Notes on Ternary Logic.

Along with ternary arithmetic, a computer built of ternary hardware can also exploit ternary logic. Consider the task of comparing two numbers. In a machine based on binary logic, comparison is often a two-stage process. First you ask, "Is x less than y?"; depending on the answer, you may then have to ask a second question, such as "Is x equal to y?" Ternary logic simplifies the process: A single comparison can yield any of three possible outcomes: "less," "equal" and "greater."

Reversible Gates

• NOP: The most dull gate (number 8) this does not change the input. It is its own complement. Applying it any number of times get you back to your intial value.
• NEG Gate: Balanced ternary gates have a tighter relationship between logical and mathmatical negation. The are the same bitwise operator. It is its own complement. Applying it multiple time every even application brings back the intial value.
• INC and DEC Gate: These gates can arithmetically be thought of as single trit increment or decrement without carry, but with roll over. These gates are also complementary . Every 3 applications of either one of these gates in a row bring back the intial value.
• Gate 2 & 6: The these gates are most intuitively expressed as combinations of NEG, INC and DEC.

To learn more, see reversible computing.

Single Input Gates

• Mathematical Properties