# 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 :
• It can represent both positive and negative numbers without using a unary minus.
• Replacing the low digits with zeroes rounds to the nearest power of 3.
• 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.
Read 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 an annotated version of this source code and a balanced ternary calculator written in Java.
Related pages :
Generalized Balanced Ternary
A 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.
Ternary Golay Codes
The 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 can find a related weighing problem.
Dense Coding in Experimental Quantum Communication - sending ternary data using quantum mechanics
Decision Diagrams for Kleenean Strong Ternary Logic (this link appears to be dead - if anyone knows where it has moved to, please let me know)
Steve Whealton's art pages including images generated using Generalized Balanced Ternary.
Abhijit Bhattacharjee's site describing balanced ternary with a Pascal program to convert decimal to balanced ternary
Other References
These pages maintained by James Allwright.