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Telephone keypad

Telephone keypad 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 Telephone keypad rather than just read about it. In short: A telephone keypad is a keypad installed on a push-button telephone or similar telecommunication device for dialing a telephone number. It was standardized when the dual-tone multi-frequency signaling (DTMF) system was developed in the Bell System in the United States in the 1960s – this replaced rotary dialing, that had been developed for electromechanical telephone switching systems.

Telephone keypad — main illustration
Telephone keypad — illustration

Key takeaways

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

Reference excerpt

A telephone keypad is a keypad installed on a push-button telephone or similar telecommunication device for dialing a telephone number. It was standardized when the dual-tone multi-frequency signaling (DTMF) system was developed in the Bell System in the United States in the 1960s – this replaced rotary dialing, that had been developed for electromechanical telephone switching systems. Because of the abundance of rotary dial equipment still on use well into the 1990s, many telephone keypads were also designed to be backwards-compatible: as well as producing DTMF pulses, they could optionally be switched to produce loop-disconnect pulses electronically. The development of the modern telephone keypad is attributed to research in the 1950s by Richard Deininger under the directorship of John Karlin at the Human Factors Engineering Department of Bell Labs. The modern keypad is laid out in a rectangular array of twelve push buttons arranged as four rows of three keys each. For military applications, a fourth column of keys was added to the right for priority signaling in the Autovon system in the 1960s. Initially, between 1963 and 1968, the keypads for civilian subscriber service omitted the lower left and lower right keys. These two keys are commonly labelled star, ⚹, and number sign/hash, #, respectively, and produce the signals associated with those symbols. These keys were added to provide signals for anticipated data entry purposes in business applications, but found use in Custom Calling Services (CLASS) features installed in electronic switching systems.

Layout

The layout of the digit keys is different from that commonly appearing on calculators and numeric keypads. This layout was chosen after extensive human factors testing at Bell Labs. At the time (late 1950s), mechanical calculators were not widespread, and few people had experience with them. Indeed, calculators were only just starting to settle on a common layout; a 1955 paper states "Of the several calculating devices we have been able to look at ... Two other calculators have keysets resembling [the layout that would become the most common layout] ... . Most other calculators have their keys reading upward in vertical rows of ten." Meanwhile, a 1960 paper – just five years later – refers to today's common calculator layout as "the arrangement frequently found in ten-key adding machines". In any case, Bell Labs' testing found that the telephone layout with 1, 2, and 3 on the top row, was slightly faster in use than the calculator layout with them in the bottom row.

Star key and square key In addition to the numbers, the ITU recommends two additional keys: the "star key", labeled ⚹, and the "square key", labeled ⌗. The square key is often known as the pound key, hash key or octothorp. The precise symbols to be used for the star and square keys is not standardised: asterisk operator (∗) and sextile (⚹) have been recommended for the star key, and a simple asterisk * is often used. The "square key" is almost invariably replaced with the # (number sign). A 1973 US patent (3,920,926) by the Northern Electric Company calls them "sextile or asterisk" and "octothorp". These can be used for special functions. For example, in the UK, users can order a 7:30 am alarm call from a BT telephone exchange by dialing: ⚹55⚹0730#. The Greek symbols alpha and omega had been suggested originally for these keys. John A. Koten (1929–2014), a corporate communications specialist with Bell Labs in Chicago, claimed credit for the choice of star and number sign, reasoning that the new keys would be easier to explain to a public already familiar with typewriter symbols.

Letters

In the Americas and a number of other countries, most dials and, later, keypads also bear letters according to the following system:

In the UK, dials and keypads also bore letters, though these were later dropped. They were arranged as follows:

For the above system, O and Q are set together on the 0 key. In addition to O and 0 being graphically similar to indistinguishable, when reciting sequences of numbers in English it is common to substitute "oh" for zero or nought; Q is visually similar to O, causing plausible confusion. Therefore, two possible mistakes were avoided. These letter assignments have been used for multiple purposes. Originally, they referred to the dialable letters of telephone exchange names. In the mid-20th century United States, before the switch to all-number calling, telephone numbers had seven symbols, including a two-symbol prefix which was expressed in letters rather than digits, e.g.; KL5-5445. The UK telephone numbering system used a similar two-letter code after an initial zero (the zero prefix selected trunk dialling) to form the first part of the subscriber trunk dialling code for a region; the letters were followed by one or more digits. For example, Aylesbury was assigned 0AY6, which translated to 0296.

The letters have also been used, mainly in the United States, as a technique for remembering telephone numbers easily. For example, an interior decorator might license the telephone number 1-800-724-6837, but advertise it as the more memorable phoneword "1-800-PAINTER". Sometimes businesses advertise a number with a mnemonic word having more letters than there are digits in the phone number. Usually, this means that the caller just stops dialing at seven digits after the area code or that the extra digits are ignored by the telephone exchange. In early cell phones, or feature phones, the letters on the keys are used for text entry tasks such as text messaging, entering names in the phone book, and browsing the web. To compensate for the smaller number of keys, phones used multi-tap and later predictive text processing to speed up the process. Touchscreen phones have made these input methods obsolete, as the screens are typically large enough to show as many virtual buttons as necessary for a full keyboard.

Key tones Pressing a single key of a traditional analog telephone keypad produces a telephony signaling event to the remote switching system. For touchtone service, the signal is a dual-tone multi-frequency signaling tone consisting of two simultaneous pure tone sinusoidal frequencies. The row in which the key appears determines the low-frequency component, and the column determines the high-frequency component. For example, pressing key 1 results in a signal composed of tones with frequencies 697 hertz (Hz) and 1209 Hz.

Letter mapping

… excerpt ends here. Continue reading the full article.

Illustrations

Telephone keypad: A telephone keypad using the ITU E.161 standard. (The 'star key' uses a sextile symbol.)
A telephone keypad using the ITU E.161 standard. (The 'star key' uses a sextile symbol.)
Telephone keypad: A standard telephone keypad
A standard telephone keypad
Telephone keypad: Telephone with letters on its rotary dial (1950s, UK)
Telephone with letters on its rotary dial (1950s, UK)
Telephone keypad: British GPO 726 telephone of 1967
British GPO 726 telephone of 1967
Telephone keypad: The official toll-free hotline for the California Department of Transportation's adopt-a-Highway program is 1-866-236-7824, but signs advertise the number as 1-866-ADOPTAHWY, with two extra digits, for memorability.
The official toll-free hotline for the California Department of Transportation's adopt-a-Highway program is 1-866-236-7824, but signs advertise the number as 1-866-ADOPTAHWY, with two extra digits, for memorability.

Worked examples

Example 1 — a first encounter with Telephone keypad

Start with the simplest possible case. Write down what Telephone keypad 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 Telephone keypad 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 Telephone keypad 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 Telephone keypad

In research
Telephone keypad 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 Telephone keypad 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
Telephone keypad is common in secondary-school and first-year university syllabi. It links to neighbouring topics Telephone numbers, Telephony equipment, so understanding it makes those chapters shorter.
In everyday life
Look for Telephone keypad 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 Telephone keypad in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Telephone keypad 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 Telephone keypad out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Telephone keypad in simple terms?

A telephone keypad is a keypad installed on a push-button telephone or similar telecommunication device for dialing a telephone number. It was standardized when the dual-tone multi-frequency signaling (DTMF) system was developed in the Bell System in the United States in the 1960s – this replaced r…

Why does Telephone keypad 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 Telephone keypad?

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 Telephone keypad.

Tags

  • Telephone numbers
  • Telephony equipment

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