So I got to thinking about computer systems and how they are all based on binary. So the math we perform is obviously based upon a binary approach. Then I started wondering if there was value in exploring math using a different base. I know in math we can shift things to a different domain to do things more efficiently (like Laplace transforms to get to the frequency domain to do freq based calcs, or quaternions to do various orientation calcs). I thought maybe a base 3 logic might do some calcs better. I searched and found that indeed some ternary computing systems had been built. I then searched for libraries that might employ ternary math as an exploration exercise. I didn't find anything except academic articles (few at that).

This idea of changing the base in the math (and possibly the frame of reference) is interesting. It is like searching for treasure and not being sure it even exists.


  • 7
    The main reason is that it's easy to use transistors as switches. What they don't have is a useful plateau between those states (and also the power losses are not nice there), that's why base 3 math isn't really useful.
  • 11
    The mathematics behind computation don't rely on binary logic at all, it just happens to be an implementation detail, so you can switch it out for any sufficiently powerful logic system, including n-ary, quantum binary (or n-ary), and other more exotic types like probabilistic models. There are many other possible types of computers than the regular one.

    It really is a function of implementation technology. It's very easy to make 2-state devices via silicon and guarantee that they'll always work because your noise immunity has to cover two states only, but at the densities we're seeing now, even this is very, very hard to do (how do you distinguish between 0 state and 1 state in a device that's a bunch atoms wide?). With ternary devices ensuring that 0, 1, and 2 are clearly distinguishable at single digit nanometer scale and 1+ GHz is very difficult, so the gains from process technology outweigh the gains from ternary efficiency. You might argue that we don't need to do that because ternary logic is more efficient and that's absolutely correct, but I haven't heard of any implementation that manages to do that trade-off successfully. Who knows, with new n-stable devices coming and optical switching and all that good stuf, we might see n-ary logic (why stop at three after all).
  • 1
    I did see some information about potentially using ternary for communication. This is due to how optical data is sent down a fiber. But that is pretty specific to a pipe that just packs more bits.
  • 1
    @Demolishun Or for storage, think TLC/QLC flash. But that's also not really calculation.
  • 1
    @RememberMe Nail, head.
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