This article does not cite any references or sources. October Please help improve this article by adding citations to reliable sources. Unverifiable material may be challenged and removed. Errors are not restricted to school pupils. Any user could carelessly rely on the calculators output without doublechecking the magnitude of the result i. e. where the decimal point is positioned. This problem was all but nonexistent in the era of slide rules and pencilandpaper calculations when the task of establishing the magnitudes of results had to be done by the user. In addition algorithmic flaws and rounding techniques can sometimes lead to minor precision errors. Some fractions such as are awkward to display on a calculator display as they are usually rounded to . Also some fractions such as which is . can be difficult to recognize in decimal form as a result many scientific calculators are able to work in vulgar fractions andor mixed numbers.
Calculators vs. computing
A fundamental difference between calculators and computers is that computers can be programmed to perform different tasks while calculators are predesigned with specific functions built in for example addition multiplication logarithms etc. While computers may be used to handle numbers they can also manipulate words images or sounds and other tasks they have been programmed to handle. However the distinction between the two is quite blurred some calculators have builtin programming functions ranging from simple formula entry to full programming languages such as RPL or TIBASIC. Graphing calculators in particular can along with PDAs be viewed as direct descendants of the s pocket computers essentially calculators with full keyboards and programming capability. The market for calculators is extremely pricesensitive to an even greater extent than the commodity personal computer market typically the user desires the least expensive model having a specific feature set but does not care much about speed since speed is constrained by how fast the user can press the buttons. Thus designers of calculators strive to minimize the number of logic elements on the chip not the number of clock cycles needed to do a computation.
CORDIC
For instance instead of a hardware multiplier a calculator might implement floating point mathematics with code in ROM and compute trigonometric functions with the CORDIC algorithm because CORDIC does not require hardware floatingpoint. Bit serial logic designs are more common in calculators whereas bit parallel designs dominate generalpurpose computers because a bit serial design minimizes the chip complexity but takes many more clock cycles. Again the line blurs with highend calculators which use processor chips associated with computer and embedded systems design particularly the Z MC and ARM architectures as well as some custom designs specifically made for the calculator market.
Personal computers
Personal computers and personal digital assistants can perform general calculations in a variety of ways Most computer operating systems at least those that support some kind of multitasking include calculator programs both text mode such as the Unix bc language and graphical mode Mac OS Calculator Microsoft Calculator KCalc Grapher. Most though not all imitate the interface of a physical calculator. Some shell programs and interpreted programming languages also provide interactive calculation functions. For more complex calculations requiring large amounts of organized data spreadsheet programs such as Excel or OpenOffice Calc provide calculation and sometimes reporting functions. Computer algebra programs such as Mathematica Maple or Matlab can handle advanced calculations. Clientside scripting can be used for calculations e. g. by entering javascriptalertcalculation written in JavaScript in a web browsers address bar as opposed to httpwebsite name. Such calculations can be embedded in a separate Javascript or HTML file as well. Online calculators such as the calculator feature of the Google search engine can perform calculations serverside.
The first calculators
The first calculators were abaci and were often constructed as a wooden frame with beads sliding on wires. Abacuses were in use centuries before the adoption of the written Arabic numerals system and are still used by some merchants fishermen and clerks in China and elsewhere. William Oughtred invents the slide rule in and is revealed by his student Richard Delamain in . Wilhelm Schickard built the first automatic calculator called the Calculating Clock in . Some years later in French philosopher Blaise Pascal invented the calculation device later known as the Pascaline which was used for taxes in France until . The German philosopher G. W. v. Leibniz also produced a calculating machine.
London Science Museums
In Charles Babbage proposed a mechanical calculator called a difference engine which was capable of holding and manipulating seven numbers of decimal digits each. Babbage produced two designs for the difference engine and a further design for a more advanced mechanical programmable computer called an analytical engine. None of these designs were completely built by Babbage. In the London Science Museum followed Babbages plans to build a working difference engine using the technology and materials available in the th century. In Per Georg Scheutz completed a working difference engine based on Babbages design. The machine was the size of a piano and was demonstrated at the Exposition Universelle in Paris in . It was used to create tables of logarithms. In Frank Baldwin in the U. S. A. invented the pinwheel calculator which was also independently invented two years later by W. T. Odhner in Sweden. The Odhner models and similar designs from other companies sold many thousands into the s. In Martin Wiberg redesigned the BabbageScheutz difference engine and built a version that was the size of a sewing machine. Dorr E. Felt in the U. S. A. invented the Comptometer in the first successful keydriven adding and calculating machine keydriven refers to the fact that just pressing the keys causes the result to be calculated no separate lever has to be operated. In he joined with Robert Tarrant to form the Felt Tarrant Manufacturing Company which went on to make thousands of Comptometers. In William S. Burroughs began commercial manufacture of his printing adding calculator. Burroughs Corporation became one of the leading companies in the accounting machine and computer businesses. The Millionaire calculator was introduced in . It allowed direct multiplication by any digit one turn of the crank for each figure in the multiplier.
