Adding machine. Adding machine and adding machines: Historical overview

Frenchman Blaise Pascal was the son of a tax collector. Watching his father's endless tedious calculations, he decided to create a computing device. At the age of 19, Blaise began work on building a adding machine. Twenty years later, Pascal died, but humanity remembered him as an outstanding mathematician, philosopher, writer and physicist. It is not for nothing that one of the most common programming languages ​​is named after Pascal.

Pascal's summing machine (mechanism)

Pascal's adding device was a box with many gears. In just one decade, the scientist managed to build more than fifty different versions of the machine. While working on the Pascaline, the summed numbers were entered by turning the dials in a certain way. Each was marked with divisions from zero to nine, which corresponded to the 1st decimal place of the number. The wheel “transferred” the excess over the nine, while making a full circle and moving the left “senior” wheel one unit forward.

Despite universal recognition, the device did not make the scientist rich. However, the very principle of linked wheels formed the basis of most computing machines over the next three centuries. For his invention, Pascal received a royal patent, according to which he retained copyright for the production and sale of machines. However, the gifted inventor did not stop there.

In 1648, Pascal completed his “experiments concerning emptiness.” He proved the absence of “fear of emptiness” in nature. The scientist analyzed the equilibrium of liquids under the influence atmospheric pressure. The results of the discoveries formed the basis for the invention of the hydraulic press, which was significantly ahead of the technology of that time.

Pascal's summing machine (appearance)

But one fine moment the scientific path became disgusting to the famous scientist. The temple of science turned out to be cramped, and Pascal wanted to enjoy the “charms” of life. The world accepted him immediately, and for several years the inventor immersed himself in the atmosphere of aristocratic salons. All these years, Pascal's younger sister, a nun from Port Royal, tirelessly prayed for the salvation of her brother's lost soul.

One November evening in 1654, Pascal had a mystical insight. When he came to his senses, he immediately wrote down the revelation on a piece of parchment and sewed it into the lining of his dress. This relic was with the scientist until his very last day.

On the day of Pascal's death, his friends discovered the parchment. The event became a turning point in the life of the inventor, who left scientific practice and experiments. From now on, his writing talent was aimed at defending Christianity. The scientist publishes several artistic essays entitled “Letters to a Provincial.”

Pascal's summing machine (circuit diagram)

Pascal devoted the last year of his life to a pilgrimage to the churches of Paris. He was plagued by terrible headaches, and doctors forbade mental stress. However, the patient managed to write down the thoughts that came to his mind on any material that came to hand. On August 19, 1662, a painful, long-term illness took over, and Blaise Pascal died.

After his death, friends discovered many bundles of notes that were tied with twine. Later they were deciphered and then published as a separate book. It is known to the modern reader under the name "Thoughts".

The programming language was named after Pascal. His father is considered to be Niklaus Wirth. Work on the Pascal language was carried out throughout 1968-1969. The year of birth of the Pascal language is considered to be 1970. The computer community has found in it an effective tool for structured programming and teaching proper programming.

Blaise Pascal's adding machine is an invention that surprised his contemporaries, but never found its own circle of clients. The mechanism, based on gears, is considered one of the ancestors of the calculator.

The history of the development of summing devices began in the 17th century. “Pascalina” is an invention of the French scientist Blaise Pascal, which is attributed to one of the stages in the development of computer technology. Pascal, already at the age of 19, began developing his own calculating machine, which can now be read about on the pages of textbooks. This invention is considered one of the prototypes of the calculator.

"Pascalina": history of origin

Creation of one of the most early models summing machines belongs to the French physicist and mathematician Blaise Pascal. Pascal's father was a tax collector, so already at the age of 19, the future scientist saw how various accounting operations were carried out. Already during this period, the first drawings of “Pascalina” were created. In total, the final development of the device took 5 years.

In theory, Pascal's mechanism was quite simple to use, but due to the poor development of the technical side, the implementation of the scientist's plan became a complex task, for which many difficulties had to be overcome.

Blaise wanted his summing machine to simplify any complex calculations, both for an educated person and for someone who understood little in arithmetic. Pascal touched upon an important issue concerning not only his family, but also the development of science in the 17th century.

Over the course of 10 years, the researcher created more than 50 calculating machines, but he was able to sell only a small fraction of his inventions. Pascal gave one of the first finished devices to Chancellor Sergier as gratitude for his help in scientific activity young Blaise.

What is Blaise Pascal's calculating machine?

“Pascalina” is a small box containing many interconnected gears (gears). Each wheel had markings from zero to nine. In order to perform the addition operation, it was necessary to dial the summing numbers using the required number of gear revolutions. The wheels moved until the desired number appeared. At full turn When the remainder (more than 9) appeared, the gear transferred to another category, moving the adjacent wheel one division.

The use of wheel revolutions for the addition process was not an innovation in Pascal’s scientific work, since this idea was voiced back in 1623 by Wilhelm Schiccard. Indeed, Blaise’s invention is considered to be the transfer of the remainder to the next digit when the gear is fully rotated.

The first “pascalines” had five gears, and with further modernization of technology in the mechanism, their number reached eight, which made it possible to work with large numbers(up to 9999999).

This mechanism was actively used in various technical devices until the twentieth century. Its advantage was the ability to automatically fold multi-digit numbers the device itself.

Researchers of the history of the emergence of counting mechanisms believe that Pascal created his adding machine almost from scratch, since he was not familiar with Schiccard’s project.

The device surprised modern science, however, due to the high cost and complexity of operation, it was never able to find its audience. Nevertheless, Pascal's invention made a huge contribution to the history of the development of computer technology.

The first working model of a adding machine was created in 1642 by the famous French scientist Blaise Pascal. For execution arithmetic operations Pascal replaced the translational movement of the knuckles in abacus-shaped instruments with the rotational movement of the axis (wheel), so that in his machine the addition of numbers corresponded to the addition of angles proportional to them.

The principle of operation of the counters in Pascal's machine is simple. It is based on the idea of ​​an ordinary gear pair - two gears meshed with each other. For each category there is a wheel (gear) with ten teeth. In this case, each of the ten teeth represents one of the numbers from 0 to 9. This wheel is called the “decimal counting wheel.”

With the addition of each unit in a given digit, the counting wheel rotates by one tooth, i.e., by one tenth of a revolution. The required number can be set by turning the wheel until the tooth representing that number aligns with the pointer or window. For example, three wheels show the number 285. We can add 111 to this number by turning each wheel to the right one tooth. Then the numbers 3, 9, 6 will appear opposite the windows, respectively, forming the sum of the numbers 285 and 111, i.e. 396. The task now is how to carry out the transfer of tens. This is one of the main problems that Pascal had to solve. The presence of such a mechanism would allow the computer not to waste attention on remembering the transfer from the low-order to the high-order.

A machine in which addition is performed mechanically must itself determine when to carry out the transfer. Let's say that we introduced nine units into the category. The counting wheel will turn 9/10 of a turn. If you now add one more unit, the wheel will “accumulate” ten units. They must be transferred to the next category. This is the transfer of tens. In Pascal's machine, this is accomplished by an elongated tooth. It engages with the tens wheel and turns it 1/10 of a turn. One ten will appear in the tens counter window, and zero will appear in the units counter window again.

The transfer mechanism operates only in one direction of wheel rotation and does not allow the subtraction operation to be performed by rotating the wheels in the opposite direction. Therefore, Pascal replaced the subtraction operation with addition with decimal's complement. Let, for example, it is necessary to subtract 11 from the number 285. The addition method leads to the following actions: 285-11=285-(100-89)=285+89-100=274. You just need to remember to subtract 100. But on a machine that has a certain number of digits, you don’t have to worry about this. Here's how this operation would be performed on a six-bit machine: 000285+999989=1000274; in this case, the one on the left drops out, since the carryover from the sixth digit has nowhere to go.

Pascal's machine was practically the first adding mechanism, built on a completely new principle, in which wheels are counted. She made a huge impression on her contemporaries, legends were formed about her, poems were dedicated to her. Increasingly, the description “French Archimedes” appeared with the name of Pascal. Only 8 Pascal machines have survived to this day, one of which is 10-bit.

Pascal's works had a noticeable influence on the entire further course of development of computer technology. They served as the basis for the creation of a large number of various systems of adding machines.

In 1640, an attempt to create a mechanical computing machine was made by Blaise Pascal (1623-1662).

There is an opinion that “Blaise Pascal’s idea of ​​a calculating machine was probably inspired by the teachings of Descartes, who argued that the brain of animals, including humans, is characterized by automatism, therefore a number of mental processes are essentially no different from mechanical ones.” An indirect confirmation of this opinion is that Pascal set himself the goal of creating such a machine. At the age of 18, he begins to work on creating a machine with the help of which even those unfamiliar with the rules of arithmetic could perform various operations.

The first working model of the machine was ready in 1642. Pascal was not satisfied with it, and he immediately began to design a new model. “I did not save,” he later wrote, addressing a “friend-reader,” “neither time, nor labor, nor money to bring it to the point of being useful to you... I had the patience to make up to 50 different models: some wooden , others from Ivory, ebony, copper..."

Pascal experimented not only with the material, but also with the shape of the machine parts: models were made - “some from straight rods or plates, others from curves, others using chains; some with concentric gears, others with eccentrics; some move in a straight line, others move in a circle; some are in the shape of cones, others are in the shape of cylinders..."

Finally, in 1645, the arithmetic machine, as Pascal called it, or the Pascal wheel, as those who were familiar with the invention of the young scientist called it, was ready.

It was a lightweight brass box measuring 350X25X75 mm (Figure 11.7). There are 8 round holes on the top cover, each with a circular scale.

Figure 11.7 - Pascal's machine with the lid removed

The rightmost hole scale is divided into 12 equal parts, the scale of the hole adjacent to it is divided into 20 parts, the scales of the remaining 6 holes have decimal division. This graduation corresponds to the division of the livre, the main monetary unit of that time, into smaller ones: 1 sou = 1/20 livre and 1 denier - 1/12 sou.

Gears located below the plane of the top cover are visible in the holes. The number of teeth of each wheel is equal to the number of scale divisions of the corresponding hole (for example, the rightmost wheel has 12 teeth). Each wheel can rotate independently of the other on its own axis. The wheel is turned by hand using a drive pin that is inserted between two adjacent teeth. The pin rotates the wheel until it hits a fixed stop fixed at the bottom of the cover and protruding into the hole to the left of number 1 on the dial. If, for example, you insert a pin between the teeth located opposite the numbers 3 and 4 and turn the wheel all the way, it will turn 3/10 of a full turn.

The rotation of the wheel is transmitted through the internal mechanism of the machine to a cylindrical drum, the axis of which is located horizontally. There are two rows of numbers on the side surface of the drum; The numbers in the bottom row are arranged in ascending order - 0, ..., 9, the numbers in the top row are in descending order - 9, 8, ..., 1,0. They are visible in the rectangular windows of the lid. The bar, which is placed on the lid of the machine, can be moved up or down along the windows, revealing either the upper or lower row of numbers, depending on what mathematical operation needs to be performed.

Unlike the well-known calculating instruments such as the abacus, in the arithmetic machine, instead of an objective representation of numbers, their representation was used in the form of the angular position of an axis (shaft) or a wheel that this axis carries. To perform arithmetic operations, Pascal replaced the translational movement of pebbles, tokens, etc. in abacus-shaped instruments with the rotational movement of an axis (wheel), so that in his machine the addition of numbers corresponds to the addition of angles proportional to them.

The wheel with which numbers are entered (the so-called setting wheel), in principle, does not have to be geared - this wheel can, for example, be a flat disk, along the periphery of which holes are drilled at 36° into which the drive pin is inserted.

We just have to get acquainted with how Pascal solved perhaps the most difficult question - the mechanism for transferring tens. The presence of such a mechanism, which allows the calculator not to waste attention on remembering the transfer from the least significant to the most significant, is the most striking difference between Pascal’s machine and known calculating tools.

Figure 11.8 shows the machine elements belonging to the same category: setting wheel N, digital drum I, a counter consisting of 4 crown wheels B, one gear K and a tens transmission mechanism. Note that wheels B1, B4 and K are not of fundamental importance for the operation of the machine and are used only to transmit the movement of the setting wheel N to the digital drum I. But wheels B2 and B3 are integral elements of the counter and, in accordance with “computing machine” terminology, are called counting wheels . On

shows the counting wheels of two adjacent digits, rigidly mounted on the axes A 1 and A 2, and the tens transmission mechanism, which Pascal called the “belt” (sautoir). This mechanism has the following device.

Figure 11.8 - Elements of the Pascal machine related to one digit of a number

Figure 11.9 - Tens transmission mechanism in Pascal's machine

On the counting wheel B 1 of the lowest category there are rods d, which, when the axis A 1 rotates, engages with the teeth of the fork M located at the end of the two-knee lever D 1. This lever rotates freely on axis A 2 of the highest order, while the fork carries a spring-loaded pawl. When, when rotating axis A 1, wheel B 1 reaches the position corresponding to number b, the rods C1 will engage with the teeth of the fork, and at the moment when it moves from 9 to 0, the fork will slip out of engagement and fall down under its own weight, dragging the dog along with you. The pawl will push the counting wheel B 2 of the highest rank one step forward (that is, it will rotate it together with the axis A 2 by 36°). Lever H, ending with a hatchet-shaped tooth, plays the role of a latch that prevents wheel B 1 from rotating in the opposite direction when lifting the fork.

The transfer mechanism operates only in one direction of rotation of the counting wheels and does not allow the subtraction operation to be performed by rotating the wheels in the opposite direction. Therefore, Pascal replaced this operation with addition with decimal's complement.

Let, for example, you need to subtract 87 from 532. The addition method leads to the following actions:

532 - 87 = 532 - (100-13) = (532 + 13) - 100 = 445.

You just need to remember to subtract 100. But on a machine that has a certain number of digits, you don’t have to worry about this. Indeed, let the subtraction be performed on a 6-bit machine: 532 - 87. Then 000532 + 999913 = 1000445. But the leftmost unit will be lost by itself, since the transfer from the 6th digit has nowhere to go. In Pascal's machine, the decimal's complements are written on the top row of the digital reel. To perform the subtraction operation, it is enough to move the bar covering the rectangular windows to the lower position, while maintaining the direction of rotation of the adjustment wheels.

With the invention of Pascal, the countdown of the development of computer technology begins. In the XVII-XVIII centuries. one inventor after another offered new design options for adding devices and arithmometers, until, finally, in the 19th century. The steadily growing volume of computing work did not create a sustainable demand for mechanical calculating devices and did not allow their serial production to be established.

Pascal's machine with the lid removed

Mechanization and automation of computing operations is one of the fundamental technical achievements of the second third of the 20th century. Just as the appearance of the first spinning machines marked the beginning of the great industrial revolution of the 18th and 19th centuries, the creation of an electronic computer became the harbinger of a grandiose scientific, technical and information revolution in the second half of the 20th. This important event preceded by a long backstory. The first attempts to assemble a calculating machine were made back in the 17th century, and the simplest computing devices, such as the abacus and counting, appeared even earlier - in antiquity and the Middle Ages.

Although an automatic computing device is a type of machine, it cannot be put on a par with industrial machines, say, a lathe or a weaving machine, because unlike them, it does not operate with physical material (threads or wooden blanks), but with ideal, non-existent ones. in nature by numbers. Therefore, the creator of any computer (be it the simplest adding machine or the latest supercomputer) faces specific problems that do not arise for inventors in other fields of technology. They can be formulated as follows: 1) how to physically (objectively) represent numbers in a machine? 2) how to enter the initial numerical data? 3) how to simulate the execution of arithmetic operations? 4) how to present the input data and calculation results to the computer?

One of the first to overcome these problems was the famous French scientist and thinker Blaise Pascal. He was 18 years old when he began working on creating a special machine with the help of which a person, even not familiar with the rules of arithmetic, could perform four basic operations. Pascal’s sister, who witnessed his work, wrote later: “This work tired his brother, but not because of the strain of mental activity, and not because of the mechanisms, the invention of which did not cause him much effort, but because the workers had difficulty understanding him." And this is not surprising. Precision mechanics was just being born, and the quality that Pascal demanded exceeded the capabilities of his masters. Therefore, the inventor himself often had to take up a file and a hammer or rack his brains over how to change an interesting but complex design in accordance with the skill of the master. The first working model of the machine was ready in 1642. Pascal was not satisfied with it, and he immediately began to design a new one. “I did not save,” he later wrote about his car, “neither time, nor labor, nor money to bring it to a state of being useful... I had the patience to make up to 50 different models...” Finally, in 1645, his efforts were crowned with complete success success - Pascal assembled a car that satisfied him in every way.

What was this first in history like? Calculating machine and how were the above problems resolved? The mechanism of the machine was enclosed in a light brass box. On its top cover there were 8 round holes, around each of which there was a circular scale. The scale of the rightmost hole was divided into 12 equal parts, the scale of the hole next to it was divided into 20 parts, the remaining six holes had a decimal division. This graduation corresponded to the division of the livre, the main French monetary unit of that time: 1 sou = 1/20 livre and 1 denier = 1/12 sou. In the holes, geared adjustment wheels were visible, located below the plane of the top cover. The number of teeth of each wheel was equal to the number of scale divisions of the corresponding hole.