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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."
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........
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.
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
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.
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.