Ternary computer
Encyclopedia
A ternary computer is a computer
that uses ternary logic
(three possible values) instead of the more common binary logic
(two possible values) in its calculations.
was built in the late 1950s in the Soviet Union at the Moscow State University
by Nikolay Brusentsov
, and it had notable advantages over the binary
computers which eventually replaced it (such as lower electricity consumption and lower production cost). In 1970 Brusentsov built an enhanced version of the computer, which he called Setun-70.
, which uses the three digits -1, 0, and +1. The negative value of any balanced ternary digit can be obtained by replacing every + with a – and vice versa. It is easy to subtract a number by inverting the + and – digits and then using normal addition. Balanced ternary can express negative values as easily as positive ones, without the need for a leading negative sign as with decimal numbers. These advantages make some calculations more efficient in ternary than binary.
to bring them back into development in the future. Possible ways on how this can happen is by the combination of an optical computer with the ternary logic
system. A ternary computer using fiber optics could use dark as 0 and two orthogonal polarizations of light as 1 and -1. This future potential has also been remarked by certain companies as Hypres which is actively engaged in ternary computing. IBM also reports infrequently on ternary computing topics (in its papers), but it is not actively engaged in it.
The Josephson junction has been proposed as a balanced ternary memory cell, using circulating superconducting currents, either clockwise, counterclockwise, or off. "The advantages of the proposed memory circuit are capability of high speed computation, low power consumption and very simple construction with less number of elements due to the ternary operation."
In 2009, a ternary quantum computer
was proposed which thus uses qutrit
s rather than qubit
s. When the number of basic states of quantum element is d, it is called qudit.
's novel Time Enough for Love
, the sentient computers of Secundus, the planet on which part of the framing story is set, including Minerva, use an unbalanced ternary system. Minerva, in reporting a calculation result, says "three hundred forty one thousand six hundred forty... the original ternary readout is unit pair pair comma unit nil nil comma unit pair pair comma unit nil nil point nil" (Chapter Variations on a Theme III: Domestic Problems, Berkley books 19th printing [1982] page 99)
Computer
A computer is a programmable machine designed to sequentially and automatically carry out a sequence of arithmetic or logical operations. The particular sequence of operations can be changed readily, allowing the computer to solve more than one kind of problem...
that uses ternary logic
Ternary logic
In logic, a three-valued logic is any of several many-valued logic systems in which there are three truth values indicating true, false and some indeterminate third value...
(three possible values) instead of the more common binary logic
Binary logic
Binary logic could refer to:* any two-valued logic, especially in social sciences* classical propositional two-valued logic, also called boolean logic in engineering, which is the logical foundation of digital electronics...
(two possible values) in its calculations.
History
One of the earliest calculating machines, built by Thomas Fowler entirely from wood in 1840, was a ternary computer. The only modern, electronic ternary computer SetunSetun
Setun was a balanced ternary computer developed in 1958 at Moscow State University. The device was built under the lead of Sergei Sobolev and Nikolay Brusentsov. It was the only modern ternary computer, using three-valued ternary logic instead of two-valued binary logic prevalent in computers...
was built in the late 1950s in the Soviet Union at the Moscow State University
Moscow State University
Lomonosov Moscow State University , previously known as Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be one of the oldest university in Russia and to have the tallest educational building in the world. Its current rector is Viktor Sadovnichiy...
by Nikolay Brusentsov
Nikolay Brusentsov
Nikolay Brusentsov, born February 7, 1925 in Kamenskoe is a Russian computer scientist, most famous for having built a ternary computer, Setun, together with Sergei Sobolev in 1958.-References:...
, and it had notable advantages over the binary
Binary numeral system
The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...
computers which eventually replaced it (such as lower electricity consumption and lower production cost). In 1970 Brusentsov built an enhanced version of the computer, which he called Setun-70.
Balanced ternary
Ternary computing is commonly implemented in terms of balanced ternaryBalanced ternary
Balanced ternary is a non-standard positional numeral system , useful for comparison logic. It is a ternary system, but unlike the standard ternary system, the digits have the values −1, 0, and 1...
, which uses the three digits -1, 0, and +1. The negative value of any balanced ternary digit can be obtained by replacing every + with a – and vice versa. It is easy to subtract a number by inverting the + and – digits and then using normal addition. Balanced ternary can express negative values as easily as positive ones, without the need for a leading negative sign as with decimal numbers. These advantages make some calculations more efficient in ternary than binary.
- "I often reflect that had the Ternary instead of the binary Notation been adopted in the Infancy of Society, machines something like the present would long ere this have been common, as the transition from mental to mechanical calculation would have been so very obvious and simple". (Fowler, 1840)
The future
With the advent of mass-produced binary components for computers, ternary computers have diminished to a small footnote in the history of computing. However, ternary logic's elegance and efficiency is predicted by Donald KnuthDonald Knuth
Donald Ervin Knuth is a computer scientist and Professor Emeritus at Stanford University.He is the author of the seminal multi-volume work The Art of Computer Programming. Knuth has been called the "father" of the analysis of algorithms...
to bring them back into development in the future. Possible ways on how this can happen is by the combination of an optical computer with the ternary logic
Ternary logic
In logic, a three-valued logic is any of several many-valued logic systems in which there are three truth values indicating true, false and some indeterminate third value...
system. A ternary computer using fiber optics could use dark as 0 and two orthogonal polarizations of light as 1 and -1. This future potential has also been remarked by certain companies as Hypres which is actively engaged in ternary computing. IBM also reports infrequently on ternary computing topics (in its papers), but it is not actively engaged in it.
The Josephson junction has been proposed as a balanced ternary memory cell, using circulating superconducting currents, either clockwise, counterclockwise, or off. "The advantages of the proposed memory circuit are capability of high speed computation, low power consumption and very simple construction with less number of elements due to the ternary operation."
In 2009, a ternary quantum computer
Quantum computer
A quantum computer is a device for computation that makes direct use of quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers are different from traditional computers based on transistors...
was proposed which thus uses qutrit
Qutrit
A qutrit is a unit of quantum information that can exist in three possible states.The qutrit is analogous to the classical trit, just as the qubit, a quantum particle of two possible states, is analogous to the classical bit.-Representation:...
s rather than qubit
Qubit
In quantum computing, a qubit or quantum bit is a unit of quantum information—the quantum analogue of the classical bit—with additional dimensions associated to the quantum properties of a physical atom....
s. When the number of basic states of quantum element is d, it is called qudit.
Ternary computers in popular culture
In Robert A. HeinleinRobert A. Heinlein
Robert Anson Heinlein was an American science fiction writer. Often called the "dean of science fiction writers", he was one of the most influential and controversial authors of the genre. He set a standard for science and engineering plausibility and helped to raise the genre's standards of...
's novel Time Enough for Love
Time Enough for Love
Time Enough for Love is a science fiction novel by Robert A. Heinlein, first published in 1973. The work was nominated for the Nebula Award for Best Novel in 1973 and both the Hugo and Locus Awards in 1974.-Plot:...
, the sentient computers of Secundus, the planet on which part of the framing story is set, including Minerva, use an unbalanced ternary system. Minerva, in reporting a calculation result, says "three hundred forty one thousand six hundred forty... the original ternary readout is unit pair pair comma unit nil nil comma unit pair pair comma unit nil nil point nil" (Chapter Variations on a Theme III: Domestic Problems, Berkley books 19th printing [1982] page 99)
Literature
Hunger, Francis: SETUN. An Inquiry into the Soviet Ternary Computer. Institut für Buchkunst Leipzig, 2008, ISBN 3-932865-48-0 (English, German)See also
- Ternary numeral systemTernary numeral systemTernary is the base- numeral system. Analogous to a bit, a ternary digit is a trit . One trit contains \log_2 3 bits of information...
- Balanced ternaryBalanced ternaryBalanced ternary is a non-standard positional numeral system , useful for comparison logic. It is a ternary system, but unlike the standard ternary system, the digits have the values −1, 0, and 1...
- SetunSetunSetun was a balanced ternary computer developed in 1958 at Moscow State University. The device was built under the lead of Sergei Sobolev and Nikolay Brusentsov. It was the only modern ternary computer, using three-valued ternary logic instead of two-valued binary logic prevalent in computers...
- Ternary logicTernary logicIn logic, a three-valued logic is any of several many-valued logic systems in which there are three truth values indicating true, false and some indeterminate third value...
- TernacTernacTERNAC is a ternary computer that was implemented in 1973 at SUNY, Buffalo.In TERNAC both fixed-point and floating-point capability were provided...
- Ternary flip-flap-flop
- Ternary SRAM