Ternary Numeral System
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The ternary numeral system is a positional numeral system with base 3. It means that every number is written using only three digits: 0, 1, and 2. This differs from the common decimal system with base 10 (ten digits: 0 through 9).
Like other positional systems, each digit position has a value determined by its place. The rightmost position is 3⁰ (1), the next is 3¹ (3), then 3² (9), and so on. For example, the ternary numeral 102 equals 1×9 + 0×3 + 2×1 = 11 when written in base 10.
Base conversion
To convert a base-10 number to ternary, divide repeatedly by 3 and keep the remainders (0, 1, or 2). Reading the remainders from last to first gives the ternary representation. The reverse conversion is done by multiplying each digit by the power of 3 at its position and summing the results.
Balanced ternary
Another well-known variant is balanced ternary. Instead of using 0, 1, and 2, it uses the values −1, 0, and +1. The main advantage is that positive and negative numbers can be represented in the same way without needing a separate sign symbol, and rounding becomes straightforward.
Use and history
Modern computers operate on base 2 (binary) because two states are easy to represent with electric current. However, some early computing experiments used balanced ternary. Base 3 also appears in pure mathematics, particularly in fractal sets such as the Cantor set, and in certain weighing puzzles solved using a two-pan balance.