Ternary Code (Base 3)

Ternary (base 3) is a number system that uses three distinct symbols, usually $0$, $1$, and $2$, to represent numbers.

Each position in a ternary number corresponds to a power of $3$, allowing for the unique encoding of whole or fractional values.

The three standard base-3 symbols are 0, 1, and 2. Some systems use variants such as 1, 2, and 3 or A, B, and C.

In standard (ternary) base 3, the symbols are $ 0 $, $ 1 $ et $ 2 $.

In balanced ternary, the possible values are $ -1, 0, +1 $, which are often written as $ -, 0, + $, but also sometimes $ 0 $, $ 1 $ and $ T $.

Balanced ternary code is a variant that uses the values ​​-1, 0, +1, allowing negative numbers to be represented without a separate sign.

This is not a simple replacement of 0, 1, and 2 with -1, 0, and 1; a different mathematical transformation must be applied.

To convert an integer (base 10 decimal) $ N $ to base 3, successively divide $ N $ by $ 3 $ and note the remainders (which are $ 0 $, $ 1 $, or $ 2 $).

Repeat until you obtain a quotient of zero. The remainders, read from bottom to top, give the base-3 representation.

Convert the absolute value of the number to base 3, then add a minus sign - in front of the result.

To convert a number from base 3 to base 10, multiply each digit by 3 raised to the power of its position (starting from 0 on the right) and add the results.