A calculator is typically a portable electronic device used to perform calculations, ranging from basic arithmetic to complex mathematics.
The first solid-state electronic calculator was created in the early 1960s. Pocket-sized devices became available in the 1970s, especially after the Intel 4004, the first microprocessor, was developed by Intel for the Japanese calculator company Busicom. Modern electronic calculators vary from cheap, give-away, credit-card-sized models to sturdy desktop models with built-in printers. They became popular in the mid-1970s as the incorporation of integrated circuits reduced their size and cost. By the end of that decade, prices had dropped to the point where a basic calculator was affordable to most and they became common in schools.
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. , basic calculators cost little, but scientific and graphing models tend to cost more.
Computer operating systems as far back as early Unix have included interactive calculator programs such as dc and hoc, and interactive BASIC could be used to do calculations on most 1970s and 1980s home computers. Calculator functions are included in most smartphones, tablets, and personal digital assistant (PDA) type devices. With the very wide availability of smartphones and the like, 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%.
Design
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 are displayed as decimal approximations, for example rounded to . Also, some fractions (such as , which is ; 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. Usually these variables are named ans or ans(0).Texas Instruments TI-30X IIB Quick Reference Guide , Page 1 - Last Answer 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. + Calculator buttons and their meanings MC or CM Memory Clear MR, RM, or MRC Memory Recall M− Memory Subtraction M+ Memory Addition C or AC All Clear CE Clear (last) Entry; 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 CHange Sign % Percent ÷ Division × Multiplication − Subtraction + Addition . Decimal point √ Square root = Result
The arrangement of digits on calculator and other numeric keypads with the -- keys two rows above the -- keys is derived from calculators and cash registers. It is notably different from the layout of telephone Touch-Tone keypads which have the -- keys on top and -- keys on the third row.
Internal workings In general, a basic electronic calculator consists of the following components:John Lewis, The Pocket Calculator Book. (London: Usborne, 1982)
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 or thermally onto a roll of paper. 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. Polling is usually implemented in software.X register and Y register Memory 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. Usually implemented in RAM.Flag registerThe function for the calculation is stored here until the calculator needs it. Usually implemented in RAM.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) Location 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 1-of-n code to simplify scanning the display and keyboard.
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.
Example
A basic explanation as to how calculations are performed in a simple four-function calculator:
To perform the calculation , one presses keys in the following sequence on most calculators: .
When is entered, it is picked up by the keyboard scanning unit; the number 25 is encoded as two BCD digits 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 is encoded as BCD 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 processor that the operation to be done is "addition"; The numbers in the X and Y registers are then loaded into the ALU digit by digit and the calculation is carried out following instructions from the permanent or non-volatile memory; The answer, 34 is deposited back to the X register. From there, it is converted to seven-segment code and shown on the display panel.
Other functions are usually performed using repeated additions or subtractions.
Numeric representation
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.
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.
History
Precursors to the electronic calculator
The first known tools used to aid arithmetic calculations were: bones (used to tally items), pebbles, counting boards, and the abacus, which have been used by Sumerians and Egyptians before 2000 BC. 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).
The Renaissance saw the invention of the mechanical calculator by Wilhelm Schickard in 1623, and later by Blaise Pascal in 1642.; "Pascal's invention of the calculating machine. Pascal invented his machine just four hundred years ago, as a youth of nineteen. He was spurred to it by sharing the burden of arithmetical labor involved in his father's official work as supervisor of taxes at Rouen. He conceived the idea of doing the work mechanically, and developed a design appropriate for this purpose; showing herein the same combination of pure science and mechanical genius that characterized his whole life. But it was one thing to conceive and design the machine, and another to get it made and put into use. Here were needed those practical gifts that he displayed later in his inventions....