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."

Comments

on, off, ?

[eric6]

does ternary processing mean you will be using on, off, and some third state of electricity? "dim"?

Re:on, off, ?

[popeyethesailor]

Close. It's like On,Off and CowboyNeal.

break the shackles of your binary programming!

[alienmole]

Disclaimer: I haven't read any of the articles.

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.

Why Tri why not just go Analog ?

[CDWert]

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 ?

Re:Why Tri why not just go Analog ?

[yellowstone]

Disclaimer: if this is a troll, then you got me. Ha, ha.

Trinary computing sounds a little like taking something that was settled on in the first place and resettling again

Apparently, you can't be bothered to read the Third Base link referenced in the body of the story. To summarize:

1. The cost of representing a particular number in a given base depends on a) how many digits there are in the number in that base, and b) how many digits there are in the base
2. Analysis of said formula gives a minimal value at e=2.718281828...
3. Dealing with numbers in irrational bases is problematic, but the same formula also suggests that using base 3 is more optimal than using base 2.
4. In the end, none of this matters, since AYBABTU.

Adopting crypto to trenary computing

[Kiwi]

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

Dude. Totally.

[glowingspleen]

"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."

Something already use ternary signalling

[hamjudo]

It's no big deal. Some comunications lines use 3 states, -v, 0v, +v. The 3 levels represent 0, 1 and same as the last bit. They use the third level so they change the voltage every clock cycle and thus only one frequency travels down the wire.

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.