Slashdot Mirror
Ternary Computing
eviltwinimposter writes: "This month's American Scientist has an article about base-3 or ternary number systems, and their possible advantages for computing and other applications. Base-3 hardware could be smaller because of decreased number of components and use ternary logic to return less than, greater than, or equal, rather than just the binary true or false, although as the article says, '...you're not going to find a ternary minitower in stock at CompUSA.' Ternary also comes the closest of any integer base to e, the ideal base in terms of efficiency, and has some interesting properties such as unbounded square-free sequences. Also in other formats."
... the choices will be 0, 1, and Maybe :)
... this might be an easier step to integrate. There was a previous article here talking about light based quantum computing- give it a few years :)
Actually not a bad step- I wonder when they look at quantum computers using light
mean we could finaly get a computer to tell us how warm our tea is?
the above is my personal opinion and does not necessarily reflect that of the little voices in my head
This is just a conspiracy to make us think in 3 dimensions. Get over it, the world is flat, it is only two dimensional.. I don't care how many PRO-E models there are........
They've finally invented my favorite circuit... the Maybe gate?
Fascism starts when the efficiency of the government becomes more important than the rights of the people.
Those pesky fat zero's are what's clogging up the communications, compared to those sleek 1's that just fit down the wires so easily.
If you are worried about zero saturation, do check out this site.
Wheeeee
...but the heat dissipation from all those vacuum tubes was enormous.
I thought the three states were 'true', 'false' and 'I don't know'.
Just think: programs would be able to make excuses instead of errors.
Most evil is done by good people, and not by accident, but deliberately; motivated by high ideals toward virtuous ends.
In theoretical CS classes, we learned all about it, it's not exactly news.
The thing is, it's simpler to manufacture binary logic than ternary.
So, no big deal really... the choices were made some time ago.
Next step: quantum computing.
Other bases more efficient than base 2 with today's hardware? Bah humbug. I've seen proposals for increasing the base size and none of them account for the fact that you must implement hardware to compute with these monsters to accomplish any useful task. So far, the most efficient (transistor-wise) designs involve base 2. I have yet to see practical logic gates for non base two systems.
Seems like someone has to bring up base3 computing every once in a while, just like asynchronous circuit design. I'm sure there are plenty of reasons why they are technically superior. But it has taken us 50+ years to get to this point with synchronous circuit design and binary logic. It would take many years to get to this point using totally new technology, and in the meantime the current computer industry would continue to grow exponentially. I'll believe in these technologies when I see a useful example of them.
Try reading Knuth's The Art of Computer Programming, Vol. 2, Section 4.1, Positional
Number Systems.
There is an extended discussion on the balanced
ternary system and some other exotic number
systems (base 2i etc). There are some merits
to the ternary system but it would be
harder to implement with transistors.
Setun operated on numbers composed of 18 ternary digits, or trits
Awww...they shied away from the obvious choice, tits.
Ternary numbers are an interesting sidetrack and some similar techniques are used in fast chip-based systems to speed up adding (each bit also caries it's own overflow and sign bits, turning the classic serial add-with-carry into a more parallel operation).
It must be remembered that, for floating point numbers, base 2 is *the* most efficient representation, as argued in the classic paper "What Every computer Scientist Should Know About Floating Point Arithmetic" by David Goldberg. The deep understanding behind IEEE754 is a masterpiece of numerical engineering that is often overlooked, IMO.
I've never heard this claim, anyone have a link, highly techincal and/or mathematical is fine with me.
Steven
-- I have marked myself unwilling to moderate-- I don't have other accounts to artificially inflate the karma of
2 4 8 16 32 64 128 256 512 1024 2048 4096...
10 seconds
3 9 27 81...ummmm...crap
10 seconds
This'll make all my computer-numbering knowledge obsolete
Last post!
What will we call the digits? Click here to find out:
http://www.schlockmercenary.com/d/20001226.html
I can't say that I don't give a fuck. I've just run out of fuck to give.
As far as I know radio astronomers user 3-level data recording for their VLBI (Very Long Baseline Interferometry) data. One of the equipment was from JPL at Caltech lab. Their problem is to detect a weak signal in presence of strong noise. In this case, it doesn't make sense to do 8-bit digitization. Instead people do 1-bit, 2-bit digitization and average out many sample of data. They found that the recording efficiency was highest when they used 3-level digitization.
I myself worked on VLBI in the same lab but our machines were using 1-bit digitization (BTW, we used regular video cassette and somewhat modified VCR to record 7 GBytes on single 2-hour tape).
It appears that they're at least one scientist shy.
For those that would die defending it, Freedom
has a sweet taste that the protected will never know.
they keep skipping me so that i get nary a turn
> comes the closest of any integer base to e, the ideal base in terms of efficiency
What does this mean? I'm pretty decent with numbers, but I've never heard e being referred to as the most efficient base. Anybody know any more about this? Math article somewhere?
I always heard that the russians were always trying to build ternary machines. Based on positive, neutral, and negative charges. The problem is that (pos and pos and neg) is neg (i.e. false) logically, but pos (i.e. true) electricly.
Because of this, you always have to put in charge reducers all over the place.
there are 2 kinds of people. those who divide people into 2 kinds, and those who don't.
OK, so we're currently operating in a binary fashion. Add an extra state to a bit (or should that be a tit? ya, ya, I know... the article says trit, for obvious reasons :) and voila! More information can be expressed in a shorter space...
What I want to know is how this would compare to quantum computing - which would be better, ternary or quantum? From the little I do know about quantum computing it is based on qubits (can't recall if that's correct or not), which in turn are based on the four basic quantum states.
So is this basically a question of Base 3 vs. Base 4 and how well the math works out for each, or are there significant benefits to quantum computing?
There is no escape from The Muffin.
Ternary also comes the closest of any integer base to e, the ideal base in terms of efficiency
:P
Unless you're in Indiana in the USA. Then pi is just as close
Screw doing it with three-bits. Use colors for each bit instead.
I have seen in one book that there was created a ternary computer long time ago. I have tried to find anything with google and found this page.
--
Ilya Martynov (http://martynov.org/)
Just when I get the powers of 2 up to 65536 memorized...
CompUSA??? Why even mention the hideous chain of stores. CompUSA has the most inept employees that are ready to 'impress' you with their Windows knowledge and sell you some worthless $50 Belkin cable.
Salesman: "you need this cable. a hot-swappable IDE ribbon is a must have."
Salesman #2: "is that the hot swappable IDE ribbon? Oh snap! that one made my AOL twice as fast and my por- er my 'files' save quicker."
Salesman #3: "guys, don't forget that he needs a terminator for that ribbon. its an extra $37.95 plus we get to grab your wifes boobies."
Customer: "What?! My wife? are you sure??"
Salesman: "positive. now lets see some boobage; i brought my star wars digital camera."
CompUSA sucks.
Close, but you are still doing digital computing! Just because it's not binary doesn't mean it isn't digital.
The problem is understanding the new metaphors required to implement new modes of math. Simply adding a third state doesn't get you a revolutionalry new mode of computation, it just gets you more bits per wire. For example, look at flash technology: they now store multiple bits per cell by designing sense amps to convert the analog level to a binary pattern.
Read the book "An Introduction to Quantum Computing". I forget the author, but it's the one that comes with the CD of mathematica examples.
In this book they discuss a simple adder that Feynman derived. The realization of the Hamiltonion operator (similar to the transfer function H(s)) requires a gate called:
Square root of NOT!
It's pretty crazy, but when you walk through the example step-by-step, it becomes more clear why it is needed to build the simple adder.
Now how you actually build a root-not gate is another problem, but I'm just making this point to illustrate how "meta" the new concepts have to be to truly revolutionize computation.
There's simply nothing better than binary right now.
https://www.accountkiller.com/removal-requested
Think about applying it to D/A and A/D conversion for AC signals. It could simplify a flash converter,a nd conversion to convention twos-complement signed integers can be performed by a hard-wired lookup table.
-jcr
The only title of honor that a tyrant can grant is "Enemy of the State."
There is a mathematical analysis right in the friggin' article!
well, equal to, greater than and less than coverage seems to be the strongest point for this puppy. how about the case where the operand is null? what then huh? dealing with databases everyday, this thing drives me nuts. we seriously need a quadritic computer with ==, >, and NULL.. native capabalities.
"Cheaper by the Threesome"
I can always go for a cheap three-some.
Pat
Humans are slow, innaccurate, and brilliant; computers are fast, acurrate, and dumb; together they are unbeatable
I actually have been thinking that it should not be too hard to come up with a Rijndael variant which uses a tenary system (using a 3^n instead of a 2^8 galois field, of course), since Rijndael is an incredibly easy to understand and very flexible cipher.
The question comes to mind, of course, if whether the galois field should use the elements (-1,0,1) or use (0,1,2) to represent a single tenary bit.
Sounds like a fun project, actually.
- Sam (who only uses crypto for https and ssh, since I, as much as I enjoy the math of crypto, have a "you are as sick as you secrets" point of view)
The secret to enjoying Slashdot is to realize that it should not be taken too seriously.
Now I will have to go out and by my new 20.1897521142866379871848676589683-threebit processor......
Tom
Someday, I'll have a real sig.
One of the advantages of digital over analog is that between the 1 and the 0 you have a ton of space that you can consider an error so if your signal is distorted (long wires), you still know what's going on- and you know when you have an error in transmission. In fact, when you read a binary signal, you can have true, false, and no output. With 3 possible inputs, the neutral zones between accepted values would become smaller and would significantly increase chances of error. In fact, the higher the base you take, the less margin of error.
How do you Pronounce (sp?) ternary? Is it ter-nary
or turn-ary? And why is it ternary and not trinary like binary?
<highlander> THERE CAN ONLY BE ONE!</highlander>
(and zero)
Something is : A member of set of elements called 'yes', a member of the set of elements called 'no' and a member of the set of elements called the intersection of 'yes' and 'no'.
This?
"If he thinks he can hide and run from the United States and our allies, he's sorely mistaken." Bush on bin Laden
... I might find that that adaptive image compression scheme I was using years ago might turn out to be useful after all. (Some parts of it would have been tons more practical if you used a ternary coding.) Now if I can find the source code amongst all those 360KB floppies that I've been meaning to burn onto CDs and convert it from FORTRAN...
CUR ALLOC 20195.....5804M
Someone had to say it.
10: PRINT "Everything old is new again."
20: GOTO 10
if YX switch right
it seems to me that this is valid logic, now if we can just come up with a transister that can do this sort of thing.
I am sure we can come up with a muti transistor system made of 2 transisters, but what would be the economic savings of having a ternary logic system if you double the transisters?
I am the Alpha and the Omega-3
...is that we no longer would have to read sentences like the following (fictional) example in supposedly learned publications like Scientific American:
"Computers are binary which means they can only answer 'yes' or 'no', 'black' or 'white', 'up' or 'down'."
As if using two digits didn't allow us FOUR answers. God I hate clueless science reporting.
324006
Although Current Digital Chip are called digital but underneeth they are still analog they just ignore a good chunk of the sine wave. So it Asumes high if it is positive or low if it is negitave. But with a Trinary chip might be torwards real acurate analog computing. True Analog computing could therioticly be extramly fast. Adding 2 numbers can be done O(1) You put Carge of value A and put charge of Value B and bang you got the answer. Floating points can be truely represented. 3d graphics will be a lot faster calulating a sine of a value will be super quick. But that is in the future. Base 3 is a good step towards base ininfinity.
If something is so important that you feel the need to post it on the internet... It probably isn't that important.
damnit
if Y<X stop
if Y=X swithch left
if Y>X switch right
I am the Alpha and the Omega-3
If bits becomes tits, then I say bytes should become teats.
And, instead of a 'nibble' being four bits, we'd have a 'suckle' equaling three tits, like that babe in the movie Total Recall.
Instead of dealing in megabits or gigabytes, we'd have gigatits, which could be abbreviated as DD, saving vast amounts of bandwidth -- which might as well be called handwidth now -- or terateets, abbreviatable as DDD.
With all the sexual content in technical lingo (e.g., male and female plugs, master/slave, unix, etc.) this is only a natural development, and given that half of these machines are used for nothing but downloading pictures of naked breasts anyways...
Is this truly the only Earth I can live on?
I looked over the article and it made a good arument for a ternary computing architecture, however there are some big problems with this that were not addressed in the article. Although I'm not a math expert, I did gain a math minor in college during my computer engineering curriculum, and I have to say ternary computing seems to have too many complex problems that need solving to be worth it.
First of all, hardware is getting smaller and smaller all the time, so the whole premise behind ternary computing (base 3 would use less hardware) doesn't apply, especially since brand new gates would have to be made in order to distinguish between 3 signal levels rather than 2, and that would be taking a HUGE step backwards.
Secondly, doing things on a chip or two is great, but the main problem in computing is communications. The major part of creating efficient communications protocols is determining the probability of a bit error. Probability is a very complicated science, even using the binary distribution, which is a very simple function (that just happens to escape me at the moment.) Now, add another bit, and you have to use a trinary distribution, which I'm sure exists but isn't very common (and not surprisingly, I can't recall that one either). Long story short, this theoretical math has been made practical in computer communications over a long period of time dating back 50 years, starting all over with 3 bits rather than 2 would be extremely complicated and VERY, VERY expensive.
Finally, figuring out logical schemes for advanced, specialized chips is a daunting task. Engineers have come up with shortcuts over the years (K-maps, state diagrams, special algorithms, etc) but adding in a 3rd state to each input would make things almost impossibly complicated. All computer engineers working at the hardware level would have to be re-educated, starting with the simplest of logical gates.
Overall, in my humble opinion, we'll never see large scale use of ternary computing. There's just too much overhead involved in switching over the way of doing things at such a fundamental level. The way hardware advances each year, things are getting smaller and smaller without switching the number base, so until we reach the limit using binary, we'll probably stick with it.
~ now you know
Thanks in advance.
...by the names of those three Gods of Hindu pantheon, namely those who are the Creator (Brahma), the Destroyer (Shiva) and the Preserver (Vishnu).
i think this would be a good system to use with quantum computers, since they can be in a superposition of waves state (both 1 and 0)
Coding projects blog - Code Slim
As if in precognition, a language has already been developed for ternary computers:
TriINTERCAL! (the link is about INTERCAL, chapter 6 is about the TriINTERCAL extension)
I can't wait until college courses are taught in this truly wonderous and -- who would have thought -- futuristic language.
The enemies of Democracy are
x <<< 3 is (usually) x*3
and x >>> 3 is (usually) x/3.
The representation of negative numbers is interesting but there is a 3's complement scheme that works. Eg.
-- SIGFPE
It seems to me that this is cooler than binary for the same reasons CISC is better than RISC. Unless manufacturing changes dramaticly, it will probibally never catch on for the same reasons RISC did.
As far as "closer to e", I'm not an expert, but I would guess that in computing applications, wouldnt a truncation of e be more useful than a rounding most of the time?
Just a thought... Could it be possible to do homebrewn quantum computing using white light (all colours = all bits are 1) and some homebrewn filters, mirrors etc. or similar setup?
Now us Geeks can Finally say that something good comes in threes!
....])
(unless M$FT decides to make an operating system for it [with our luck
rm -rf /tern/laden
Kind of spoils the meaning, doesn't it?
Bill Clinton: Pimp we can believe in. - The Shirt!!!
INTERCAL is the only language in which you can not only program in trits, but n-digit number systems. It's an elegant and beautiful language - it's so beautiful, it will drive you mad. =)
With a binary system, you can change from a 1 to 0 state, and a 0 to 1 state without having to pass through an intervening state. (You can call 1 high voltage, 0 low, or 1 a high tone and 0 a low tone) Only two states to worry about.
I don't see how one can design something as fast as a binary system, and still allow us to go from 0 to 2 without going through 1. If you are doing voltages, the intermediate value theorem forces you to go through state 1. Similarly if you are doing tones.
One can design a logic system, with "forbidden" state transitions. But then you would have to argue that "ternary logic with forbidden transitions" is significantly better than "binary logic." It seems to me that you would lose 90% of your advantage if you forbade 0 - 2 and 2 - 0 transitions.
God is real unless declared integer
and rain on the computer scientist's parade, but...
.5? Is it your ternary maybe, or is it the circuit switching from 0 to 1? And what about the case when your manufacturing process introduces errors greater than you expected? What if 1 comes out .75? Is that in the maybe range or the 1 range?
The reason that you can't get, and won't for a long time, anything greater than base 2 is that setting and sensing more than two logical levels in a given voltage range is very hard. Those ones and zeros you like to look at and think about discretely are not really ones and zeros, but voltages close to those that represent one and zero, close enough to not confuse the physics of the device in question.
For example, if you arbitrarily define 0 volts to be a 0 and 1 volt to be 1 in an equally useless and arbitrary circuit, and you monitor the voltage, what do you assume is happening if one of your discrete samples is
Now, I remember something about double flash memory densities by sensing 4 voltage ranges in each cell, but I imagine the timing precision required to do that correctly is orders of magnitude easier to do (and still a royal pain) than putting ternary logic into a modern microprocessor (with tens of millions of transistors, implementing everything created in the entire history of computing that might be even marginally useful so that you can 3 more frames per second in quake3).
Outside of a dog, a book is a man's best friend. Inside a dog, its too dark to read.
In particular, since e is irrational (NB it's even a bit worse than that), if you were to represent an integer in base e, it would have to be represented in floating-point. So efficient integer arithmetic will only be good for this special class of numbers which are not integers. On the other hand, I also can't see how having an integer base close to e helps at all either. Doing logarithms in base e is best for certain mathematical reasons, but if you're off, you're off. Perhaps there's a definition of efficiency here that I don't know, but it's the obvious tradeoff: if by efficiency you mean short expressions, then the bigger the base, the better... of course, the bigger the base, the harder it is to implement in hardware. This is why humans use decimal and hexadecimal but computer use binary. So, in summary, I can't see what e has to do with anything.
Come on, give it up, that's
I vaguely remember discussing this in a Computer Science class on circuit design four or five years back. While this might be possible for some sort of non-copper processor, I imagine the difficulty would be in rapidly distinguishing correct voltages for each bit on today's technology.
In simplistic terms, presently, if you have two bits, at a clock cycle, the electrical current is either 0 (0 volts) or 1 (3.3 volts). Theoretically, you could have an infinite number of bits, provided you had infinite voltage precision. Thus, 0=0v, 1=.1v, 2=.2v,
However, your processor is probably designed with a tolerance in mind, thus 3.1 volts is probably a 1, and
I'm sure there's a PhD EE somewhere in this crowd that can explain this even better, but my point is that I don't think anything but binary computers are useful with current electrical technology. Presently, there's a reason we use two bits - because it's easy and *fast* to check "on or off" without having to determine how "on" is "on". Now, if one was able to use fiber and send colors along with the pulses, then you might have something...
I think the computer in "Moon is a Harsh Mistress" was a "ternary logic", and it developed a sense of humor. =)
--- even the safest course is fraught with peril
Electron, proton, neutron
Up, down, top,
bottom, strange, charmed
blue, red, green
Yikes!
I like what was written, and it is interesting, but I don't think that this will change much in terms of how computation is performed or perceived.
One of the earlier posters had something mentioned about it all being two dimensional... actually, a good way to look at computation is using what Turing devised - a one dimensional model of computation based upon a single tape.
In studying Turing Machines, the mathematical model based upon (potentially infinitely long) tapes is used extensively. Move the tape right, left, and modify what is under the head, for example, are the primitive operations. A set of functions defines how symbols are changed, and when computation halts, as well as the resulting halt state.
A basic examination of binary versus ternary systems, based on Turing Machines, and some (basic) complexity Theory...
In binary systems, computation trees build at the rate of 2^n, where n is the number of computational steps...
In a trinary system, we are looking at 3^n.
So, performance could be considered in terms of - I believe 3^n - 2^ n, i.e., polynomial, not exponential) differences in processing power.
But, any binary system could by used to -simulate- a 3^n system through the use of a (at worst polynomially larger) set of functions and / or chunkings of data (to represent the 3 states in binary, repeatedly). Also, necessary encodings could be performed by 'chuncking' the ternary data into blocks.
Polynomial gains are nice, but at best, we don't have an earth-shattering enhancement.
P.S. Some of this may be a bit rusty, so if anyone has a more concrete analysis or corrections, feel free...
Sam Nitzberg
sam@iamsam.com
http://www.iamsam.com
The entire theory "ternary is most efficient" hinges on the idea that the 'best' base is the one that minimizes digits per number * possible digits.
In other words, base 1000 has 1000 different possible digits, but will require very few digits to represent numbers compared to (say) base 2.
According to the article, the 'most efficient' base according to this property is base e (2.7182818...), which they round to 3. My retort is: who cares? Why on earth would you judge a base system by digits per number * possible digits?
Digits per number is important, obviously -- base 16 requires far fewer digits than base 2 to represent most numbers. However, the complexity of building hardware which can efficiently represent 16 different digits is overwhelming, which is why no computer (to my knowledge) has ever used higher than base 10. Even the early ternary computers used a pair of bits rather than genuine trits, because they didn't have hardware capable of representing three states.
I'd argue that minimizing the number of possible digits far, far outweighs the number of bits per number, as evidenced by the fact we all seem pretty darned happy with binary. Storage is cheap, meaning bits per number just isn't a significant measure anymore, whereas designing and building every part of the computer to use ternary rather than binary is an expensive proposition.
In short: the measure they used to prove ternary 'best' was pulled from their nether regions, not based on anything in real life. As such, the basic premise of the article is flawed.
ZFS: because love is never having to say fsck
Redoing the math wouldn't be that difficult, you could follow the same derivation, just use different functions for the probabilities. However, the big point is that, while sending binary information, communications systems don't used binary symbols. Most modern communication systems use 2^n symbols to be compatible with binary (the methods are a little too complicated to be explained here), but 3^n would not be that much of a leap.
This topic seems to come up all the time in math discussions, and usually ignores a simple reason why 3 is much worse than 2.
The obvious simplification which we all have made from base 2 is that 2 symbols really require the detection of only ONE symbol's presence or absence. i.e. you don't have to confirm that a digit is "1" if you can confirm that it's NOT "0". The the number of recognized symbols in a number system is ONE LESS than the number of actual symbols in the number system.
Using this type of metric, one can infer that the "r*w" cost really should be "(r-1)*w" which when compard for the case of 2 and 3 clearly shows that 3 is highly inferior as a number base to 2.
Thus this article's 1 million code example simplifies to:
Binary (20 bits, r=2) --> (r-1)*w = 20
Ternary (13 tits, r=3) --> (r-1)*w = 26
Decimal (6 digits, r=10) --> (r-1)*w = 54
Comments?
Intercal is a language designed in jest. He was making an obscure humor reference. But I guess that went right over your head.
Maybe you'll get the tit references and find them funny instead.
The discussion of ternary computing came up in an earlier /. article about asynchronous processing. Rather than the three being true, false, maybe... It was thought that the third piece would represent "Not ready yet." This would certainly seem to be a nice step forward towards the production of clockless CPU's. Food for thought.
I believe the word you're looking for is quaternary.
<g>
-l
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As a matter of fact, there was a ternary computer built in Russia, called Setun' (apostrophe signifies a soft n).
Russian translation of Knuth's Volume 2 was quite funny. Knuth is saying that "Somewhere, some strange person might actually build a ternary computer". The russian translation had a translators footnote "Actually, it has been built in russia in 1960s".
See this page for more information about setun:
http://www.computer-museum.ru/english/setun.htm
I am shocked, shocked to discover that a fundamental computer architecture explored in the 1950's, rejected as unworkable, and forgotten is in fact unworkable.
The feeling that this induces has no word in English, but in Japanese it's called yappari.
Base 2 is very convenient for digital circuits because it relies on the inherent non-linear regions of the transistors for representing values while saving power. In a typical CMOS inverter, you have two transistors - a PMOS over an NMOS - with a tied gate. One transistor is always in the on state (saturation), the other is in the off state (cutoff). Therefore, whether the gate presents a logic 1 or logic 0, you have no power consumption because it's either a gate looking at a ground (no voltage), or a voltage rail looking at an insulating gate (voltage but very very high resistance). In this way, almost no power is consumed in the static state with the exception of some leakage currents which are for now manageable (but getting much worse in smaller geometry technologies).
When switching, however, the transistors both go into the linear conduction region, which is why they consume power - there is a resistive path between the supply and ground. This is the region used for amplification of sound and for other electronic circuits. But it consumes a lot of power.
How you could even construct a trinary circuit which has the same power characteristics as complimentary MOS is highly problematic at best. The number one and two problems on chips are timing closure and power, respectively. IC packages can't even handle the power. The more time the circuit spends in the linear region, the worse the power consumption. To me, any potential savings in size for such a circuit are virtually impossible to fathom. Not to mention some insurmountable difficulties as the author of the parent article mentioned on design methodology and tools to support a trinary system.
HOWEVER, it should be noted that signaling via pseudo-trinary methods is possible to alleviate timing problems at the expense of absolute performance. Motorola has an embeddable core which uses pairs of wires that have four states - 1, 0, ack, and a null state which is not valid anyway. But even this is not power efficient or fast - it's just easier to implement in some ways.
ah, at last, justification for my favorite language...
n /s 06.html
http://www.tuxedo.org/~esr/intercal/
http://www.muppetlabs.com/~breadbox/intercal-ma
Ternary computing is an old idea; in fact it is said that there were a group of computer scientists in the old USSR who were quite enamored with the idea, especially the balanced ternary form (-1, 0 +1).
The problem is that although you reduce the number of gates, the gates themselves get horribly complex. There are only 16 possible two-input binary gates, of which two are trivial, two are wires, two are NOTs, two are ANDN, two are ORN, and one each of AND, NAND, OR, NOR, XOR and XNOR. All of these are familiar gates. However, there are no less than 19683 two-input ternary gates. If you sacrifice some of the combinations, you suddenly are doing less than true ternary computation, and you're wasting the power of your machine.
That, in combination with the sheer commonality of true/false type states, means, in my opinion, that binary is here to stay.
And you need a towercase like this to cool it http://www.clearwatercoolers.com/images/watercoole rs.jpg
----- Whats wrong with this picture? http://www.revoh.org:1234/whatswrong
A friend and I were thinking about representations on a ternary system. We had to figure out what units of storage would be available.
;-)
Obviously, there's the basic unit of storage (1, 0, -1; on, off, undefined; true, false, maybe; whatever). We called this a trit for obvious reasons of parallel to the binary world.
Ok, good enough so far. Then, there's the basic unit that's used to store characters or very simple numbers. We decided that 9 trits would be good (this was to allow for UNICODE-like representations). This seemed to be a shoe-in for the title, tryte.
Then, you occasionally want to have something that is used in firmware to sub-divide trytes into various fields. In binary we call this a nibble, so in honor of Star Trek we called this one (3 trits) a tribble.
But, there it stopped, as we soon realized what we'd be measuring the system's word-size in.... Man, I thought SCSI was a painful phrase to use all the time
It occurred to me while reading the article that even if you could build a ternary microprocessor with more bang for the buck than the standard binary variety, in order to be useful in a microcomputer, you would need ternary RAM as well, so I began think about the problem.
Most desktop computers use dynamic RAM to achieve high densities at low cost. (It's not unusual for new desktop systems to have 1G of RAM in about 4 modules.) They work on the principal of charging tiny capacitors. Charged represents a 1 for instance and not charged represents a 0. But capacitors can be charged in one of two polarities (one plate negative with respect to the other, or positive). Thus it seems that it would be a small step to go from binary dynamic RAM to ternary. The supporting electronics and refresh circuitry would be a bit more sophisticated, but the capacitor array might be basically the same, resulting in increased capacity (log3/log2) with about the same real estate! So perhaps dynamic RAM is really optimal in ternary as well.
I'm not an electrical engineer; the above is merely speculation off the top of my head. Does anyone more qualified than myself have any thoughts on this?
This is interesting stuff. Does anyone have links to software experiments in ternary computing? Obviously, running on binary hardware, such projects probably won't have storage or execution advantages, but are there application domains where ternary representation makes a more elegant software solution?
So I may have to exchange my geek insult "couldn't figure out the logarithm to the base 2 of 65536 without a calculator" into "couldn't figure out the logarithm to the base 3 of 19683 without a calculator."
Quattuor res in hoc mundo sanctae sunt: libri, liberi, libertas et liberalitas.
Base 2 has the property that there is no base that is more simple. It fits the old maxim, "Make it as simple as possible, but no simpler".
(Unless you count base 1. I consider the tally mark to be base 1, but it has some problems fitting in as a true number base.)
Software sucks. Open Source sucks less.
Excellent. This will translate Tri-Intercal, with native bitwise trinary operators, into much more efficient machine code.
Touché!
Being called a dork on Slashdot must be like being called the retard in special ed.
We just did some testing, comparing those search algorithms with eachother. Although hashes are more or less comparable in speed with ternary trees, binary trees are much slower.
Some sample output: (btw, we didn't balance the ternary tree, although we did some really basic balancing on the binary tree).
Clearly the ternary tree and hash are much faster than the binary tree. Although there are still some optimisations to make, we believe that the ternary tree will outperform the binary tree at all times.
We also made some (very) cool graphs with Graphviz, but unfortunately have no good place to share it with the rest of the
This is a replacement signature.
Imagine a Beowolf Cluster of THESE!!!
How is the problem of distinguishing a .75 voltage in your ternary system different than distinguishing a .5 voltage in a binary system?
A/D controllers do this all the time, for larger bases, often on the order of 256 to 24 million. Granted, the digital results don't have logical consequences. But you can't ignore the fact that binary systems have to set tolerance levels just the same as ternary systems.
Software sucks. Open Source sucks less.
As long as we're turning the world on its ear, lets go all the way, and use triacs. We implement it (the tri-state gate, that is) like an inverter, more-or-less. These have two (non-linear ) on states plus off, and are just right for implementing an inverter. They'd probably be great for trinary logic, too.
I just dug out my old physical electronis book (Micro Electronics, by Jacob Millman, First edition), and can't find them in there, so here's a slightly less academic reference.
There might be some problems with trying to get the clock speed high enough to compete with the Intel/AMD marketing, though; it says that they can be triggered into conduction by high dV/dt.
See what I've been reading.
Good Link on ternary systems
Free unix account: freeshell.org
I've read a lot of posts on how this will be difficult to implement using voltages and circuits....and you know what? It *IS* difficult to sense 3 different voltage.
The solution? Don't use electric circuits...don't use transistors.
Electric circuits will only get us so far, and then we'll have to move on to more 'exotic' hardware -- optical computing, molecular computing, quantum computing.......
Suppose a qubit's state is describe by the spin polarization of an electron pair -- they can either be both up, both down, or one of each -- you can't tell which one, so it's actually 3 states (balanced at that)......
In optical computing, suppose you can push the frequency of the lasers a little in either direction of 'neutral'...this is also base 3.
So what I'm trying to say is, don't just say "base-3 computing is not practical with current technology" -- because it isn't, but it WILL be practical (perhaps even more so than binary computing) with future technology.
And to finish with something lighter...
troolean x, y, z;
x = true;
y = false;
z = existentialism;
:)
"You have the option of insanity. I do not. And that makes me crazy!" - Brian to Angela, My So-Called Life
I don't like this.
Any system that can't spell "42" is not worth it.
Don't make fun of my speling, english is my 2nd language...
Fry: It was just a dream, Bender. There's no such thing as 2.
-- Futurama
Close, but you are still doing digital computing! Just because it's not binary doesn't mean it isn't digital.
Did anyone say it wasn't digital? Or did you confuse "variants of digital computing" with "alternatives to digital computing"?
Read the title of the parent post "NONDIGITAL COMPUTING"
Yep. Look at the thread's title.
-- Kaufmann
To the editors: your English is as bad as your Perl. Please go back to grade school.
What an attitude! I find it hard to believe you'll ever get hired as an engineer. Making stuff like this work is the dream of a good engineer. Your desire to explore needs to be greater than your desire to be comfortable.
A lot of these challenges have already been solved. Some of them were solved 100 years ago (read the article). Many of your examples are things that may seem complicated to us using 3-way logic, but may actually be more efficient once we fully understand the properties.
Free unix account: freeshell.org
Then came my Epiphany of the File Cabinet a few weeks ago ...
When counting, thou shalt not stop at One. Neither shalt thou go on to Three.
The only crazy thing about quantum computing is the implications from a many-worlds interpretation point of view. What is actually happening is that an exponentially rising quantity of universa collaborates and shares the results! Sort of the Open Source of physics.
Opinions stated are mine and do not reflect those of the Illuminati
People count by tens and machines count by twos
.... I guess before they evolved into the current form and shape, they probably had 12 fingers, 16 toes, or something like that.
Well, at least, not the Brits and Americans. They count by 12, 16,
C is defined for a binary machine, like most programming languages (if they are defined properly at all). That's why it's hard to believe that we're going to see non-binary computing anytime soon. It would be very inefficient to reuse old software, making the theoretical effiency gain rather worthless. (Hmm, but this didn't prevent Intel/HP/et al. from developing the IA-64 architecture, may be they start trinary computing next?).
By the way, Ada does have support for trit operations (in some bizarre way), but this was merely an accident.
Anyone remember that big rabble about Bio Computers? Using the 4 acids (or whatever) in DNA to do the work and move the info around?
:]
I dunno, I remember seeing an article somewhere about it, thought to myself "hey, that'd be cool", and that was about it. I still think it'd be a neat idea, though, except for the possibility of having to feed your computer, and that a virus could mean a trip to the drug store
If anyone knows much about this, please, do tell
--eoPh
There's a bird called the Tufted Titmouse. The name for a group of these birds is a "rack".
They tried this on Star Trek, and it went berserk and blew up starships. It'll all end in tears, mark my words.
Then explain like the other poster here did - what a transistor is, how it works, and how design methods are better in base 3 versus base 2. To call someone not an engineer because he thinks that base 3 is inefficient is idiotic. Maybe you'll blame him for hating base 1.5 as well?
There is nothing strange about sqrt of NOT, except its name.
yes, but you say that and then you go on to give a really strange explanation!
the interesting point is:
a -- sqrtNot --> b
...is a probability, but...
a --> sqrtNot --> sqrNot --> b
...is absolutely certain as it reduces to a = ~b. kinda like the three-polaroid filter experiment for light, i guess.
regardless, i think in the early stages of any new science it's ok to use the term 'weird', maybe even, 'bizzarre', or as some may so, 'hella dope".
https://www.accountkiller.com/removal-requested
It's not nice to put words in someone else's mouth. I did read the article. The article didn't address the technical problems I was speaking of and others have posted. As an engineer I also am responsible for delivering working products, not just a bunch of theoretical promise. The most important thing in engineering is not chasing down wild new concepts and getting them to work (that's what professors are for,) it's making money using your problem solving skills.
~ now you know
It'd be an interesting exercise to try this out on an existing app like the Gimp where there are complex menu options.
...ternary computing is harder to do than binary, unary computing should be trivially easy.
Think of it. We'd have, uh, uits. Or maybe its. We'd all have to remember 1 to various powers. We wouldn't need stoopid transistors, just wires to carry a single signal. This is looking better and better!!
Lately democracy seems to be based on the skybox, the Happy Meal box, the X-box, and the idiot box.
Another advantage of binary is the power
dissipated in a transister. Ideally, when the
transister is off, the current is zero and
when the transister is on the voltage across
the transister is zero.
Either way the power is zero.
It's the only known numeric base that allows resolution of an exact value for Pi.
Little known fact.
The hypoteticaly "cheap" ternary system assumess, that the need for hardware scales linearly with the base. That is, e.g. it binary gate requires 2 transistors, ternary needs 3 transistors. In such a case 2^3=8 is less than 3^2=9.
So system with 2*3=6 transistors can count to 9 in ternary while in binary only to 8. When searching maximum for f(x) = x^(const/x), one ends up with e for all const>1. That's why the mention that the 3 is the closest to e - an number base ideal. I remember having that case in mathematics competition way back in 8th grade.
In engineering practice, that is quite far from truth. In ECL logic the ternary half-adder requires the same number of transistors as in binary logic. It requires the same number of wires to carry ternary digit as binary one. However we all know why is ECL nearly extinct - its high consumption prevents high integration.
The benefits of binary logic can be seen in CMOS, where we have two states, each of which consumes also no power and still has low output impedance.
Petrus
Can you imagine a beowulf cluster of those!
God became man to enable men to become sons of God. -C.S. Lewis
I'm glad to know that unbounded square-free ternary sequences exist. Life has a meaning now.
>The Number of The Beast, wherein the prevalence >of 3 phase wiring led to trinary computing.
;-)
The article overlooked another advantage of base-3 - the sinister 666 is reduced to the pathetic 22020.
... greater than, less than and equals.
:)
The real use for ternary is to implement the new booleans; Yes, No and Maybe.
The first language to implement that, is the one I'll be programming in...
Actually apart from the colors, all the other
particles are come in (isospin) pairs.
Under SU(2) (weak force pairs)
Electron Neutrino
up down
strange charmed
bottom top
proton neutron (which is up down again)
blue red green because color has
SU(3) symmetry
I can see the value of most of your points. You're right about the little tricks we engineers use to simplify logic circuits, but the potential advantages (might) outweigh the challenges. There has never really been an in-depth analysis of this, or a true attempt to make it work in quite some time.
As for the argument that it will take too much commitment in overhead before it becomes widespread, you are right. Inertia drives so many things in human nature, that it is extremely difficult for new concepts and/or ideas to gain broad acceptance. The same can be said for any radical change in technological architechture, be it Quantum Computing, Ternary logic, or Asynchronous Computing, all have great benefits to be offered, with few persueing them because of "Old-School" barriers. Don't say something will never be done, or shouldn't be done purely because of such barriers.
Erioll
You really couldn't be more wrong! Ternary logic is at the basis of some of the hottest research in asynchronous logic design right now.
For instance, if you had a group of transistors that computed multiplication and stored the output in a register you might see the value of that register change several times until the computation was completed. Right now, the only way that you know a computation is complete is that logic is designed to complete an action in X cycles; as long as you feed in the data and wait X cycles you will get the proper result. Clock cycles can be waisted here, because a simple multiplication might be completed in a single clock while harder multiplications might take the full amount of time the logic area is spec'ed for.
Using async logic, this can be done much more effciently. The multiplication happens just as soon as input data is given and the next stage of the logic knows when the operation is complete because its wires has three states: 0, 1, and not-yet-done. As soon as all the wires are 0 or 1, the computation is finished (consequently, this is how input works to). There are no "wasted" clock cycles, stuff moves through the logic as quickly as it is completed.
Of course, there has been some debate whether three states are needed on each wire, or an just additional acknowledgement wire is needed (say 8 wires + 1 for an 8-bit computation block). But, believe it or not there are already patents for both methods!
I guess, by having true ternary logic on each wire, you could have logic that will grab a result just as soon as X% of the wires report they are done with the computation to get "good enough" answer if the logic is iteratively improving a problem.
-AP
Since a binary digit is called a "bit", a trinary digit would make ... a lot of boys want to take that class!
Think about flip-flops for a second. Isn't it just pure luck that it works at all? From my understanding it's an anomally of nature that when you have a gate and it's stuck to one side because of an electrical current, then when you stop and start the current again, the gate flip-flops and sticks to the other side. Not much rhyme or reason... it just does. And all of computer science is based on this weirdness.
So my question is, what's a FLAP? Where does that fit in? It's not one side or the other of a gate, but a third option like "straight through"? It's nice to say this in theory, but the question is does nature DO that?
-Russ
Me
Digital circuits are binary simply because this
is the easiest way to design them reliably. A ternary circuit may as well be a quatanary (sp?)
circuit since the complexity is about double
that. At the other extreme, everything could be
done using analog techniques, but this is difficult and prone error due to noise.
Have you ever wondered if scientist one day create a ternary computer... We would talk about CPU in terms of tits instead of bits ;)
we could see Penthouse, Hustler and Playboy publish articles on the computer industry: "Intel launched today its new 64-tits processor, code-named 'Pamela Handerson'. The popular former playmate claimed to be honored. Competitor Motorala maintains its 'Ally McBeal' processor line, claiming that although there is less processing units, it has firmer support."
#DEFINE QUESTION (2b)||(!2b) -- William Shakespeare
Finally, it will be easy (relativly so) to program in Malbolge and Dis!!
I wish he had a simple quicksort where he could show massively improved performance by having trinary numbers. Maybe he could write the program with normal binary numbers, and find a fudge factor to slow down normal commands, but speed up (to simulate trinary improvements) those commands that trinary could really improve.
A theoretical benchmark would be interesting.
Was his file folder insertion example meant to make us think of ways we could use trinary lookups on an actual filesystem?
This wonderful name for a trinary bit was first brought to my attention by the wonderful commentary that accompanies this strip of one of my favorite web-comics.
Howard Tayler writes:
Enjoy!
Didn't I read somewhere that reality is encoded in some kind of "dense base one" number system. It would be interesting to see memory elements that can store an indefinite amount of information at one address. (Sorry for not remembering where exactly I read it)
What Goldberg shows is that base 2 is more efficient than base 10 or 16 on a binary machine.
He does not show that base 2 floating point on a binary machine is superior to base 3 floating point on a ternary machine.
Because of the wonderful properties of balanced ternary representation, I suspect the opposite. Base 3 balanced ternary floating point may well turn out to have nicer properties, and the hardware for adds, multiplies, etc, might well be more efficient.
Doug Moen
I have written a truly remarkable program which this sig is too small to contain.
I'm just an idiot and you can have the patent.
-- SIGFPE
Another reason that the computer industry grows exponentially is because the computer industry uses computer technology... which is growing exponentially. In other words, if I design my chip using a computer, as computers get faster so does chip design. As chip design gets faster, it becomes feasible to design more complicated chips... thereby allowing me to design more complicated chips which allow me to design more complicated chips...
Edu. sig-line: Choose rhymes with lose. Chose rhymes with goes. Loose rhymes with goose.
Comparing? THEN use THAN.
Three items is the best size for menus when you have to go through them in sequential order from start to end (as in the example of an automated phone response system - press 1 for blah, 2 for foo, etc). That is just simple mathematics - i.e. if you have 81 options, you'll only have to sit through 12 total choices if organized into 3-size menus nested 4 levels deep, compared with 18 total choices if organized into 9-size menus nested 2 levels deep.
However, for a "random access" menu system, it would be quite a pain if I had to go through 4 levels of choices if I knew I wanted File->Save. In that case, it is better to organize them with basic usability in mind.
Slashdot is entertaining like pro wrestling is entertaining
think ab0ut it, crackers wi11 0ve it, this can make cracking passwds much faster!!! just feed the asci numbers t the thing, it it says that it shu01d be sma11er, then use 1ess characters, that did n0t make sence but y0u get my p0int
PS n0t trying t0 be weird. but my keyb0ard is brken im s0rry if y0u have a hard time reading this!!!
Sig you!
Imagine what you could do with Cesium OS running on a ternary computer. Even better, a distributed system of Beowulf clusters running Cesium-based ternary processes! And perhaps a Natlie Portman wall paper, while looking at your fake Britney Spears porno at 3am, eating a taco with an old X-Files on television in the background...
You forget that, in the long run, 3^x dominates 2^x. Hence, if your theory about exponential growth is correct, then, given enough time, trenary computing will kick binary computing's ass!
/that/ much better, businesses won't be able to ignore this...or else they won't be there in the long run.
Unfortunately, businesses don't often think in terms of the long run. So this kind of stuff will probably get done at Universities for a while, or maybe at places like IBM. But if it really is
Checkout taccom my worl war II simulator
I'm surprised nobody has mentioned this yet, but signalling with greater than two voltage levels per wire (and hence more than one simultaneous bit per wire) is already common practice in at least one area: Ethernet.
100Mbit ethernet uses 3 levels. Gigabit uses five. (Hope I got this right, I'm speaking from memory, and it's a while since I read the specs).
So, 100Mbit ethernet uses trits, and GBit ethernet uses quits?
Of course, it's really implimented with binary logic behind the scenes, and the conversion to & from multi-level logic happens right at the line trancievers.
This is not just a bad troll, it's a stupid joke. Not a single person reading this will spend ten seconds thinking about your lack of skill at telling jokes, writing stories, or coming up with clever comments. They are just going to look at it, roll their eyes, and move on. If they've got mod points they'll slap it down, but other than that no one, except me, is going to dignify it with a reply. Are you doing this for a reason, or do you just get off on shitting your pants in public?
in a deep pile of rancid festering diseased feces at the bottom of an abandoned cyanide mine in between two active volcanoes at the distant apex of an uninhabited island far to the south in a vast ocean. Because it's just not funny anymore. Are you old enough to remember "Where's the beef?" commercials? Do you also remember how the novelty of the phrase wore the fuck out after about two weeks. Do you remember how people using it as a joke more than six months later frequently got punched hard in the arm with brass knuckles? That's how not funny this joke is. Get a new fucking line.
Check it at google.com .
This comment was stolen off of Usenet.
'nuff said.
A ternary ciruit could be implemented using zener diodes..
state 1 -> current flowing in the forward direction (diode conducts)
state 2 -> current flowing reverse (diode conducts)
state 3 -> no current (diode is in cutoff)
Then again, we could even use TRI-COLOR LEDs to implement an optical circuit.
Find a job you like and you will never work a day in your life.
You're right about the communication problem, IMO. That's why if ternary computing takes on, it will be limited to "inside" a single chip for a while. For example, an FPU or a DSP processor could make use of ternary arithmetic internally, converting to and from binary when you need to go off-chip. That may have advantages. A general-purpose ternary computer, however, probably won't be useful for a very long time if at all.
sub f{($f)=@_;print"$f(q{$f});";}f(q{sub f{($f)=@_;print"$f(q{$f});";}f});
Whoops! Thanks :).
won't ternary be slower for using the &~^| operators?
228 of 319 posts? What the shit is that?! You trolls aren't trying hard enough, I never want to see another slashtrash story with over 1/2 posts valid!
2) DNA is written in base 4 -- native language.
3) Half the representation cost of base 2.
4) Your own hands are naturally base 4 -- the thumb is a carry.
DNA is a Turing machine. You, however, being dynamic and emergent, are not.
I read many, lots, more than I can rember, articles a year or so ago about how nanotubes have the property of preserving spin of electorns... I.e. Up or down. My first thought when reading about this, for a project on crypto was 'this would make computers faster!!!' I ran it by a CS professor and he was like 'Damn, I suggest you read 'Why the future doesn't need us any more' " Any way if we used Nanot tubes as our wires we could have a ballanced ternary system. Negative, off, possitive.
It's a really interesting and challenging field of study. A nice story about the history of clockless computing can be read here:
Technology Review: It's Time for Clockless Chips
Two quotes:
An alternative, used by Theseus and others, is to open up a separate communication channel on the chip. Clocked chips represent ones and zeroes using low and high voltages on a single wire; "dual-rail" circuits, on the other hand, use two wires, giving the chip communications pathways, not only to send bits, but also to send "handshake" signals to indicate when work has been completed. Fant additionally proposes replacing the conventional system of digital logic with what he calls "null convention logic," a scheme that identifies not only "yes" and "no," but also "no answer yet"--a convenient way for clockless chips to recognize when an operation has not yet been completed. All of these ideas and approaches are different enough that executing them could confound the mind of an engineer trained to design to the beat of a clock.
In 1997, Intel developed an asynchronous, Pentium-compatible test chip that ran three times as fast, on half the power, as its synchronous equivalent.
The Drowned and the Saved - Primo Levi
The article clearly described using a ternary system for building a tree of choices and this is closely related to it.
Perhaps people with moderator rights should read the articles before criticising sensible and ontopic posts.
/me goes off shaking his head.
From a more philosophical point of view... On a meta level you always have to rely on binary logic. In the case of a base 3 logic you have to decide which one of the three possibilities is actually happen. If you go with the states 0,1,2 or -1,0,1, you or the device have to "know" whether it is 0 or 1 or 2 (resp. -1 or 0 or 1). The "decision" which state is the current one is not a decision based on ternary logic, but based on binary logic. You can say, e.g. at the moment we have state 1 (true) and not 0 or 2 (which are both false). The decision isn't made on ternary logic itself, but falls back to binary. Ternary logic is NOT self-reflexive, because you can't apply ternary logic to itself. If you do you will end in an endless regress, so it is unlikely to have an advantage after all.
However we all know why is ECL nearly extinct
Any evidence to back that up? ECL still gets used a fair bit in my experience. I challenge you to make a prescaler capable of operating at the 4GHz region without using ECL or SCL.
Roger
Do you have any better hostages?
Working ternary computer was done by Brusentzov in Moscow Uni in ~1970-1975. It's name was 'Setun'. Many books are written about (in Russian, sorry).
As an idle note, databases already use ternary logic, as (usually) any value can be officially unknown. So for a boolean field you can always have T,F, and ?.
Im surprised no-ones mentioned the idea of a beowulf cluster of these!
Electronic Music Made Using Linux http://soundcloud.com/polyp
Perhaps the possibility (if still a while off) of ternary computing devices will encourage some people to avoid meaningless powers of two when picking arbitrary limits. I'm talking about things like the maximum length of a filename: no point making it 64 characters, when 50 or 100 would work just as well and not cause the reader of the code to worry about whether the power-of-two-ness was significant.
Of course for buffer sizes you sometimes want the space to fit into an exact multiple of pages in memory. But a structure definition that has one int, one char and an int[128] is really pointless. Just make it a round number in base ten!
-- Ed Avis ed@membled.com
Microsoft will love this.
Now a bit can be true, false, or have crashed!
Well have that, over in our labs currently. We however are working on LIGHT based cpu systems, and there are a few ways to do this level of processing the cost is pretty low, pert near about 3.50 per chip.
The problem is funds, as even though the funds are bonded, the funds are kind of low.
But some insider trader ago, said its all a question of the switches as to how fast the cpu works.
However we do wonder what the current cost of 3 bit computing is?
Um, sorry. Listen to something.
Doesn't matter what, but your speakers and sound card are well able to reporduce a signal to within 0.5 V.
There are operational amplifiers working at radio frequencies, that have plenty of resolution and precision.
Besides, if you were looking to do a ternery computer, you'd use -5V, 0V and +5V as your markers, drawing on decades of knowledge from analouge tecniqies, and then not have to worry.
For those that don't know, the standard RS-232C serial bus uses a tri-state signal. Has done scince it's introduction.
I know tits have already been mentioned, but here goes anyway:
:)
If a Binary digIT is a BIT, it stands to reason that a Ternary digIT would have to be a tit. This is important as an advantage to Ternary based computers, as it will be a first opportunity for many in the computer programming and design industries, not to mention software authors, to actually get to play with tits! Not just a pair, but many many thousands!!!
Have you hugged your consitiutionally guaranteed right to freedom of expression today?
How about Quadnery? Yes! :)
The values would be "less than," g"reater than," "equal to," and "who cares?"
If I'm not mistaken, the martians from Heinlein's "Stranger in a Strange Land" also used a base-three system of mathematics. Interesting. I wonder why he was so fond of it.
---If you can't trust a nerd, who can you trust?
We have been using horse pulled carriages for as long as anybody seem to remember. It tooks us many centuries to reach the current state in traffic planning and efficent manure collection and disposal.
I will believe that the car is a viable means of transport when I see one that goes faster than 10mph.
IANAL but write like a drunk one.
The article states that e is the "best" notational base, and that three is really good. But how much better is "3" than "2"? How does "3" compare with "4"? If the improvement is only a small percentage, then we're probably looking at a purely academic discussion. However, if the improvement were truly significant, then maybe we should explore ways of improving circuit design... Based on one of the graphs in the article, the curves depicting base versus "compactness" seemed pretty flat around 2, 3, and e. That tells me that there's only a small improvement to be gained from a much more complicated system.
Nitpick: you don't add more bits (binary digits), you change to (more) trits (in the case of Trinary)- or should they be called tits?
Lars T.
To the guy who modded me down from perfect to terrible Karma - Apple haters still suck
Spootnik, you are now on notice. Whenever I don't have mod points, I'm going to do a Google search and rat you out. Whenever I do have mod points, you're taking a -1 Overrated in the ass.
"What an awful dream. Ones and zeroes everywhere. [shudder] And I thought I saw a two." -Bender
"It was just a dream, Bender. There's no such thing as two." -Fry
So if in binary you have 1 bit, 2 bits = 1 nibble, 2 nibbles = 1 byte, does that mean in terary you have 1 trit, 3 trits = 1 tribble, 3 tribbles = 1 tribe?
This remains funny right up and until you envision yourself on IRC, trying to explain the difference between megaTits and megaTeats to an idiot 15-year-old who thinks his cable modem gets more handwidth than your T1.
It starts being funny again when you try to figure out which image compression format bets more Tits per megaTit.
Etc.
- Fatzilla
StoneCypher is Full of BS
I'm talking about Steve Grubb of Trinary.cc. His website has everything you wanted to know about trinary logic.
Interesting to note there are six unary gates: invert, rotate up/down, shift up/down. I independently verified every one of the 27 unary functions can be created using those six.
More interesting is the binary operators. Min analogous to OR, Max to AND, XMax to XOR. There's even a Mean and Magnitude to average and compare values of two trits, respectively. It's not all theory, though.
- Half and Full adders
- Multiplexers and Demultiplexers - interesting to note, I designed a four-relay 1-trit demux independently from trinary.cc.
- Flip-flops: Level/Edge triggered
- Async and Sync counters
- Shift Registers: Serial <-> Parallel
- Magnitude Comparator
- Classical and Checksum Parity
- Trinary <-> Binary
- Analog <-> Digital
Heck, Steve even has tested schematics of trinary gates. Too bad they're so complex, I expect something simplier is possible.Yet, chip manufacturers won't budge. Until trinary is more well-researched, I don't expect them too either. As Steve Grubb said,
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