A Resulta-BS7 adding machineAn older adding machine. Its mechanism is similar to a car odometer.Adding machine for the Australian pound c.1910, note the complement numbering, and the columns set up for shillings and pence.
An adding machine is a class of mechanical calculator, usually specialized for bookkeeping calculations. In the United States, the earliest adding machines were usually built to read in dollars and cents. Adding machines were ubiquitous office equipment until they were phased out in favor of electronic calculators in the 1970s and by personal computers beginning in about 1985. The older adding machines were rarely seen in American office settings by the year 2000.
Blaise Pascal and Wilhelm Schickard were the two original inventors of the mechanical calculator in 1642.[1] For Pascal, this was an adding machine that could perform additions and subtractions directly and multiplication and divisions by repetitions, while Schickard's machine, invented several decades earlier, was less functionally efficient but was supported by a mechanised form of multiplication tables. These two were followed by a series of inventors and inventions leading to those of Thomas de Colmar, who launched the mechanical calculator industry in 1851 when he released his simplified arithmometer (it took him thirty years to refine his machine, patented in 1820, into a simpler and more reliable form). However, they did not gain widespread use until Dorr E. Felt started manufacturing his comptometer (1887) and Burroughs started the commercialization of differently conceived adding machines (1892).[2]
To add a new list of numbers and arrive at a total, the user was first required to "ZERO" the machine. Then, to add sets of numbers, the user was required to press numbered keys on a keyboard, which would remain depressed (rather than immediately rebound like the keys of a computer keyboard or typewriter or the buttons of a typical modern machine). The user would then pull the crank, which caused the numbers to be shown on the rotary wheels, and the keys to be released (i.e. to pop back up) in preparation for the next input. To add, for example, the amounts of 30.72 and 4.49 (which, in adding machine terms, on a decimal adding machine is 3,072 plus 449 "decimal units"), the following process took place: Press the 3 key in the column fourth from the right (multiples of one thousand), the 7 key in the column second from right (multiples of ten) and the 2 key in the rightmost column (multiples of 1). Pull the crank. The rotary wheels now showed 3072. Press the 4 key in the third column from the right, the 4 key in the second column from right, and the 9 key in the rightmost column. Pull the crank. The rotary wheels now show a running 'total' of 3521 which, when interpreted using the decimal currency colour-coding of the key columns, equates to 35.21. Keyboards typically did not have or need 0 (zero) keys; one simply did not press any key in the column containing a zero. Trailing zeros (those to the right of a number), were there by default because when a machine was zeroed, all numbers visible on the rotary wheels were reset to zero.
A manual adding machine manufactured in the 1950s.
Subtraction was impossible, except by adding the complement of a number (for instance, subtract 2.50 by adding 9,997.50).
Multiplication was a simple process of keying in the numbers one or more columns to the left and repeating the "addition" process. For example, to multiply 34.72 by 102, key in 3472, pull crank, repeat once more. Wheels show 6944. Key in 3472(00), pull crank. Wheels now show 354144, or 3,541.44.
A later adding machine, called the comptometer, did not require that a crank be pulled to add. Numbers were input simply by pressing keys. The machine was thus driven by finger power. Multiplication was similar to that on the adding machine, but users would "form" up their fingers over the keys to be pressed and press them down the multiple of times required. Using the above example, four fingers would be used to press down twice on the 3 (fourth column), 4 (third column), 7 (second column) and 2 (first column) keys. That finger shape would then move left two columns and press once. Usually a small crank near the wheels would be used to zero them. Subtraction was possible by adding complementary numbers; keys would also carry a smaller, complementary digit to help the user form complementary numbers. Division was also possible by putting the dividend to the left end and performing repeated subtractions by using the complementary method.[3]
Some adding machines were electromechanical – an old-style mechanism, but driven by electric power.
Some "ten-key" machines had input of numbers as on a modern calculator – 30.72 was input as 3, 0, 7, 2. These machines could subtract as well as add. Some could multiply and divide, although including these operations made the machine more complex. Those that could multiply, used a form of the old adding machine multiplication method. Using the previous example of multiplying 34.72 by 102, the amount was keyed in, then the 2 key in the "multiplication" key column was pressed. The machine cycled twice, then tabulated the adding mechanism below the keyboard one column to the right. The number keys remained locked down on the keyboard. The user now pressed the multiplication 0 key which caused tabulation of the adding mechanism one more column to the right, but did not cycle the machine. Now the user pressed the multiplication 1 key. The machine cycled once. To see the total the user was required to press a Total key and the machine would print the result on a paper tape, release the locked down keys, reset the adding mechanism to zero and tabulate it back to its home position.
Modern adding machines are like simple calculators. They often have a different input system, though.
To figure this out
Type this on the adding machine
2+17+5=?
2 + 17 + 5 + T
19-7=?
19 + 7 - T
38-24+10=?
38 + 24 - 10 + T
7×6=?
7 × 6 =
18/3=?
18 ÷ 3 =
(1.99×3)+(.79×8)+(4.29×6)=?
1.99 × 3 = + .79 × 8 = + 4.29 × 6 = + T
Note: Sometimes the adding machine will have a key labeled × instead of T. In this case, substitute × for T in the examples above. Alternatively, the plus key may continuously total instead of either a × or T key. Sometimes, the plus key is even labeled thus: +⁄=
Burroughs's calculating machine
Patent drawing for Burroughs's calculating machine, 1888.
William Seward Burroughs received a patent for his adding machine on August 25, 1888. He was a founder of American Arithmometer Company, which became Burroughs Corporation and evolved to produce electronic billing machines and mainframes, and eventually merged with Sperry to form Unisys. The grandson of the inventor of the adding machine is Beat author William S. Burroughs; a collection of his essays is called The Adding Machine.
Marguin, Jean (1994). Histoire des instruments et machines à calculer, trois siècles de mécanique pensante 1642–1942 (in French). Hermann. ISBN978-2-7056-6166-3.
Taton, René (1963). Le calcul mécanique. Que sais-je? n° 367 (in French). Presses universitaires de France. pp.20–28.
An electronic calculator is typically a portable electronic device used to perform calculations, ranging from basic arithmetic to complex mathematics.
Addition is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or sum of those values combined. The example in the adjacent image shows two columns of three apples and two apples each, totaling at five apples. This observation is equivalent to the mathematical expression "3 + 2 = 5".
The ANITA Mark VII and ANITA Mark VIII calculators were launched simultaneously in late 1961 as the world's first all-electronic desktop calculators. Designed and built by the Bell Punch Co. in Britain, and marketed through its Sumlock Comptometer division, they used vacuum tubes and cold-cathode switching tubes in their logic circuits and nixie tubes for their numerical displays.
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method for representing numbers that uses only two symbols for the natural numbers: typically "0" (zero) and "1" (one). A binary number may also refer to a rational number that has a finite representation in the binary numeral system, that is, the quotient of an integer by a power of two.
Napier's bones is a manually operated calculating device created by John Napier of Merchiston, Scotland for the calculation of products and quotients of numbers. The method was based on lattice multiplication, and also called rabdology, a word invented by Napier. Napier published his version in 1617. It was printed in Edinburgh and dedicated to his patron Alexander Seton.
A telephone keypad is a keypad installed on a push-button telephone or similar telecommunication device for dialing a telephone number. It was standardized when the dual-tone multi-frequency signaling (DTMF) system was developed in the Bell System in the United States in the 1960s – this replaced rotary dialing, that had been developed for electromechanical telephone switching systems. Because of the abundance of rotary dial equipment still on use well into the 1990s, many telephone keypads were also designed to be backwards-compatible: as well as producing DTMF pulses, they could optionally be switched to produce loop-disconnect pulses electronically.
In mathematics and computing, the method of complements is a technique to encode a symmetric range of positive and negative integers in a way that they can use the same algorithm for addition throughout the whole range. For a given number of places half of the possible representations of numbers encode the positive numbers, the other half represents their respective additive inverses. The pairs of mutually additive inverse numbers are called complements. Thus subtraction of any number is implemented by adding its complement. Changing the sign of any number is encoded by generating its complement, which can be done by a very simple and efficient algorithm. This method was commonly used in mechanical calculators and is still used in modern computers. The generalized concept of the radix complement is also valuable in number theory, such as in Midy's theorem.
Wilhelm Schickard was a German professor of Hebrew and astronomy who became famous in the second part of the 20th century after Franz Hammer, a biographer of Johannes Kepler, claimed that the drawings of a calculating clock, predating the public release of Pascal's calculator by twenty years, had been discovered in two unknown letters written by Schickard to Johannes Kepler in 1623 and 1624.
The Comptometer was the first commercially successful key-driven mechanical calculator, patented in the United States by Dorr Felt in 1887.
A mechanical calculator, or calculating machine, is a mechanical device used to perform the basic operations of arithmetic automatically, or (historically) a simulation such as an analog computer or a slide rule. Most mechanical calculators were comparable in size to small desktop computers and have been rendered obsolete by the advent of the electronic calculator and the digital computer.
The arithmometer was the first digital mechanical calculator strong enough and reliable enough to be used daily in an office environment. This calculator could add and subtract two numbers directly and could perform long multiplications and divisions effectively by using a movable accumulator for the result.
Pascal's calculator is a mechanical calculator invented by Blaise Pascal in 1642. 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.
A pinwheel calculator is a class of mechanical calculator described as early as 1685, and popular in the 19th and 20th century, calculating via wheels whose number of teeth were adjustable. These wheels, also called pinwheels, could be set by using a side lever which could expose anywhere from 0 to 9 teeth, and therefore when coupled to a counter they could, at each rotation, add a number from 0 to 9 to the result. By linking these wheels with carry mechanisms a new kind of calculator engine was invented. Turn the wheels one way and one performs an addition, the other way a subtraction.
There are various ways in which calculators interpret keystrokes. These can be categorized into two main types:
A keypad is a block or pad of buttons set with an arrangement of digits, symbols, or alphabetical letters. Pads mostly containing numbers and used with computers are numeric keypads. Keypads are found on devices which require mainly numeric input such as calculators, television remotes, push-button telephones, vending machines, ATMs, point of sale terminals, combination locks, safes, and digital door locks. Many devices follow the E.161 standard for their arrangement.
The American Arithmometer Company was an American manufacture organized in St. Louis, Missouri in 1886 by William S. Burroughs that produced adding machines.
The stepped reckoner or Leibniz calculator was a mechanical calculator invented by the German mathematician Gottfried Wilhelm Leibniz. The name comes from the translation of the German term for its operating mechanism, Staffelwalze, meaning "stepped drum". It was the first calculator that could perform all four basic arithmetic operations.
A Leibniz wheel or stepped drum is a cylinder with a set of teeth of incremental lengths which, when coupled to a counting wheel, can be used in the calculating engine of a class of mechanical calculators. Invented by Leibniz in 1673, it was used for three centuries until the advent of the electronic calculator in the mid-1970s.
The Millionaire was the first commercially successful mechanical calculator that could perform a direct multiplication. It was in production from 1893 to 1935 with a total of about five thousand machines manufactured.
A numeric keypad, number pad, numpad, or ten key, is the palm-sized, usually-17-key section of a standard computer keyboard, usually on the far right. It provides calculator-style efficiency for entering numbers.
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