## Pascaline bleibt am Ball | UNICEF

Die jährige Pascaline aus Niger musste die Schule abbrechen, um Geld zu verdienen. Lest hier wie sie nun doch lernen und Fußball. Die Pascaline ist eine mechanische Rechenmaschine, die von Blaise Pascal erfunden wurde. Sie galt lange Zeit als erste mechanische Rechenmaschine überhaupt, bis im Jahrhundert Unterlagen gefunden wurden, welche die Konstruktion einer. Pascaline (Replik). Zweispezies-Rechenmaschine. Blaise Pascal baute im Alter von 19 Jahren eine Rechenmaschine für Addition und Subtraktion.## Pascaline What is Pascaline? Video

La Pascaline*Pascaline*stones to add and subtract.

Later on Pascal manufactured machines with 6, 8, and even 10 digital positions. Some of the machines are entirely decimal i. The dimensions of brass box of the machine for 8 digital positions variant is The input wheels are divided by 10, 12 or 20 spokes, depending of the scale.

The spokes are used for rotating of the wheels by means of a pin or stylus. The stylus rotates the wheel until it get to an unmovable stop, fixed to the lower part of the lid.

The result can be seen in the row of windows in upper part, where is placed a plate, which can be moved upwards and downwards, allowing to be seen upper or lower row of digits, used for addition or subtraction.

The input wheels used for entering of numbers are smooth wheels, across which periphery are made openings. Counter-wheels are crown-wheels, i.

The movement is transferred from the input wheel marked with in the sketch , which can be rotated by the operator by means of a stylus, over the counter, which consists of four crown-wheels marked with B1 , B2 , B3 and B4 , pinion-wheel , and mechanism for tens carry , to the digital drum , which digits can be seen in the windows of the lid.

The tens carry mechanism called by Pascal sautoir , works in this way: On the counter-wheel of the junior digital positions B1 are mounted two pins C1 , which during the rotating of the wheel around its axis A1 will engaged the teeth of the fork M , placed on the edge of the 2-legs rod D1.

This rod can be rotated around the axis A2 of the senior digital position, and fork has a tongue E with a spring. When during the rotating of the axis A1 the wheel B1 reach the position, according to the digit 6, then pins C1 will engaged with the teeth of the fork, and in the moment, when the wheel moves from 9 to 0, then the fork will slide off from the engagement and will drop down, pushing the tongue.

It will push the counter wheel B2 of the senior position one step forward i. The rod L , which has a special tooth, will serve as a stop, and will prevent the rotating of the wheel B1 during the raising of the fork.

The tens carry mechanism of Pascal has an advantage, compared e. This advantage however is paid by a some shortcomings—during the carrying is produced a noise, and if the box is hit, may occur unwanted carrying.

The wheels of the calculating mechanism are rotating only in one direction and there are not intermediate wheels provided designated to reverse the direction of the rotation.

This means, that the machine can work only as a adding device, and subtraction must be done by means of a arithmetical operation, known as complement to 9.

This inconvenience can be avoided by adding of additional intermediate gear-wheels in the mechanism, but Pascal, as well as all next inventors of calculating machines Leibniz , Lepine , Leupold , etc.

The rotating of the wheels is transferred via the mechanism to the digital cylinders, which can be seen in the windows see the photo below.

On the surface of cylinders are inscribed 2 rows of digits in this way, that the pairs are complemented to 9, for example if the upper digit is 1, the lower is 8.

On the lid is mounted a plate marked with 2 in the lower sketch , which can be moved upwards and downwards and by means of this plate, the upper row of digits must be shown during the subtraction, while the lower one—during the addition.

If we rotate the wheels, we will notice that digits of the lower row are changing in ascending order from 0 to 9 , while the digits of the upper row are changing in descending order from 9 to 0.

Zeroing of the mechanism can be done by rotating of the wheels by means of the stylus in such way, that between the two starting spokes marked on the wheel to be seen 9 see the lower sketch.

Each dial is associated with a one-digit display window located directly above it, which displays the value of the accumulator for this position.

The complement of this digit, in the base of the wheel 6, 10, 12, 20 , is displayed just above this digit.

A horizontal bar hides either all the complement numbers when it is slid to the top, or all the direct numbers when it is slid toward the center of the machine.

It thereby displays either the content of the accumulator or the complement of its value. Since the gears of the calculator rotated in only one direction, negative numbers could not be directly summed.

To subtract one number from another, the method of nine's complement was used. The only two differences between an addition and a subtraction are the position of the display bar direct versus complement and the way the first number is entered direct versus complement.

For a digit wheel N , the fixed outside wheel is numbered from 0 to 9 N The numbers are inscribed in a decreasing manner clockwise going from the bottom left to the bottom right of the stop lever.

To add a 5, one must insert a stylus between the spokes that surround the number 5 and rotate the wheel clockwise all the way to the stop lever. The number displayed on the corresponding display register will be increased by 5 and, if a carry transfer takes place, the display register to the left of it will be increased by 1.

To add 50, use the tens input wheel second dial from the right on a decimal machine , to add , use the hundreds input wheel, etc On all the wheels of all the known machines, except for the machine tardive , [8] two adjacent spokes are marked; these marks differ from machine to machine.

On the wheel pictured on the right, they are drilled dots, on the surveying machine they are carved; some are just scratches or marks made with a bit of varnish, [9] some were even marked with little pieces of paper.

These marks are used to set the corresponding cylinder to its maximum number, ready to be re-zeroed. To do so, the operator inserts the stylus in between these two spokes and turns the wheel all the way to the stopping lever.

This works because each wheel is directly linked to its corresponding display cylinder it automatically turns by one during a carry operation.

To mark the spokes during manufacturing, one can move the cylinder so that its highest number is displayed and then mark the spoke under the stopping lever and the one to the right of it.

Four of the known machines have inner wheels of complements, which were used to enter the first operand in a subtraction. They are mounted at the center of each spoked metal wheel and turn with it.

The wheel displayed in the picture above has an inner wheel of complements but the numbers written on it are barely visible.

On a decimal machine, the digits 0 through 9 are carved clockwise, with each digit positioned between two spokes so that the operator can directly inscribe its value in the window of complements by positioning his stylus in between them and turning the wheel clockwise all the way to the stop lever.

On four of the known machines, above each wheel, a small quotient wheel is mounted on the display bar. These quotient wheels, which are set by the operator, have numbers from 1 to 10 inscribed clockwise on their peripheries even above a non-decimal wheel.

Quotient wheels seem to have been used during a division to memorize the number of times the divisor was subtracted at each given index.

Pascal went through 50 prototypes before settling on his final design; we know that he started with some sort of calculating clock mechanism that used springs which apparently "works by springs and which has a very simple design", was used "many times" and remained in "operating order".

Nevertheless, "while always improving on it" he found reason to try to make the whole system more reliable and robust.

This could easily handle the strength of an operator input. Pascal adapted a pawl and ratchet mechanism to his own turret wheel design; the pawl prevents the wheel from turning counterclockwise during an operator input, but it is also used to precisely position the display wheel and the carry mechanism for the next digit when it is pushed up and lands into its next position.

Because of this mechanism, each number displayed is perfectly centered in the display window and each digit is precisely positioned for the next operation.

This mechanism would be moved six times if the operator dialed a six on its associated input wheel. The sautoir is the centerpiece of the pascaline's carry mechanism.

When it is time to propagate a carry, the sautoir, under the sole influence of gravity, [15] is thrown toward the next wheel without any contact between the wheels.

During its free fall the sautoir behaves like an acrobat jumping from one trapeze to the next without the trapezes touching each other "sautoir" comes from the French verb sauter , which means to jump.

All the wheels including gears and sautoir have therefore the same size and weight independently of the capacity of the machine.

Pascal used gravity to arm the sautoirs. One must turn the wheel five steps from 4 to 9 in order to fully arm a sautoir, but the carry transfer will move the next wheel only one step.

Thus much extra energy is accumulated during the arming of a sautoir. All the sautoirs are armed by either an operator input or a carry forward.

To re-zero a 10,wheel machine, if one existed, the operator would have to set every wheel to its maximum and then add a 1 to the "unit" wheel.

The carry would turn every input wheel one by one in a very rapid Domino effect fashion and all the display registers would be reset.

The Pascaline is a direct adding machine it has no crank , so the value of a number is added to the accumulator as it is being dialed in.

By moving a display bar, the operator can see either the number stored in the calculator or the complement of its value.

Subtractions are performed like additions using some properties of 9's complement arithmetic. The 9's complement of any one digit decimal number d is 9- d.

So the 9's complement of 4 is 5 and the 9's complement of 9 is 0. Similarly the 11's complement of 3 is 8. In other words, the 9's complement of the difference of two numbers is equal to the sum of the 9's complement of the minuend added to the subtrahend.

The same principle is valid and can be used with numbers composed of digits of various bases base 6, 12, 20 , like in the surveying or the accounting machines.

Die Ergebnisse erschienen in Kästchen über den Wählscheiben. Direkte Subtraktion war mit der Pascaline nicht möglich; es musste die Komplementärmethode verwendet werden siehe auch Zweierkomplement für das Analogon im Binärsystem.

Eine Pascaline aus der Zeit um steht im Mathematisch-Physikalischen Salon der Staatlichen Kunstsammlungen im Dresdner Zwinger.

Der Titel dieses Artikels ist mehrdeutig. Modern calculators are descendants of a digital arithmetic machine devised by Blaise Pascal in Later in the 17th century, Gottfried Wilhelm Leibniz created a more-advanced machine, and, especially in the late 19th century, inventors produced calculating machines that….

Adding machine , a type of calculator q. History at your fingertips. Sign up here to see what happened On This Day , every day in your inbox!

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GashoGanz richtig! Ich denke, dass es die gute Idee ist.