  Mathematically, ternary coding is more efficient than binary coding. It is
little used in computation because technology for binary processing is already
established and the implementation of ternary coding is more complicated, but
remains relevant in algorithms that use decision trees and in communications.
In this paper we present a new comparison of binary and ternary coding and
their relative efficiencies are computed both for number representation and
decision trees. The implications of our inability to use optimal representation
through mathematics or logic are examined. Apart from considerations of
representation efficiency, ternary coding appears preferable to binary coding
in classification of many real-world problems of artificial intelligence (AI)
and medicine. We examine the problem of identifying appropriate three classes
for domain-specific applications.
