A Concise History of computers (i): From the calculation of the multiplication machine _ mathematics

Everything has its history, the modern computer has experienced the addition machine, multiplication machine, analysis machine, Turing machines and other stages. How does today's computer actually develop to this appearance now? I'm sure you'll be interested.

The first people I guess is to use the finger to count, so most of the ancient civilization is used in the decimal. But found that 10 fingers are not enough, so people use a number of sticks, stones, rope and other things to count. But the first real computing tool in the world is China's invention in the spring and Autumn period. In the counting method, the number of units is expressed by two kinds of arrangement, 1-5 of which are arranged in vertical and horizontal way to calculate the corresponding number, and 6-9 are represented by the above calculation and the corresponding calculation. When the number of digits, a bit with longitudinal, 10-bit with horizontal, hundred with longitudinal, thousands with horizontal, and so on, with zero empty. This counting method follows the 100-carry system. Later, China invented the abacus, which shows that China in the field of mathematics has always been ahead of the world.

Like an abacus, this computing tool needs to be manipulated by people, and not only inefficient but also prone to error in large computations. As a result, it is natural for people to realize a mechanical computer. The world's first mechanical computer was invented by the Frenchman Passaca in 1642. Pascal, a very familiar name. is the pressure unit in physics not called Pascal? Isn't there a programming language called Pascal? Yes, they are the same person. Pascal was a versatile man, a mathematician, a physicist, a philosopher and an essayist. Unfortunately, he died at the age of 39, although he was very short in the world, but there are many things for posterity, interested people can see his "mind record".

The basic principle of the Pascal Adder is that there is a set of wheels in the machine, with 10 digits from 0 to 9 engraved on each wheel. The number on the right first wheel represents a 10-digit number, and so on. In addition to the two number, first in the add machine on the wheel of a number, and then according to the second number on the corresponding wheel rotation of the corresponding number, and finally will get the sum of the two numbers. If the sum of the two digits exceeds 10, the addition machine will automatically carry the gear. Because a small wheel rotates 10 digits, it forces the next small wheel to rotate a number exactly. The calculated results are shown on the Reading window on the addition machine panel, and the wheels are restored to 0 digits. It can be seen that Pascal's invention of the addition machine is not a fully mechanical computer, should belong to semi-automatic computer, but in the Carry on the automatic. But his adder has at least led people to a path that can replace people's memories and thoughts with a purely mechanical device.

Adding machine as the name implies can only be added subtraction operation, for multiplication and division operation but powerless. After a lapse of 32 years, however, the multiplication machine was invented by another great genius, Leibniz. The name is not very familiar. Yes, he was the one who invented the calculus and the binary in the same way as Newton. The great part of Leibniz's inspiration came from Pascal's addition machine. How to use the machine to achieve multiplication. It is obvious that the mechanical device does not memorize multiplication formulas, it can only be achieved by continuous addition. In order to achieve continuous addition, Leibniz invented a device called "Walking Wheel". The step wheel is a long cylindrical body with 9 teeth, and 9 teeth are distributed sequentially on the cylinder surface, and a small gear next to it can be moved along the axis to engage with the stepping wheel. Whenever a small gear turns a lap, the stepper wheel can be based on the number of teeth meshing with the pinion, rotating 1/10, 2/10 laps respectively ... until the 9/10 lap, so that it can repeat the addition.

Leibniz designed the multiplication machine can carry out subtraction four kinds of operations, to the mathematical calculation of the time to bring great convenience. And for future generations to design a more powerful computer laid a solid foundation.