Ternary Computing

eviltwinimposter writes: "This month's American Scientist has an article about base-3 or ternary number systems, and their possible advantages for computing and other applications. Base-3 hardware could be smaller because of decreased number of components and use ternary logic to return less than, greater than, or equal, rather than just the binary true or false, although as the article says, '...you're not going to find a ternary minitower in stock at CompUSA.' Ternary also comes the closest of any integer base to e, the ideal base in terms of efficiency, and has some interesting properties such as unbounded square-free sequences. Also in other formats."

Comments

CompUSA??

[vacamike]

CompUSA??? Why even mention the hideous chain of stores. CompUSA has the most inept employees that are ready to 'impress' you with their Windows knowledge and sell you some worthless $50 Belkin cable.

Salesman: "you need this cable. a hot-swappable IDE ribbon is a must have."
Salesman #2: "is that the hot swappable IDE ribbon? Oh snap! that one made my AOL twice as fast and my por- er my 'files' save quicker."
Salesman #3: "guys, don't forget that he needs a terminator for that ribbon. its an extra $37.95 plus we get to grab your wifes boobies."
Customer: "What?! My wife? are you sure??"
Salesman: "positive. now lets see some boobage; i brought my star wars digital camera."

CompUSA sucks.

We would have to come up with new crypto

[Kiwi]

Ternary systems, of course, would have to use new crypto systems, since all of the current block ciphers assume binary data.

I actually have been thinking that it should not be too hard to come up with a Rijndael variant which uses a tenary system (using a 3^n instead of a 2^8 galois field, of course), since Rijndael is an incredibly easy to understand and very flexible cipher.

The question comes to mind, of course, if whether the galois field should use the elements (-1,0,1) or use (0,1,2) to represent a single tenary bit.

Sounds like a fun project, actually.

- Sam (who only uses crypto for https and ssh, since I, as much as I enjoy the math of crypto, have a "you are as sick as you secrets" point of view)

Ternary trees

[mauddib~]

Dr. Dobbs recently had an interesting article about ternary trees (http://www.ddj.com/articles/1998/9804/9804a/9804a .htm), which also discussed some performance comparisons between binary trees and hashes.
We just did some testing, comparing those search algorithms with eachother. Although hashes are more or less comparable in speed with ternary trees, binary trees are much slower.

Some sample output: (btw, we didn't balance the ternary tree, although we did some really basic balancing on the binary tree).

testing binary tree
elements = 235807
235807 insertions in 97.995633 seconds
tree depth = 7882
235807 lookups in 95.111857 seconds

testing hash table
elements = 235807
235807 insertions in 0.442643 seconds
tree depth = 63709 (number of buckets in use)
235807 lookups in 0.345933 seconds

testing ternary tree
elements = 235807
235807 insertions in 0.744229 seconds
tree depth = 93
235807 lookups in 0.386081 seconds

Clearly the ternary tree and hash are much faster than the binary tree. Although there are still some optimisations to make, we believe that the ternary tree will outperform the binary tree at all times.

We also made some (very) cool graphs with Graphviz, but unfortunately have no good place to share it with the rest of the /. reading audience.