 5 trits in 8 bits, etc... You don't need special hardware.
Cyclic groups are integers modulo n where n is 2,4,p^m,or 2*p^m where p is an ODD prime. This means that (mod 2^m) is not a cyclic group while (mod 3^m) is. Cyclic groups have manifested themselves in numerous cryptographic and number theory applications and ternary computers can implement a (mod 3^m) group as quickly as a binary computer can implement a (mod 2^m) field, all you have to do is discard the most significant digits
I have been trying to implement a Number Theoretic Transform based multiplication system and not being able to choose a power of two as my modulus is causing a major speed loss. Even though switching to a ternary base (in hardware) would not lead to more than a linear speed difference, having low level functions run two to eight times faster, and doing away with the ugly code used to modulo a prime) is nice.
One of his claims is that trinary logic is "better" than binary because it uses another "natural" state of electricity: flow forwards, flow off, and flow backwards. He uses example power supplies of +3v, 0, and -3v.
However, this is *no different* than power supplies of 0, +3v, and +6v. Shifting your voltage reference does *not* change the power consumed.
Trinary also does not change your noise margins. Noise margins are a function of the actual circuit, and in an ideal world the noise margins on the high and low sides would be at half the representation voltage. 2.5 volts for 5-volt TTL logic, for example. 1.5 volts for 6-volt trinary logic, for example. See the noise margins decrease? You would have to increase the voltage range to 10 volts to maintain the noise margins. And therefore you would increase the power consumed. And power rises as the *square* of the voltage.
So let's see. Assuming your gates are feeding 1k resistors, binary logic would consume either 0mA (for a 0) or 25mA (for a 1). Assuming uniformly random distribution of bits, each bit would consume an average of 12.5mA.
For trinary, and maintaining the noise margins, a 0 would consume 0mA, a 1 would consume 25mA, and a 2 would consume 100mA. Average of 41.7mA. Since each "trit" conveys 3/2 as much information as a bit, the equivalent power consumption per bit for trinary logic is 27.8mA.
So trinary logic consumes more power per bit than binary logic.
Bummer.
Electrically, implementation is inevitably binary, at its core... electrical comparisons of boundary conditions. "Trinary" is just a minimal case of "analog", with all of the same disadvantages.
You want the same noise margins? You'll have to double your voltage. That means you're cutting your speed in half. So overall you're taking a loss because at half speed you could have gotten two whole bits for your money instead of one lousey trit.
Not to mention the fact that you're using more power, switching between these trinary states due to the longer transition and detection times. Oh boy! Hotter chips! Bleah!
update comments set karma=-1, reason='offtopic' where sid=26315
I was thinking, if properly designed a trinary processor's VM instructions could designate parts of memory, both code and data, with a "binary" bit. This would have the processor emulate binary in microcode much more efficiently than a compiler/emulator would.
Of course, using an expensive trinary computer and running everything binary on it, it wouldn't seem to make much sense, but this is the same as Intel's Itanium/AMD's Sledgehammer project.
And it makes sense too, MS could very quickly get a version of WinWhatever out (just rewrite some critical sections in trinary). A linux distro would recompile everything by default in binary except those package whose autoconf recognizes a trinary system.
Of course, non of this may ever happen, or it might happen in 5,10,25 years *shrug*.
The whole premise of CMOS and small geometry process technology (e.g. 0.13um) is that in the static state, the basic gate consumes virtually no significant power. This is because at least one of the two transistors in a basic inverter configuration are operating in cut-off mode non-linear regions, which means that they do not allow current to flow between power and ground. (Actually they do but the charge carriers are in the minority by at least 10 orders of magnitude typically, but it is unmeasurable).
I also counted five resistors, two independent voltage sources, and the transistors are bipolar junction transistors in the basic inverter. Resitors are expensive and take up real-estate on a chip, not to mention consuming major power and the fact that in a CMOS gate there are no resistors. It would be impossible to get two voltages to every gate in a design, unlike CMOS which uses a single routed voltage for internal digital gate operation and the substrate for ground. Finally, bipolar junction transistors are larger to fabricate than their CMOS equivalents, take more processing steps which makes them inherently lower yield, and consume measurable power and provide a path from voltage source to ground at all times.
You also have the fact that no major design tools even support trinary computing or methods, and that all major I/O interfaces for computing today have, as their input, binary, and it becomes difficult to even interface with new electronics, much less design with them. Certainly, none of the big design tool manufacturers have or will have trinary support to do any of this type of design on a large scale, pardon the pun.
In other words, besides being an interesting hobby project, this is definitely NOT the wave of the future for practical purposes. I give him a lot of credit for developing an entirely new system of algebra and even giving something that can actually be built - this is quite an intelligent person here. Perhaps quantum computing will take advantage of non base-2 math if there are more than two quantum states, for example (and I'm not a quantum physicist, so I don't know, sorry...). But even the slightest thought of using this in a commercial application is not really believable.
Looking at the schematics I see that it is based on a analog design style. The transistors are bipolar and there are plenty of resistors used for biasing. All in all, it looks more like an amplifier than a digital gate.
A previous poster commented on returning to analog computing. While there are several major problems with analog computing, I want to just mention a few.
High Implementation Cost
Currently, resistors are considered a somewhat "expensive" item in VLSI designs, since they use a lot of area and lead to static power dissipation. Using bipolars instead od MOSFETS is probably a mistake from a fabrication standpoint, but I don't see why the schematic couldn't be modified to take this into account.
In other words, any design using these gates would be big and power hungry. This isn't to say that a base-3 system is infeasible, only that this implementation doen't map very well to existing technology.
I think a MOSFET only implementaion would be required before we can take base-3 really seriously. Maybe something using depletion mode MOSFETS would work better.
No Component Architecture
Analog components are difficult to interconnect. Without going into too much detail, they don't just snap togeater like legos; rather, each brick must be modified slightly depending on what it connects to.
The schematics shown also exibit this problem; the author freely admits it. While I feel that this problem could be partially solved by automated tools, it is still a big hassle. Not just because I'm lazy either. Many tools operate using O(n ln n) or even O(n^2) algorithms. Increasing the time constant or adding unnecessary coupling means that the tools won't finish their production times for very long periods of time. A Xilinx FPGA synthesis run, which is comparativly simple, can allready take several hours to complere. This hurts the design cycle time, since even small changes can require a full recompile totaling hours. No telling how long it would take to make a full microprocessor - many days I am sure.
A true digital design, by contrast, does not exibit this problem. Again, I don't feel that this problem is insurmountable. The problem here is all those resistors whose values must be changed. Remove them and remove the problem as well.
Problem with interconnect
One more problem is that in most modern designs the design area is dominated by interconnect. Active areas (made of real transisotrs) are connected by routing channels, and the channels are getting to be quite large. Ternary logic doesn't exactly help with this, since we now have three power rails. This is at worst a second order problem though, since it doesn't really increate the interconnection between any two components, just the interconnection between all the components.
Underdeveloped logic family
While on the topic of power rails, I can't help but wonder about the clock. It seems underutilized. What should a negative (-1) pulse on the clock do? Or the control lines on a flip flop. Take a D-type flip flow for example. if load=1 loads a new value, and load=0 hold the old value, what does load=-1 do? load an inverted value perhaps? Until clocking a flip flop behavior is defined, I don't see any complete designs coming out. These ideas probably just need some more "brain time".
Error Correction and Asthetics
Lastly, let me say what I do like. The fundamental advantage of digital gates are that signals can be regenerated. In a five volt system, if you have a 4.89 volt signal, it is probably supposed to be a 5.00, so the gate boost it up and passes it on. This means that error do not propogate. This is the essence of Digital design.
The ternary design style we see is not incompatable with this notion. In binary, The decision is made around the transisors meta-stability point, typically 2.5V. This means that the fundemental decision is to determine if a signal is [ s>2.5V ] | [ 0V ] | [s
Machines are good at jumping though hoops and are just as happy counting in base 2 as base 22! I do think people would be better off not using base ten. For example base 12 has the advantage of being evenly divisible by 2, 3 and 4 so you can evenly divide things in half, thirds or quarter which are the most common divisions. Base ten chokes on dividing things into thirds. Using base 12 or base 16 would also allow a more compact representation which would be a big help dealing with screens which are always too small. Of course base 16 has the major advantage of easy translation to base 2. So everyone would be comfortable with hex numbers since those would be normal numbers. The US seems to be willing to ignore the base 10 metric system forever maybe we can introduce a base 12 or base 16 measurement system. :-)
I just took a quick glance at the schematics for some simple gates in ternary logic, and it seems to me that they are quite a bit more complex than their couterparts using binary logic (i.e. they use a lot more gates to do the same thing). Therefore they are more expensive. It seems to me that that could hold up moving to ternary logic, as everything about design is geared towards making things cheaper.
All circuits busy.
if a bit stands for "binary digit", so by analogy, shouldn't a "ternary bit" be called a tit?
"I am busily ignoring some thousand of implications I have determined to be irrelevant."
Ternary computing?
Dude we are working on Light based CPU systems.
We have a slight problem making the switches really small. but other than that, its pretty easy.
So yeah some think 3 step computing is neat, however others have seen that years ago.
Does this mean that we're going to give up our bits for tits? Sounds good to me.
ByteMyCode.com: A Web 2.0 code sharing community.
Hm, this seems to mean that one is never late learning Intercal. B-)
PLEASE DO. Argh.
The ternary design style we see is not incompatable with this notion. In binary, The decision is made around the transisors meta-stability point, typically 2.5V. This means that the fundemental decision is to determine if a signal is [ s>2.5V ] | [ 0V ] | [s
The ternary design style we see is not incompatable with this notion. In binary, The decision is made around the transisors meta-stability point, typically 2.5V. This means that the fundemental decision is to determine if a signal is s>2.5V or 0V or s
Binary operations can be done on any base numbers by implementing them using base-neutral arithmetic. "shift left" become "multiply by a power of 2" etc. It would be easy to add to a C compiler.
When you knew you were writing for ternary computers you wouldn't want to use a lot of binary operators, since they're not very efficient, but a ternary computer could definitely run programs in binary-based languages. Naturally, there are analogous digit operations for any base, and to take full advantage of the computer, you'd want a more appropriate programming language that lets you access them.
To quote the core argument of the article:
Evidently we need to optimize some joint measure of a number's width (how many digits it has) and its depth (how many different symbols can occupy each digit position). An obvious strategy is to minimize the product of these two quantities. In other words, if r is the radix and w is the width in digits, we want to minimize rw while holding r^w constant.
This may be an "obvious" strategy, but is it a useful one? A modern computer typically contains hundreds of millions of digits in base two. According to this theory, the cost of a computer (ie, the value we are trying to minimize) is equal to the radix times the width. If this is true, we can reverse the radix and the width to get a system that has precisely the same cost: thus, a machine that stores one hundred million digits in base two costs the same as a machine that stores two digits in base one hundred million, because two times one hundred million equals one hundred million times two.
In practice, building an electronic computers capable of distinguishing between one hundred million distinct voltage levels is a practical impossibility. Early attempts to build machines that had just ten distinct voltage levels were abandoned, not because of any theoretical arguments about data density, but because these devices turned out to be extremely difficult to manufacture and notoriously unreliable in operation. A computer with one hundred million distinct voltage levels, if it could be built at all, would certianly cost several million dollars to construct, and it would probably require a special power supply and several pounds of electromagnetic sheilding. It would certianly not "cost the same" as a typical desktop computer.
Even if we were to ignore the absurdity of the basic premise of the theory, and take for granted that the trinary computer is better than binary in some abstract way, there is still no compelling reason to switch. We have already invested billions of dollars into binary technology, and the benifits of that investment are undeniable. If you think companies like Sun and Apple has a hard time selling theoretically superior hardware in a market dominated by cheap PC clones, imagine how much harder it would be to introduce a computer that is so fundamentally incompatable that it does not even work with binary data. The dominance of the Windows platform proves that people don't want theoretical perfection: they want something that gets the job done, they want it to be cheap, and they want it now.
Consider again the task of representing all numbers from 0 through decimal 999,999. In base 10 this obviously requires a width of six digits, so that rw=60. Binary does better: 20 binary digits suffice to cover the same range of numbers, for rw=40. But ternary is better still: The ternary representation has a width of 13 digits, so that rw=39. (If base e were a practical choice, the width would be 14 digits, yielding rw=38.056.) so the theoretical approximate is less than 2% efficiency increase. But what they don't say is that it takes 2 operantions to distinguish a ternary system: v < 1 ? 0 : v < 2 ? 1 : 2 as oppose to binary: v < 1 ? 0 : 1 In the real world you can't do "equal to" because there is the potential for infinite precision -- you can always measure more closely. And you can't measure on/off, because then your circuit is dead and no further calculations can be done. You can't use positive/negative, because you want three. So you need something that can detect voltage levels. The problem is, that if such a device can be created that distinguish 3 different voltage levels, and do so more efficiently than using to binary operations (see above ternary notation :) -- it could also be used to perform 2 binary operations which doubles the efficiency of the binary system
rw = 40 / 2 = 20
almost twice as efficient as the ternary circuit.
A friend of mine who's into digital pro audio looked into building logarithmic audio gear, but the recording industry went to 24-bit linear instead, which provides more headroom.
One big disadvantage of trinary is the number of transistors involved. I don't know if the author's schematics were minimal or not, but his inverter required 2 transistors and 5 resistors. A standard CMOS inverter requires 2 transistors and *zero* resistors. On top of that, the transistors were BJT (Bipolar Junction Transistors), not CMOS which are what current most common.
The other functions will take a lot more real estate if realized in trinary too. The Full Adder he had listed has 20 gates of varying complexity, that would take at least 2 transistors per gate, probably resistors as well considering his schematics. A binary/CMOS implementation can be done in about 30 transistors.
...my gallium arsenide quantum ternary clockless computer.
It's going to kick some wicked ass, especially with those 12-gigabyte multilayer CD-ROMS and fungus-based hard-drives.
Hmm.. at my fictional computer company (Zapitron -- an in-joke among my friends), we always called 'em trits, trytes (9 trits), and words (27 trits). But now that everybody's moving from those old 27-trit computers to the new-fangled 81-trit machines, "word" might get redefined.
BTW, one of the neat things about Zapitron computers is that unlike conventional computers with their software emulated null devices, Zapitron machines have hardware null devices, so that you can burst-read EOFs at billions of EOFs per second. Ain't innovation great?
As copyright owner of this comment, I authorize everyone to defeat any technological measure which limits access to it.
The economic claim for trinary computation is bogus, because we do not know that the cost of building width w base r device is proportional to r*w. The cost is likely to increase more than linearly with the base. For example if it is r^k*w, the "optimal" base would be r=exp(1/k). For k=2, r=1.65, and for k=1.5, r=1.95. In these cases binary or a _smaller_ base is better.
However, there would be a real benefit in using trinary logic, as it can be used to represent true, false and unknown. In many real situations a lot of extra logic is devoted to dealing with unknowns because the binary system forces a decision. This would be cleaned up quite a bit in trinary system. In fact, the ease of rounding using trancation is a nice little demonstration of this property.
it takes 2 operantions to distinguish a ternary system: v < 1 ? 0 : v < 2 ? 1 : 2 as oppose to binary: v < 1 ? 0 : 1
You're applying binary logic to ternary digits. I would foresee that the logic would be something like this: cmp(v) ? -1 : 0 : 1;
C's '?' operator inherently assumes binary digit. So, I think that if we were going to implement trit-based computer, we have to slightly change programming language structures.
Anyway, it won't happen, because people don't like radical changes. Besides, a lot of investments already take place in bits...
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Error 500: Internal sig error
One of the professors in our department has been doing some heavy research into computations using more than one base. The idea goes like this:
- 6 = 2^1 * 3^1
- 18 = 2^1 * 3^2
- 231.67 ~= 2^3 * 3^3.0637
Keep in mind that there are many possibilities for your mapping (he's developed optimizations for finding good mappings)Obviously this isn't a universal solution, but think about DSP hardware, where multiplications are expensive and needed all the time. Not to mention exponentiation for cryptography. Also, this brief explanation doesn't do justice to the full potential/applications of DBNS. A lot of work has gone into it.
If you want to find out more about DBNS, there is a primer at www.rcim.ca/Research/Video_Rate/DBNS/, miscellaneous papers at people.atips.ca/~eskritt and a collection of a few published papers at www.atips.ca/research. Also, some older presentations are archived at wooster.hut.fi/geta/courses/graham/Applications/.
Disclaimer: I'm the web guy for our research group at the U of Calgary. The guy who came up with DBNS is a professor here (Dr. V. Dimitrov).
http://www.computer-museum.ru/english/setun.htm
It worked and it was a good computer.
The last time ternary logic came up, I was disappointed to see no proposed schematics. Now there are schematics, but I'm still disappointed. One thing is that they designed with bipolar transistors rather than CMOS -- you cannot put more than a few thousand bipolar transistors on one chip without serious heatsinking... Beyond that, these designs lack quite a lot in speed, power consumption, and reliability as compared to even the 7400-series of TTL bipolar logic chips of the late 60's. And the first one I looked at doesn't even work.
Their ternary inverter is simply a two-transistor inverting _analog_ amplifier running on +/-3V supplies. If the input is -, Q2 turns on, bringing the base of Q1 low, turning Q1 off, so R2 pulls the output (which isn't explicitly shown) to the + rail. If the input is +, Q2 is off, and apparently this circuit depends on leakage to then bias Q1 on. This brings the output almost to the - rail. So it would work as a binary inverter. It's not nearly as good as a
TI 7404 (see page 2). The major difference is that R2 was replaced by a transistor, which turns on for high. This speeds up the low-to-high transition, since you get the full output current of the transistor until the output node is charged up. It also saves power, because one
output transistor is always off and the other always on, so when not switching only leakage currents flow at the output. (This two transistor output is called a "totem pole", and CMOS similarly depends on transistor pairs, one always off so little current flows.) Two more intermediate transistors are added, to control the top transistor on the totem pole and to reduce the resistor count. (On-chip, resistors are not cheaper than transistors.) But if you used it as a binary circuit, trinary.cc's inverter is basically the stripped-down ancestor of the 7404 circuit.
As a trinary circuit, it also has to take a 0V input and output 0V. This inverter does not do this reliably. It probably could be made to work by adjusting the resistor values until 0.0V in gave 0.0V out, but warm or cool the transistors a few degrees, and the amplifier bias will shift so that the output swings to the + or - rail. When you are trying to put the mid-level through it, you are running it like an analog amplifier, and analog amplifiers are unstable without negative feedback.
Nor would adding a few transistors and a negative feedback loop to stabilize it make it work well enough. A trinary inverter should take an input that is not right at any logic level, decide which level is closest, and output the corresponding nomimal voltage. For highs and lows (2 and 0), it does that, since it pins the output to the opposite rail. But even if you can be sure that 0.0V in = 0.0V out, with a circuit that is basically an analog amp, -0.1V in will give more than +0.1V out. So a chain of gates would allow the logic levels to get worse at each gate, until the mid-level became misinterpreted as + or -. To restore the mid-level would take a much more complicated circuit. I lay no claims to being a good designer at the transistor level, but I can't see any possibilities that are not nearly twice as complex as the corresponding binary circuits.
"It was just a dream, Bender. There's no such thing as two." -Fry
It is tertiary, not ternary.
Yes... Setun was a machine that used 3-state logic, 0,1 and -1 from physical level.
It was about 80 of them produced.
A bit orgy. ::laughs::
You're quite right. It is very common to use -1, 0, and 1. This is known as symetrical numbering and can only be done with odd numbering systems. If you will that - for negative one it would count something like:
1 1- 10 11 1-- 1-0 1-1 10- 100 101 11- 110 111
and so on.
Negatove numbers are just inversed so...
- -1 -0 -- -11 -10 -1- -01 -00 -0- --1 --0 ---
and so on.
Once you get used to this system it is very simple to do algebra and even calculus (though i wouldn't recommend it).
The practical difference is in electricity. You either have a negative voltage or, more simply, use 2 different volatages and 0. For example, 0v,5v,12v. You could however use the direction of the current to determine the voltage.
Any trinary machine can mimic a binary machine simply by getting rid of one of its states. So if we switch to ternary, the first ports of crypto libraries will just be binary libraries running on ternary machines.
Second, separate theory from implementation, please. Very few areas of information theory and cryptography are dependent on base-2. That'd be counter to the entire point of math, which is to think abstractly enough that the principles apply to any base. Your statement is sort of like saying "moving from base 10 to base 16 is hard, since we learn arithmetic in base 10 and we'd have to relearn all our arithmetic". It's just not the case. A + B = B + A, no matter what base you use. And likewise, the integer factorization problem and the discrete logarithm problem are damn hard no matter what base you use.
Implementations are highly dependent on binary systems, yeah--but that's only because we only have binary computers right now. As soon as someone comes up with a ternary computer, rest assured, Blowfish and 3DES and RSA and El Gamal and AES and all sorts of crypto goodness will be running on it in no time flat.
Think about this one for a moment. Computers are Turing machines. We write in Turing-complete languages.
But there's nothing in the definition of a Turing machine which requires that it be binary, trinary, or base radical two. The Turing machine doesn't care.
Binary Digit == Bit
So maybe a Ternary Bit would be a Trit.
and a Ternary Byte would be a Trite.
And a Nibble, of course...
Hobbes
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I for one am embarrassed this silly subject reached this forum. The only people who go ga-ga over trinary are fools who don't really understand digital computing.