non-binary hardware (was: Absolute

[joe at modcomp.UUCP]

u-dmfloy at sunset.utah.edu.UUCP writes [edited]:

> I've been toying with an idea [on trinary and up logic].  I've done some
> preliminary research and it's real sketchy.  I've looked at several
> alternative trinary logic levels.  No one has given me a convincing
> argument about which is correct yet.
> 
> For example;  Trinary 'AND':
> 
>     0 1 2              0 1 2
> =========          =========
> 0 | 0 0 0          0 | 0 0 0
> 1 | 0 1 2          1 | 0 1 2
> 2 | 0 2 2          2 | 0 2 1
> 
> 
> Both have merits. I suppose you could define them as AND2 and AND1.
> 
> Let's see what all of you have to say.

I haven't been able to divine what your underlying theories are from just
the logic charts you presented, so I remain unconvinced that either is
valid.

My own pet theory is that n-ary logic should be based on analog logic.  By
that reasoning, AND returns the lowest of the m input values and OR
returns the highest.  Inversion should simply flip across the n-ary range.
For example, let's look at trinary:

   AND    0 1 2        OR    0 1 2    INVERSION
      =========          =========        =====
      0 | 0 0 0          0 | 0 1 2        0 | 2
      1 | 0 1 1          1 | 1 1 2        1 | 1
      2 | 0 1 2          2 | 2 2 2        2 | 0

It should be possible to build XOR gates, adders, and so on with this
logic.  However, I haven't tried it.  Any takers?  More to the point, what
have you computer scientists out in net-land, who surely have studied this
subject to death decades ago, have to say?
--
Joe Korty              "flames, flames, go away
uunet!modcomp!joe      come back again, some other day"