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Beyond Binary Computing?
daksis writes "Non base two computing is nothing new. But it is an idea that, for various reasons, never really caught on. Embedded.com is running an op/ed piece that asks if hardware and software engineers are ready to move to ternary or quaternary logic. A move to multi-valued logic provides more computational capability without the standard increase in die size or transistor count. Is the need to make do with the current fabrication technology enough to drive the move to multi-valued logic? Or will Moore's law continue without the need for doing more with less silica based real estate?"
It's been a long time since I read an article about that, but AFAIK ternary system is most efficient in storing information (basically if you want to store numbers 0..700, you need 28 states (8+10+10) for decimal system, 20 states (10*2) for binary and 18 for ternary (6*3). This has something to do with 3 being closest to the value of e (2.718...) but I dont remember what exactly. Any /.-ers to fill in?
Increasing the number of states requires you to increase the overall voltage required of the device to acount for noise in the system. So in return for more states you are running at a higher voltage and thus at a higher power consumption level. You still have the same problem.
Now, for a binary number system, digit 0 is [0, 2.5) volts, and digit 1 is (2.5, 5] volts. Clearly, the noise margin of the binary number system is much better than the noise margin of the base-3 number system.
Now consider the voltages of modern digital circuits. Consider a voltage range of [0, 1.5] volts. In a base-3 number systm, digit 0 would be [0, 0.5) volt. Digit 1 would be (0.5, 1.0) volt, and digit 2 would be (1.0, 1.5] volts.
For a binary number system, digit 0 is [0, 0.75) volt, and digit 1 is (0.75, 1.0] volt. Again, the noise margin of the binary number system is much better than the noise margin of the base-3 number system.
In fact, the noise margin of the binary number system is consistently 50% better than the noise margin of the base-3 number system. The noise margin of the binary number system is always better than the noise margin of the base-n number system, where n > 2. For this reason, engineers have not built and will not build digital systems with any non-binary number system.
We have 10 fingers, 10 toes, etc. We can handle base-10 math easily, but not base-2 math.
Maybe you only use your 10 fingers to count to 10, but any self-respecting geek will use those 10 fingers to count, in binary, up to 1023 by using both states of their fingers to represent a one or zero (up or down). A base-1 system on your fingers is just a waste of states. With some practice you can even handle the unusual states like 21 and 27 easily (I use my thumb as 2^0).
Things you think are in the Constitution, but are not.
Here's why (I think) the minimum of m*n is considered optimal:
Each additional "base" value takes more complex circuitry (base 2 being the simplest).
But for small values of the base, we need more "bits" to represent a given value. A single hex value can represent the same number as four binary values.
Those of us old enough to remember using octal notation probably remember wishing that getting to 7 as a largest value was getting close, but not quite, to 9.
Binary (base 2) was adopted in the early days of computers because (1) electronically it was very easy to design circuits that either were saturated (max current) or cut-off (zero current), and (2) Boolean algebra had been around for 200 or so years, making the transition straightforward (although not easy).
It's been a long time since I took a semiconductor course, but I would think that a tri-state logic circuit (using -1.5V, 0V, and +1.5V, for example) should be fairly straightforward today.
Yes, truth-tables and such would become much more complicated, and de-Morgan's theorem would be relegated to the scrap heap, but it would seem to be a way to continue to increase processing power once Moore's Law begins to poop out as feature sizes become sub-atomic.
Moore's Law itself could continue, just taking advantage of better technology to move to quad-bit, penta-bit, and so forth, computing.
In deference to those who might be easily offended, I have abstained from using the obvious acronym for a 3-state digit.
(Exponential Growth = Unbreakable) => Tripe
I hate to add fuel to this sort of fire, but is Moore's "Law" a law, or an "observation"? They are not equivalent.
"...historical trend that hasn't been broken in thousands of years." - What codswallop. In a theoretically infinite universe this may be the case, but real life is never that simple. Exponential growth of velocity - diminishing returns as you approach the speed of light. Exponential population growth - always a ceiling....
I could go on and on - but I won't.
Q.
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