# 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