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ternary programming and operations

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    This optional chapter looks at ternary (three-state) programming, logic, and operations.

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ternary programming and operations

    This optional chapter looks at ternary (three-state) programming, logic, and operations.

n-state logic

    Almost all modern computer hardware and software is built with binary logic, simple switching machines.

    In the early days of computers, there were both binary (two-state) and decimal (10-state) computers. Modern computers that have decimal hardware actually store and work with the decimal information in an underlying binary format, called Binary Coded Decimal, or BCD.

    Some of the earliest computers used ternary (three-state) logic. In 1940 a team of mathematicians at Cambridge University, that included Alan Turing and Konrad Zuse, built a ternary logic computer called Trinity.

    There are modern companies that build various n-state logic circuits and machines.

ternary logic

    Base three has been proposed for computers on the argument that three state logic is almost as easy to build as two state logic and that the storage of numbers (and therefore, countable items) in base three is more efficient than binary base two.

    The ternary number system uses the digits 0, 1, and 2. The balanced ternary system uses the digits -1, 0, and +1.

    A single digit in either ternary number system is called a trit. A ternary tryte of either six trits (as ion the Setun computer) or nine trits (theoritcal) is the computer equivalent of a binary byte.

    A ternary string is a string that contains only 0s, 1s, and 2s.

    Every integer can be expressed as a balanced ternary expansion of the form:

e_k3^k + e_k-13^k-1 + … + e₁3 + e₀

    The experimental Russian Setun computer, built at Moscow State University in 1958, used balanced ternary notation. Fifty Setun computers (named for the Setun River, which ends near moscow) were built between 1958 and 1965. The Forth-like programming language DSSP (Dialog System for Structured Programming) was created by computer science students at Moscow State university for the Setun computer.

    “perhaps the symmetric properties and simple arithmetic of this number system will prove to be quite important some day—when the “flip-flop” is replaced by the “flip-flap-flop”.”—Fundamental Algorithms; The Art of Computer Programming; Vol. 1; by Donald Knuth

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