Balanced Ternary Notation
Balanced Ternary Notation
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".
111100=1×32+1×16+1×8+1×4+0×2+0×1
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.
11110=81-27+9-3+0
Details
Details
A nice article on balanced ternary notation is The Balanced Ternary Machines of Soviet Russia by Andrew Buntine.
External Links
External Links
Permanent Citation
Permanent Citation
Ed Pegg Jr, Paul Abbott
"Balanced Ternary Notation"
http://demonstrations.wolfram.com/BalancedTernaryNotation/
Wolfram Demonstrations Project
Published: January 25, 2008