page_title: Pascal's calculator
section_title: Design
hierarchical_section_title: Pascal's calculator / Design
caption_attribution_description: Detail of a Pascaline's carry mechanism
context_page_description: Pascal's calculator is a mechanical calculator invented by Blaise Pascal in the mid 17th century. Pascal was led to develop a calculator by the laborious arithmetical calculations required by his father's work as the supervisor of taxes in Rouen. He designed the machine to add and subtract two numbers directly and to perform multiplication and division through repeated addition or subtraction.
  Pascal's calculator was especially successful in the design of its carry mechanism, which adds 1 to 9 on one dial, and carries 1 to the next dial when the first dial changes from 9 to 0. His innovation made each digit independent of the state of the others, enabling multiple carries to rapidly cascade from one digit to another regardless of the machine's capacity. Pascal was also the first to shrink and adapt for his purpose a lantern gear, used in turret clocks and water wheels. This innovation allowed the device to resist the strength of any operator input with very little added friction.
  Pascal designed the machine in 1642. After 50 prototypes, he presented the device to the public in 1645, dedicating it to Pierre Séguier, then chancellor of France.
context_section_description: The calculator had spoked metal wheel dials, with the digit 0 through 9 displayed around the circumference of each wheel. To input a digit, the user placed a stylus in the corresponding space between the spokes and turned the dial until a metal stop at the bottom was reached, similar to the way the rotary dial of a telephone is used. This displayed the number in the windows at the top of the calculator. Then, one simply redialed the second number to be added, causing the sum of both numbers to appear in the accumulator.
  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 10-digit wheel (N), the fixed outside wheel is numbered from 0 to 9 (N-1). 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 500, use the hundreds input wheel, etc...
  On all the wheels of all the known machines, except for the machine tardive, 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, 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. The marks on two adjacent spokes flank the digit 0 inscribed on this wheel.
  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 eac
caption: Detail of the carry mechanism and of the sautoir
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