Calculator
A calculator is a portable, handy electronic calculating machine, with the help of numerical calculations can be performed. Some recent technical and scientific calculators dominate symbolic mathematics using a computer algebra system ( CAS), that can change or solve some equations.
Virtually all of today's calculators use electronic integrated circuits, LCD displays as a display and be powered from a battery or solar cell power.
- 3.1 Situation in Germany
- 3.2 Situation in Austria
- 3.3 Situation in Switzerland
History
Even before the introduction of the electronic calculator, there was a need for " always- there - calculating devices ". This was met with mechanical calculators and slide rules. Mostly, these were simple adding machines. Even four -species machine - ie calculating machines, addition, subtraction, multiplication and division dominated - it was in pocket- size USEFULLY. The best known example is the Curta.
Forerunner of the electronic calculators were also electronic desktop computer, where the degree of integration of Schaltungstechik was even lower and therefore had greater dimensions.
The first electronic, actually palm-sized calculator was developed in 1967 by Texas Instruments. A 1.5 -kg prototype of this first pocket calculator is now on display in the Smithsonian Institution. Also, this prototype was already running on batteries, former computer needed a power connector. The first commercial calculators were produced in 1969 and 1970 by the Japanese company Compucorp, Sanyo, Sharp and Canon. Intel developed for the Japanese company Busicom one of the first microprocessor, the Intel 4004, which came on the market in 1971 and was used in the model Busicom 141- PF. As the first calculator that was affordable with a retail price of 10,000 yen for the masses, who in 1972 published Casio Mini applies. In 1972, Texas Instruments calculator SR 10 with its own microprocessor TMS1000 out. This calculator possessed little more than the four basic arithmetic operations. In 1971, the first Bowmar calculators available in the U.S. here ( Bowmar 901B / " Bowmar Brain", dimensions: 131 mm × 77 mm × 37 mm). He had four functions and an eight -digit red LED display. It was sold for $ 240 U.S.. Bowmar had to close in 1976.
In 1972, the HP -35 from Hewlett -Packard, the first technical-scientific calculator with trigonometric, logarithmic and Exponentialrechnungs functions. He was a sales success and ran the end of the then widespread slide rule a. One of its developers was Steve Wozniak, who a few years later, the company co-founded Apple and as a computer engineer the development of the personal computer significantly influenced.
Above all, Hewlett Packard and Texas Instruments developed from 1974 onwards also programmable calculator.
Distinguishing features
Input logic
Depending on the nature of the computer for the computation of the same function, a different input required:
- Sequential input: immediate execution of operations:
- Algebraic Notation: The operator precedence is taken into account:
- Algebraic notation with parentheses:
- Conventional algebraic notation:
- Direct algebraic logic - is depending on the manufacturer with " DAL " or " VPAM " - engl. for Visually Perfect Algebraic Method - referred to and is printed normally on the body:
- Reverse Polish Notation (RPN ) based on a stack machine architecture:
- The two-dimensional input - editor:
Variants
- Simple ( basic arithmetic, percentage )
- Finance (interest account, ...), for example, the " classic" HP -12C (manufactured since 1981 ), HP 17 B (II ) (produced since 1988)
- Boolean calculations ( calculation with dual, octal and hexadecimal numbers, such as TI Programmer)
- Scientifically ( trigonometric functions, logarithms, mathematical statistics, ... ), for example TI -30 ( same since 1976 type designation for internal dramatically different devices )
- Programmable Calculators
- Graphics-capable calculator ( Funktions-/Kurvendarstellung ) - from 1985 devices from Casio ( fx series, current model fx 9860G SD ), 1989 to date, the HP -48 -49- series, from 1993, the TI -82 and its successor, the current TI -84 Plus and TI -Nspire. Graphing calculators are typically also programmable.
- Computer algebra computer ( graphics-capable calculator with built-in computer algebra core ); first common device was the HP -48 from Hewlett- Packard ( 1989 ), later devices, for example, TI -92 ( ) (from 1995), TI -89 (from 1998) and Voyage 200 (from 2002), TI -Nspire CAS (from 2007) from Texas Instruments, Casio ClassPad 300 of, HP- 49g by Hewlett -Packard.
Most current models contain one or more of the above functional groups, sometimes even with a simple spreadsheet.
Numerical accuracy
Even if today's calculators usually have little bugs in simple calculations can be between different calculator models different accuracies and resolutions determined for numerical calculations. The reasons lie in the numerical approximation methods (eg, Horner and CORDIC ), with which, for example, transcendental functions such as the sine function are calculated. More specifically, it depends on the number of stored coefficients for the function approximations: the space needed for this was mainly in the early days of an extreme bottleneck. These small differences in the methods and different accuracies can also be used as an identifying mark for a particular firmware.
For example, provides the numerical calculation of sin ( 22) in radians at various calculators following divergent results:
Recent Developments
- Calculator with exact arithmetic and natural representation of terms: They speak, for example, rationalizing the denominator. Thus, they are advancing into areas that were previously reserved for the computer algebra computers. Examples are Casio FX- 85ES, Casio fx- 991ES or Texas Instruments TI -30X multiview.
- Integrated / interactive calculator or computer: Calculator, which integrate the basic mathematical software types ( Computer Algebra, Dynamic geometry, spreadsheet ) into a coherent system and thus go well beyond the previously known computer algebra calculator. The first representatives since 2002, the Casio ClassPad 300 models since 2007 Texas Instruments TI -Nspire and TI -Nspire CAS.
Licensing requirements in schools
Situation in Germany
In the schools, various abbreviations have been formed for the respective device classes:
- WTR: Scientific Calculator, Scientific Calculator
- GTR: Graphic Calculator, numerical graphing calculators
- CAS: Graphic Calculator with Computer Algebra System
The following table has been developed on the basis of information provided by the Ministries of Culture of the Länder. As far as these were not found, the details of the various calculators manufacturer were used. You are the realities of schools for the authorization checks in again, as the use in the classroom because of the pedagogical freedom of the teacher is possible anywhere.
For example, Casio fx- 991ES, TI -30X MultiView
For example, Casio FX- CG20, TI -84 Plus
Casio ClassPad 300, for example, TI -Nspire CAS
Situation in Austria
Currently there is no uniform national rules for the authorization of certain aids to Matura, as the Matura, is thus created by the teachers themselves decentralized locally. The decision whether a particular resource is registered or not, that is the responsibility of each teacher.
Situation in Switzerland
Currently, there is neither broad nor Switzerland canton -wide uniform rules for the authorization of certain aids to Matura examination because the examination is decentralized ie created by the teachers themselves. The decision whether a particular resource is registered or not, that is the responsibility of each teacher.
Gallery
HP -35, the first scientific pocket calculator (1972 ), Reverse Polish Notation and LED display
MBO Calculator with LED Display ( circa 1972 ), one of the first pocket calculator from a German production
TI calculator with scientific notation SR 10 (1973 )
Calculators ( from 1975): LED display with exponential notation, one of the first with Gon functions
Pocket calculator with vacuum fluorescent display ( to 1975)
Calculators from the year 1976 ( price at the time 49 DM, which corresponds to about 61 EUR now )
Interior view of Casio FX 20 ( about 1976 )
Braun ET 23 (1977 )
Brown ETS 77 (1987 )
HP -15C with numerical integration, root finding and matrix calculation
DDR calculator MR 609, identical to the School calculators SR1
Front view of the Sharp PC -1403, a Pocket Computer
TI Programmer
Calculator as a helper on a larger computer
After calculator in daily (professional ) life has become for many users at a very frequently used tools, their functionality was also brought to the desktop computer and the smartphone in software form. On Windows, you can find it, for example, under the category " Accessories". In addition to versions usually kept simple (so that the operation is not too complicated and the development of software is not too expensive), as they are supplied by the OS vendor, there is also a wide selection of third-party products, often referred to as free programs that additionally more complex functionalities such as programmability or conversions of various physical quantities have each other. Interpreter languages that support the direct mode, such as GW -BASIC or the IBM ROM BASIC some PCs can calculate terms entered using the PRINT command, such as PRINT 3 * 5/sin (2). Also spreadsheet calculations are able. As mainly the mobile phones are now virtually always available, the need for pure calculators goes back more and more. On the office desk but still prefer many users such real equipment without software solutions on the PC.