Balanced Ternary Web Pages
If you thought the binary system was elegant, you should look at
balanced ternary. Briefly, balanced ternary is a base 3 positional
number system using the digits 0, 1 and -1. Among its properties :
on for details of how to do arithmetic in it, how to construct
yourself a set of scales using it and how a monetary system based on it
could stop you accumulating a mountain of small change (also available
as PostScript. There is also
source code in
C for performing arithmetic in balanced ternary as well as
annotated version of this source code and
ternary calculator written in Java.
- It can represent both positive and negative numbers without using a
- Replacing the low digits with zeroes rounds to the nearest power
- A number can be negated simply by negating each digit.
- Addition and multiplication are almost as simple as in binary; with
no digit larger than 1 in the tables.
- A suprising division algorithm.
Related pages :
Logical Alternative to the Existing Positional Number System (stored as
PostScript) - looks at what happens if you disallow the zero digit and only
allow positive digits.
Counterfeit Coin Problem which can be found in the rec.puzzles archive as
balance.p at NCSA and
weighing/balance in the Netherlands (see also weighing/optimal.weights). Elsewhere you
a related weighing
Dense Coding in
Experimental Quantum Communication - sending ternary data using
Diagrams for Kleenean Strong Ternary Logic (this link appears to
be dead - if anyone knows where it has moved to, please let me know)
art pages including images generated using Generalized Balanced
Bhattacharjee's site describing balanced ternary with a
Pascal program to convert decimal to balanced ternary
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