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Beyond Binary Computing?

Posted by michael on from the base-three-for-fun-and-profit dept.

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?"

14 of 412 comments (clear)

  1. Trinary Computing by Liselle · · Score: 5, Informative

    Didn't the Soviets already do this? I don't remember it catching on very splendidly, though I guess than can be chalked up to the limitations of the times.

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    1. Re:Trinary Computing by DataPath · · Score: 5, Interesting

      The reason for doing work in trinary computing is that it is closest to the theoretically optimal computing base. The reasoning was something like this:

      Representations of numbers in a particular base have two defining characteristics - the number of values that can occupy a digit (m), and the number of digits it takes to represent that value (n).

      (Here's where the theory takes a leap, at least to me) The most efficient base (or simplest) base for performing computations is the one at which the m*n product is minimized. As an example, we'll take THE ANSWER, 42(base10).
      THE ANSWER in base 16 has a result of 16*2=32
      THE ANSWER in base 10 has a result of 10*2=20
      THE ANSWER in base 8 has a result of 8*2=16

      Here are the interesting cases, though:
      THE ANSWER in base 2 has a result of 2*6=12
      THE ANSWER in base 3 has a result of 3*3=9
      THE ANSWER in base 4 has a result of 4*3=12

      IIRC, according to the article I was reading, the most effective base is actually "e" (euler's constant).

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    2. Re:Trinary Computing by isomeme · · Score: 5, Informative

      The most effective base being e is not coincidental. Consider that the number of digits required to represent a number is proportional to the log to the base in use of that number. Since e is the base of the natural logarithms, with the property that the slope of the curve e^x equals e^x for all x, the product of a base and the logarithm of any number to that base will always reach a minimum for base = e.

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  2. Sounds like a good idea. by digital+bath · · Score: 5, Interesting

    Looks like systems working with more than ones and zeros would just need a way to encode these different values with different strengths of signals (as opposed to off=0, on=1). Something like no voltage=0, 1/3 voltage = 1, 2/3 voldage = 2 and 3/3 voldage=4. Seems like a very good way to wrap more information in the same signal/clock, but how would the logic work? How would and/or/xor work?

    My mind is too used to binary :) But I'd be willing to learn..

    Sounds like a good idea.

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  3. Re:Truth Tables * n? by stratjakt · · Score: 5, Informative

    The whole concept of AND/OR/NAND is a Boolean construct. The gates define the 16 functions that can be expressed by two boolean variables. Ternary or quarternary logic would more basic functions, and different ones, but it would be easy to implement boolean logic as well (like your quarternary example).

    Try reading this for a quick primer.

    It wont happen all at once, its a different paradigm and a definate learning curve, like the difference between imperative, functional and object oriented programming. But it has definate advantages, beyond the Moores law tripe.

    --
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  4. Ternary by Anonymous Coward · · Score: 5, Informative

    For reference, Slashdot has done two other stories on ternary computing here and here.

  5. Ternary system is the way to go by a_ghostwheel · · Score: 5, Insightful

    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?

    1. Re:Ternary system is the way to go by Andorion · · Score: 5, Informative

      Here's a link to what you're talking about:

      Third Base

      It's a good read, stuff I didn't know until I read your post and looked it up =)

      ~Berj

  6. Survey ... by BabyDave · · Score: 5, Funny

    Do you think three-valued logic is a good idea?

    1. Yes
    2. No
    3. Maybe
  7. Re:Truth Tables * n? by Maimun · · Score: 5, Informative

    I have studied little multi-value logic. In m-valued logic: AND is minimum. OR is maximum. XOR is complement modulo m A friend of mine that was doing testing of multi-value circuits (purely theoretical work, of course) said that some phenomena are seen "more clearly" when the base is bigger than 2. HTH.

  8. Balanced Ternary, and Ternary circuits by Sparr0 · · Score: 5, Interesting

    One of the best parts of Ternary (Trinary, base 3) is that you can use BALANCED Ternary, in which the digits are not 0, 1, and 2, but are -1, 0, and 1. This allows you to represent any integer without a sign bit. Letting N represent -1 digit you can represent -17 in balanced ternary as 101N (1*(3^0),0*(3^1),1*(3^2),N*(3^3)).

    You can check out http://www.trinary.cc/Tutorial/Tutorial.htm for many examples of ternary circuits using ternary logic gates.

  9. Perfect for women by marvin2k · · Score: 5, Funny

    The quaternary system would be perfectly suited for women:

    0 = No
    1 = Yes
    2 = No (But I mean yes)
    3 = Yes (But I mean no)

  10. Re:It's commonly assumed that people are base-10.. by Mr.+Sketch · · Score: 5, Insightful

    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).

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  11. Base 3 or 4 logic is NOT smaller than base 2. by Eric+Smith · · Score: 5, Informative
    A move to multi-valued logic provides more computational capability without the standard increase in die size or transistor count.
    No, it doesn't. Let's see you design a 16-quat full adder that takes fewer transistors or less die area than an 32-bit full adder.

    Base 3 or higher are a lose for implementing logic. Base 4 is useful in some kinds of memory, and this has been done by Intel since around 1980-81. Intel used a quaternary ROM (two bits per cell) for the microcode store of the 43203 Interface Processor, and (IIRC) for the 8087. More recently this technique has been used in flash memory.