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mathematics

Calculator

Calculator is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Calculator rather than just read about it. In short: 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.

Calculator — main illustration
Calculator — illustration

Key takeaways

  • Calculator belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Calculator to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Calculator from memory before moving on to harder problems.

Reference excerpt

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. As of 2016, 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 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. Usually these variables are named ans or ans(0). 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.

The arrangement of digits on calculator and other numeric keypads with the 7-8-9 keys two rows above the 1-2-3 keys is derived from calculators and cash registers. It is notably different from the layout of telephone Touch-Tone keypads which have the 1-2-3 keys on top and 7-8-9 keys on the third row.

Internal workings In general, a basic electronic calculator consists of the following components:

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).

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 25 + 9, one presses keys in the following sequence on most calculators: 2 5 + 9 =.

… excerpt ends here. Continue reading the full article.

Illustrations

Calculator: An electronic pocket calculator with a seven-segment liquid-crystal display (LCD) that can perform arithmetic operations
An electronic pocket calculator with a seven-segment liquid-crystal display (LCD) that can perform arithmetic operations
Calculator: A modern scientific calculator with a dot-matrix display
A modern scientific calculator with a dot-matrix display
Calculator: Scientific calculator displays of fractions and decimal equivalents
Scientific calculator displays of fractions and decimal equivalents
Calculator: The interior of a Casio FX-991s calculator
The interior of a Casio FX-991s calculator
Calculator: An office calculating machine with a paper printer
An office calculating machine with a paper printer

Worked examples

Example 1 — a first encounter with Calculator

Start with the simplest possible case. Write down what Calculator claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Calculator before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Calculator ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Calculator

In research
Calculator appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Calculator in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Calculator is common in secondary-school and first-year university syllabi. It links to neighbouring topics 20th-century inventions, American inventions, Calculators, so understanding it makes those chapters shorter.
In everyday life
Look for Calculator outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Calculator in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Calculator means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Calculator out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Calculator in simple terms?

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.

Why does Calculator matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Calculator?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Calculator.

Tags

  • 20th-century inventions
  • American inventions
  • Calculators
  • Electronic calculators
  • Mathematical tools
  • Office equipment

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