# Ternary computer

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A ternary computer (also called trinary computer) is a computer that uses ternary logic (three possible values) instead of the more common binary logic (two possible values) in its calculations.

## History

One early calculating machine, built by Thomas Fowler entirely from wood in 1840, operated in balanced ternary. The first modern, electronic ternary computer Setun was built in 1958 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. In the USA, the ternary computing emulator Ternac working on a binary machine was developed in 1973.

## Balanced ternary

Ternary computing is commonly implemented in terms of balanced ternary, 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 denary 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.

## Potential future applications

With the advent of mass-produced binary components for computers, ternary computers have diminished in significance. However, ternary logic's elegance and efficiency is predicted by Donald Knuth to bring them back into development in the future. One possible way this could happen is by combining 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. 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 quantum computer was proposed which uses a quantum ternary state, a qutrit, rather than the typical qubit. When the number of basic states of quantum element is d, it is called qudit.

## Ternary computers in popular culture

In Robert A. Heinlein's novel Time Enough for Love, the sapient 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".

Virtual Adepts in the roleplaying game Mage: The Ascension use ternary computers.

In Howard Tayler's webcomic Schlock Mercenary, every modern computer is a ternary computer. AIs use the extra digit as "maybe" in boolean (true/false) operations, thus having a much more intimate understanding of fuzzy logic than is possible with binary computers.

The Conjoiners, in Alastair Reynolds' Revelation Space series, use ternary logic to program their computers and nanotechnology devices.

## References

Ternary computer Wikipedia

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