Balanced Ternary Notation

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A number represented in binary is a sum of the powers of 2 (1, 2, 4, 8, 16, ...) multiplied by 0 or 1. For example, 60 in binary notation is , using six "bits".


Balanced ternary notation multiplies each power of 3 (1, 3, 9, 27, ...) by -1, 0, or 1. In balanced ternary, 60 is , with 1 indicating -1; 60 requires five "trits". With weights 1, 3, 9, 27, and 81, the notation can be used to balance any unit amount from 1 to 121 by putting the weights on either side of the balance pan.


Contributed by: Ed Pegg Jr (January 2008)
Modified by: Paul Abbott
Open content licensed under CC BY-NC-SA



A nice article on balanced ternary notation is The Balanced Ternary Machines of Soviet Russia by Andrew Buntine.

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