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."

Comments

Ternary has been known to be efficient...

[ponos]

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.

Re:Ternary has been known to be efficient...

[Asic Eng]

but it would be harder to implement with transistors.

Very apt. A binary transistor has two states, idealized "on" and "off". From a more analog view that's low current and high current - appropriately connected with a resistor that results in low and high voltages.

The nice feature is, that a high voltage at the input opens the transistor, a low voltage closes it. So we get a relatively complete system, I can get from hi to lo, from lo to hi.

Tertary would put us into "middle" voltage. But middle on the input, creates middle on the output, no direct way to get either high or low - making basic circuits more complex.

But the real killer with "middle" is manufacturing. Let's say we use 2.8 Volts for the high level, 0.2 Volts for the low level. Due to manufacturing tolerances some chips transistors would be "fully" open at 2.3 Volts, others at 2.7 Volts. Easy to compensate on binary designs, you just use the 2.8 to switch the transistor, but for the middle level? What's required to switch a transistor to middle on one chip, is sufficient to open the transistor completely on another chip...

So your manufacturing tolerances become way smaller, and that of course reduces yield which increases cost.

Add to that, that chips today work with a variety of "hi" voltages like 5, 3.3, 2.8 ... Most lower-voltage chips are compatible with higher-voltage ones, they produce voltages which are still over the switching point and accept higher voltages than they operate on.

With ternary that becomes impossible and chip manufacturers need to progressively lower the voltages for higher speed.

Plus disadvantages in power consumption and and and...

Admittedly the article doesn't seem to suggest that ternary is viable, just that it's pretty. Which may be true for a mathematician. :)

Good Old binary and Floating Point.

[RGreen]

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.

astronomers used it since 80's

[Anonymous Coward]

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).

Re:Less than, greater than, or equal?

[po_boy]

I thought the three states were 'true', 'false' and 'I don't know'.

Nope: one, zero, and CowboyNeal.

SETUN - Russian ternary computer

[m_ilya]

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.

Re:Trits?

[tswinzig]

Awww...they shied away from the obvious choice, tits.

No, I think that was a good decision. When I think of tits, I always imagine them in pairs.

Yes! Tits!

[corebreech]

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...

Fascinating, but not practical, here's why:

[Uttles]

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.

Gratuitous rain?

[leighklotz]

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.

Don't get hung up on transistors.

[nels_tomlinson]

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.