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or functions are included in most personal digital assistant pda type devices in addition to general purpose calculators there are those designed for specific markets for example there are scientific calculators which include trigonometric and statistical calculations some calculators even have the ability to do computer algebra graphing calculators can be used to graph functions defined on the real line or higher dimensional euclidean space as of 2016 update basic calculators cost little but scientific and graphing models tend to cost more with the very wide availability of smartphones tablet computers and personal computers dedicated hardware calculators while still widely used are less common than they once were in 1986 calculators still represented an estimated 41 of the world s general purpose hardware capacity to compute information by 2007 this had diminished to less than 0 05 1 design scientific calculator displays of fractions and decimal equivalents input electronic calculators contain a keyboard with buttons for digits and arithmetical operations some even contain 00 and 000 buttons to make larger or smaller numbers easier to enter most basic calculators assign only one digit or operation on each button however in more specific calculators a button can perform multi function working with key combinations display output calculators usually have liquid crystal displays lcd as output in place of historical light emitting diode led displays and vacuum fluorescent displays vfd details are provided in the section technical improvements large sized figures are often used to improve readability while using decimal separator usually a point rather than a comma instead of or in addition to vulgar fractions various symbols for function commands may also be shown on the display fractions such as 1 3 are displayed as decimal approximations for example rounded to 0 33333333 also some fractions such as 1 7 which is 0 14285714285714 to 14 significant figures can be difficult to recognize in decimal form as a result many scientific calculators are able to work in vulgar fractions or mixed numbers memory calculators also have the ability to save numbers into computer memory basic calculators usually store only one number at a time more specific types are able to store many numbers represented in variables the variables can also be used for constructing formulas some models have the ability to extend memory capacity to store more numbers the extended memory address is termed an array index power source power sources of calculators are batteries solar cells or mains electricity for old models turning on with a switch or button some models even have no turn off button but they provide some way to put off for example leaving no operation for a moment covering solar cell exposure or closing their lid crank powered calculators were also common in the early computer era key layout the following keys are common to most pocket calculators while the arrangement of the digits is standard the positions of other keys vary from model to model the illustration is an example usual basic pocket calculator layout mc mr m m c 7 8 9 4 5 6 1 2 3 0 calculator buttons and their meanings mc or cm m emory c lear mr rm or mrc m emory r ecall m m emory subtraction m m emory addition c or ac a ll c lear ce c lear last e ntry sometimes called ce c a first press clears the last entry ce a second press clears all c or chs toggle positive negative number aka ch ange s ign percent division multiplication subtraction addition decimal point square root result internal workings the interior of a casio fx 991s calculator in general a basic electronic calculator consists of the following components 2 power source mains electricity battery and or solar cell keypad input device consists of keys used to input numbers and function commands addition multiplication square root etc display panel output device displays input numbers commands and results liquid crystal displays lcds vacuum fluorescent displays vfds and light emitting diode led displays use seven segments to represent each digit in a basic calculator advanced calculators may use dot matrix displays a printing calculator in addition to a display panel has a printing unit that prints results in ink onto a roll of paper using a printing mechanism processor chip microprocessor or central processing unit processor chip s contents unit function scanning polling unit when a calculator is powered on it scans the keypad waiting to pick up an electrical signal when a key is pressed encoder unit converts the numbers and functions into binary code x register and y register they are number stores where numbers are stored temporarily while doing calculations all numbers go into the x register first the number in the x register is shown on the display flag register the function for the calculation is stored here until the calculator needs it permanent memory rom the instructions for in built functions arithmetic operations square roots percentages trigonometry etc are stored here in binary form these instructions are programs stored permanently and cannot be erased user memory ram the store where numbers can be stored by the user user memory contents can be changed or erased by the user arithmetic logic unit alu the alu executes all arithmetic and logic instructions and provides the results in binary coded form binary decoder unit converts binary code into decimal numbers which can be displayed on the display unit clock rate of a processor chip refers to the frequency at which the central processing unit cpu is running it is used as an indicator of the processor s speed and is measured in clock cycles per second or hertz hz for basic calculators the speed can vary from a few hundred hertz to the kilohertz range an office calculating machine with a paper printer example a basic explanation as to how calculations are performed in a simple four function calculator to perform the calculation 25 9 one presses keys in the following sequence on most calculators 2 5 9 when 2 5 is entered it is picked up by the scanning unit the number 25 is encoded and sent to the x register next when the key is pressed the addition instruction is also encoded and sent to the flag or the status register the second number 9 is encoded and sent to the x register this pushes shifts the first number out into the y register when the key is pressed a message signal from the flag or status register tells the permanent or non volatile memory that the operation to be done is addition the numbers in the x and y registers are then loaded into the alu and the calculation is carried out following instructions from the permanent or non volatile memory the answer 34 is sent shifted back to the x register from there it is converted by the binary decoder unit into a decimal number usually binary coded decimal and then shown on the display panel other functions are usually performed using repeated additions or subtractions numeric representation main article binary coded decimal most pocket calculators do all their calculations in binary coded decimal bcd rather than binary bcd is common in electronic systems where a numeric value is to be displayed especially in systems consisting solely of digital logic and not containing a microprocessor by employing bcd the manipulation of numerical data for display can be greatly simplified by treating each digit as a separate single sub circuit this matches much more closely the physical reality of display hardware a designer might choose to use a series of separate identical seven segment displays to build a metering circuit for example if the numeric quantity were stored and manipulated as pure binary interfacing to such a display would require complex circuitry therefore in cases where the calculations are relatively simple working throughout with bcd can lead to a simpler overall system than converting to and from binary for example cds keep the track number in bcd limiting them to 99 tracks the same argument applies when hardware of this type uses an embedded microcontroller or other small processor often smaller code results when representing numbers internally in bcd format since a conversion from or to binary representation can be expensive on such limited processors for these applications some small processors feature bcd arithmetic modes which assist when writing routines that manipulate bcd quantities 3 4 where calculators have added functions such as square root or trigonometric functions software algorithms are required to produce high precision results sometimes significant design effort is needed to fit all the desired functions in the limited memory space available in the calculator chip with acceptable calculation time 5 calculators compared to computers this section does not cite any sources please help improve this section by adding citations to reliable sources unsourced material may be challenged and removed march 2009 learn how and when to remove this template message the fundamental difference between a calculator and computer is that a computer can be programmed in a way that allows the program to take different branches according to intermediate results while calculators are pre designed with specific functions such as addition multiplication and logarithms built in the distinction is not clear cut some devices classed as programmable calculators have programming functions sometimes with support for programming languages such as rpl or ti basic for instance instead of a hardware multiplier a calculator might implement floating point mathematics with code in read only memory rom and compute trigonometric functions with the cordic algorithm because cordic does not require much multiplication bit serial logic designs are more common in calculators whereas bit parallel designs dominate general purpose computers because a bit serial design minimizes chip complexity but takes many more clock cycles this distinction blurs with high end calculators which use processor chips associated with computer and embedded systems design more so the z80 mc68000 and arm architectures and some custom designs specialized for the calculator market history precursors to the electronic calculator main article mechanical calculator see also human computer the first known tools used to aid arithmetic calculations were bones used to tally items pebbles and counting boards and the abacus known to have been used by sumerians and egyptians before 2000 bc 6 except for the antikythera mechanism an out of the time astronomical device development of computing tools arrived near the start of the 17th century the geometric military compass by galileo logarithms and napier bones by napier and the slide rule by edmund gunter 17th century mechanical calculators in 1642 the renaissance saw the invention of the mechanical calculator by wilhelm schickard 7 and several decades later blaise pascal 8 a device that was at times somewhat over promoted as being able to perform all four arithmetic operations with minimal human intervention 9 pascal s calculator could add and subtract two numbers directly and thus if the tedium could be borne multiply and divide by repetition schickard s machine constructed several decades earlier used a clever set of mechanised multiplication tables to ease the process of multiplication and division with the adding machine as a means of completing this operation there is a debate about whether pascal or shickard should be credited as the known inventor of a calculating machine due to the differences like the different aims of both inventions 10 schickard and pascal were followed by gottfried leibniz who spent forty years designing a four operation mechanical calculator the stepped reckoner inventing in the process his leibniz wheel but who couldn t design a fully operational machine 11 there were also five unsuccessful attempts to design a calculating clock in the 17th century 12 the grant mechanical calculating machine 1877 the 18th century saw the arrival of some notable improvements first by poleni with the first fully functional calculating clock and four operation machine but these machines were almost always one of a kind luigi torchi invented the first direct multiplication machine in 1834 this was also the second key driven machine in the world following that of james white 1822 13 it was not until the 19th century and the industrial revolution that real developments began to occur although machines capable of performing all four arithmetic functions existed prior to the 19th century the refinement of manufacturing and fabrication processes during the eve of the industrial revolution made large scale production of more compact and modern units possible the arithmometer invented in 1820 as a four operation mechanical calculator was released to production in 1851 as an adding machine and became the first commercially successful unit forty years later by 1890 about 2 500 arithmometers had been sold 14 plus a few hundreds more from two arithmometer clone makers burkhardt germany 1878 and layton uk 1883 and felt and tarrant the only other competitor in true commercial production had sold 100 comptometers 15 patent image of the clarke graph based calculator 1921 it wasn t until 1902 that the familiar push button user interface was developed with the introduction of the dalton adding machine developed by james l dalton in the united states in 1921 edith clarke invented the clarke calculator a simple graph based calculator for solving line equations involving hyperbolic functions this allowed electrical engineers to simplify calculations for inductance and capacitance in power transmission lines 16 the curta calculator was developed in 1948 and although costly became popular for its portability this purely mechanical hand held device could do addition subtraction multiplication and division by the early 1970s electronic pocket calculators ended manufacture of mechanical calculators although the curta remains a popular collectable item development of electronic calculators the first mainframe computers using firstly vacuum tubes and later transistors in the logic circuits appeared in the 1940s and 1950s this technology was to provide a stepping stone to the development of electronic calculators the casio computer company in japan released the model 14 a calculator in 1957 which was the world s first all electric relatively compact calculator it did not use electronic logic but was based on relay technology and was built into a desk early calculator light emitting diode led display from the 1970s ussr in october 1961 the world s first all electronic desktop calculator the british bell punch sumlock comptometer anita a n ew i nspiration t o a rithmetic a ccounting was announced 17 18 this machine used vacuum tubes cold cathode tubes and dekatrons in its circuits with 12 cold cathode nixie tubes for its display ...
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