trinary

Trinary, also known as ternary, refers to numeral systems and computational concepts that use three distinct states rather than two. The most common form uses digits 0, 1, and 2, with place values that are powers of 3. A number is expressed as a sum of digits times powers of 3, analogous to how binary uses powers of 2. The basic unit in a trinary system is called a trit, analogous to a binary bit.

Balanced ternary is a variant that uses three digits, typically −1, 0, and +1. This symmetric representation around zero can simplify certain arithmetic operations and the encoding of signed numbers, sometimes without requiring a separate sign bit. The digits are often denoted as −1, 0, and +1, or with symbols such as T, 0, and 1.

In computation and logic, trinary concepts extend beyond number representation. Three-valued logic, for example, generalizes Boolean logic to three truth values, such as true, false, and unknown, leading to various logical systems and calculi. Trinary computing has interested researchers for potential efficiency gains in specific arithmetic or data encoding schemes, although mainstream hardware overwhelmingly relies on binary.

History and use: trinary concepts have appeared in experimental and historical devices. The Setun computer, built in the Soviet Union in 1958, used ternary logic with three-state cells, illustrating that ternary machines are feasible in principle. In modern practice, binary hardware remains dominant due to manufacturing simplicity and established infrastructure, but ternary ideas influence niche memory technologies, error-correcting codes, and theoretical studies.

In summary, trinary describes base-3 representation, three-valued logic, and related computational ideas, with balanced ternary as a notable variant.