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Stepped Reckoner

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	Topics Stepped Reckoner Topic Home Description It is unclear how many different variants of the calculator were made. Some sources, such as the drawing above, show a 12 digit version. This section describes the surviving 16 digit prototype in Hannover. The machine is about 67 cm (26 inchInch Summary An inch is the name of a unit of length in a number of different systems, including English units, Imperial units, and Unit... es) long, made of polished brass and steel, mounted in an oak case. It consists of two attached parallel parts; an accumulatorAccumulator (computing) In a computer CPU, an accumulator is a register in which intermediate arithmetic and logic results are stored.... section to the rear, which can hold 16 decimal digits, and an 8 digit input section to the front. The input section has 8 dials with knobs to set the operandOperand In mathematics, an operand is one of the inputs of an operator.... number, a telephone-like dial to the right to set the multiplier digit, and a crank on the front to perform the calculation. The result appears in the 16 windows on the rear accumulator section. The input section is mounted on rails and can be moved along the accumulator section with a crank on the left end that turns a worm gearWorm gear A worm gear, or worm wheel, is a type of gear that engages with a worm to greatly reduce rotational speed, or to allow... , to change the alignment of operand digits with accumulator digits. There is also a tens-carry indicator and a control to set the machine to zero. The machine can: add or subtract an 8 digit number to / from a 16 digit number multiply two 8 digit numbers to get a 16 digit result divide a 16 digit number by an 8 digit divisor Addition or subtraction is performed in a single step, with a turn of the crank. Multiplication and division are performed digit by digit on the multiplier or divisor digits, in a procedure equivalent to the familiar long multiplication and long divisionLong division In arithmetic, long division is a procedure for calculating the division of one integer, called the dividend, by another int... procedures taught in school. Sequences of these operations can be performed on the number in the accumulator; for example it can calculate rootsNth root In mathematics, an nth root of a number a is a number b, such that bn=a.... by a series of divisions and additions. History The first mechanical calculators were Wilhelm SchickardWilhelm Schickard Wilhelm Schickard built the first automatic calculator in 1623.... 's calculating clock built around 1623, and Blaise PascalFacts About Blaise Pascal Blaise Pascal was a French mathematician, physicist, and religious philosopher.... 's Pascaline, invented around 1645. These were able to add and subtract only. They consisted of a series of wheels, each with a dial attached numbered 0 - 9, each representing one digit of the result. The innovation of Schickard and Pascal was the carry system, a mechanism connecting each wheel to the next, so that when a wheel was rotated by one complete turn, from 0 to 9 and back to 0 again, the next wheel, representing the next digit to the left, was advanced by one. A similar system is still used in mechanical odometerOdometer An odometer is a device used for indicating distance traveled by an automobile or other vehicle.... s in cars. Leibniz got the idea for a calculating machine in 1672 in Paris, from a pedometerPedometer Summary A pedometer or step counter is a device, usually portable and electronic, which counts each step a person makes.... . Later he learned about Pascal's machine when he read Pascal's PenseesPensées The *Penses* represented a defense of the Christian religion by Blaise Pascal, the renowned 17th century philosopher and m... . He concentrated on expanding Pascal's mechanism so it could multiply and divide. He presented a wooden model to the Royal Society of London on February 1, 1673, and received much encouragement. In a letter of March 26, 1673 to Johann FriedrichJohn Frederick, Duke of Brunswick-Lüneburg Overview John Frederick was duke of Brunswick-L?neburg and ruled over the Calenberg subdivision of the duchy from 1665 until his dea... , where he mentioned the presentation in London, Leibniz described the purpose of the "arithmetic machine" as making calculations "leicht, geschwind, gewiß" [sicSIC SIC, SiC, or Sic may mean:... ], i.e. easy, fast, and reliable. Leibniz also added that theoretically the numbers calculated might be as large as desired, if the size of the machine was adjusted; quote: "eine zahl von einer ganzen Reihe Ziphern, sie sey so lang sie wolle (nach proportion der größe der Machine)" [sic]. In English: "a number consisting of a series of figures, as long as it may be (in proportion to the size of the machine)". His first preliminary brass machine was built 1674 - 1685. His so-called 'older machine' was built 1686 - 1694. The 'younger machine', the surviving machine, was built from 1690 to 1720. In 1775 the 'younger machine' was sent to Gottingen University for repair, and was forgotten. In 1876 a crew of workmen found it in an attic room of a Gottingen University building. It was returned to Hannover in 1880. In 1894-1896 Artur Burkhardt, founder of a major German calculator company restored it, and it has been kept in the Niedersaächsischen Landesbibliothek ever since. Operation The machine performs multiplication by repeated addition, and division by repeated subtraction, as a modern computerComputer A computer is a machine for manipulating data according to a list of instructions known as a program.... does. The basic operation performed is to add (or subtract) the operandOperand In mathematics, an operand is one of the inputs of an operator.... number to the accumulatorAccumulator (computing) In a computer CPU, an accumulator is a register in which intermediate arithmetic and logic results are stored.... register, as many times as desired (to subtract, the operating crank is turned in the opposite direction). The number of additions (or subtractions) is controlled by the multiplier dial. It operates like a telephone dialRotary dial The rotary dial is a device mounted on or in a telephone or switchboard that is designed to send interrupted electrical puls... , with ten holes in its circumference numbered 0 - 9. To multiply by a single digit, 0 - 9, a knob-shaped stylus is inserted in the appropriate hole in the dial, and the crank is turned. The multiplier dial turns clockwise, the machine performing one addition for each hole, until the stylus strikes a stop at the top of the dial. The result appears in the accumulator windows. Repeated subtractions are done similarly except the multiplier dial turns in the opposite direction, so a second set of digits, in red, are used. To perform a single addition or subtraction, the multiplier is simply set at one. To multiply by numbers over 9: The multiplicand is set into the operand dials. The first (least significant) digit of the multiplierMultiplier Summary The term multiplier may refer to:... is set into the multiplier dial as above, and the crank is turned, multiplying the operand by that digit and putting the result in the accumulator. The input section is shifted one digit to the left with the end crank. The next digit of the multiplier is set into the multiplier dial, and the crank is turned again, multiplying the operand by that digit and adding the result to the accumulator. The above 2 steps are repeated for each multiplier digit. At the end, the result appears in the accumulator windows. In this way, the operand can be multiplied by as large a number as desired, although the result is limited by the capacity of the accumulator. To divide by a multidigit divisor, this process is used: The dividendDivision (mathematics) Overview In mathematics, especially in elementary arithmetic, division is an arithmetic operation which is the inverse of multiplicat... is set into the accumulator, and the divisorDivisor In mathematics, a divisor of an integer n, also called a factor of n, is an integer which evenly divides n... is set into the operand dials. The input section is moved with the end crank until the lefthand digits of the two numbers line up. The operation crank is turned and the divisor is subtracted from the accumulator repeatedly until the lefthand (most significant) digit of the result is 0. The number showing on the multiplier dial is then the first digit of the quotient. The input section is shifted right one digit. The above two steps are repeated to get each digit of the quotient, until the input carriage reaches the right end of the accumulator. It can be seen that these procedures are just mechanized versions of long divisionLong division In arithmetic, long division is a procedure for calculating the division of one integer, called the dividend, by another int... and multiplication. External links Pictures of machine and diagrams of mechanism News article in chess magazine showing closeup pictures of Hannover machine.