The Babylonians use separately Combinations of two symbols To represent each digit from 1 to 59. That is great confused, isn’t it? Our decimal system seems simple by comparison, with 10 digits from 0 to 9 to express each number visualized.
Computers only need two digits: 0 and 1. But that binary system is not only optional for these machines. Previously, experts passed the calculations of machines working in three numbers, a ternary system, which they would expect to give more efficient information processing. However today’s ternary computers are hobby projects. How did it make?
In principle, any number can be represented by any number system, if the latter becomes base 10, base 60, base 3 or base (base 2
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To the usual decimal system, the number 17 (which is, a 1) indicates that you need to calculate 10 + 7 × 1 (1 × 10).
If you want to express 17 on base 3, as it is: 1710 = 1 × 32 + 2 × 31 + 2 × 30 = 1223 . (Lower numbers symbolize the base used.) In binary notation, the number 1710 = 1 × 24 + 0 × 23 + 0 × 22 + 0 × 21 + 1 × 20 = 10,0012.
Comparing these numbers, familiar notimal notation is the most efficient distance: only two numbers are required to write 17, which can be useful for a computer. On the other hand, the machine needs to work with a basic 10 different numbers, with a practice problem.
In concrete computers, 0 and 1’s represented by the state of a particular piece of electrical hardware, such as a capacitor or transistor. Many of these devices interpret a state-like transistor transfer or off-to a 0 or 1 of a way that does not support gradations or degrees needed for base 10 computing. Consider designing a switch with 10 different positions between off state-this method can be complicated immediately.
For practical reasons, the notice of recognition can rule as a basis for a computer. There is so much number. But have a better number system for information processing than binary system ubiquitous today?
The perfect basis for computers
To answer that question, you need Find a compromise between the length of the representation l to a number N and the number chamanyhi of numbers used on a basis. To do this, you can view the product in two amounts, chamanyhi × L, And ask yourself which base it is the smallest. The height of a number N represented by the basis chamanyhi equivalent to approximately with Quient Log (N) / log (chamanyhi). The question is: For what basis chamanyhi is the product chamanyhi × log (N) / log (chamanyhi) A little?
If you remember your school days, you might even know how to calculate the optimal amount of B: You get the product name in terms of B, put it equal to zero and then resolve the equation for chamanyhi. Alternatively, you can get the equation – that y = chamanyhi × (log (N) / log (chamanyhi)) – On a piece of paper and identify the point of the curve closest to X-Saxis. Any method you choose, to say that you don’t have the wrong one, the optimal value FOR chamanyhi = e ≈ 2.718, Euleler number.
An unreasonable result can be confusing at first sight. How do you create a system number for a standard unreasonable? If you consider all numbers, including unreasonable qualities such as PI (π), then a number system with basic e may have advantages. But if you want to represent integers like 1, 2 or 3 this way, it can easily be complicated. So it is important that it means to count the euler number: so with integers, 3 as the optimal basis of information processing.
Ternary System: With perfect balance
A system number with three digits such as 0, 1 and 2 is known as a Ternary System. This, however, can also be represented by what mathematicians think of a balanced way using three numbers -1, 0 and 1.
In this “balanced ternary” system, the number 1710 As it is:
1710 = 1 × 33 + (-1) × 32 + 0 × 31 + (-1) × 30 = 1 (-1) 0 (-1)
Experts find the balanced ternary system more attractive because of its symmetry. For example, in the second number of his book series The art of computer programming,, Computer scientists Donald E. Knuth describe “the most beautiful system of all.”
The Ternary System not only stimulates the theory. In 1840 English inventor Thomas Fowler established a calculated machine working on the Balance Ternary System, a mechanical computer calculated in numbers -1, 0 and 1. It used different computers. If you combine two digits of the Ternary System, you just don’t get 0 or 1 (which often matches the real or lie in the binary system) but also a third result.
Some calculations can be shortened as a result: eg, if you want to compare both numbers with each other to know one step when a number is small, bigger than another. In the binary system, on the other hand, two calculation measures are required: First you will check if they differ and are more or less.
A ternary computer behind Iron Curtain
The mechanical device in Fowler is not the only computer to be counted in three. At the beginning of the Cold War, the Soviet Union attempted to develop the first electronic computers. Because it is very difficult to hold transistors (electronic components where custom computers are based), the Soviets seek other options to achieve their goal.
In 1958 the first electronic Ternary computer, called Setun, was built at the Moscow state University. It uses magnetic cores and diodes in processing of Ternary digit information, or “trits.” Over the years, about 50 setun computers are made.
But ternary computers are not covered, in part because of hardware and existing conventions. It is difficult to code electronic components with three different states. With Setun, researchers should use two magnetic components per trit-but if they work in binary, they can encode several parts of these components.
All computers currently work with transistors. It has two inputs in which any current can flow (encoding a 1) or not (a 0) and an output that even passes through today (a 1). By clearly connecting transistors together, logic gates can be built to perform all calcilable operations.
Many hobbyists Develop ternary computers – but it’s totally fun. Because ternary machines and binary computer are perfectly different numbers and use different logic, both cannot be connected. That’s a mercy, I think, even if a ternary computer doesn’t make more than usual devices.
This article originally appeared Spectrum of science and has been reproduced with permission.
