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Topic: Clock arithmetic


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In the News (Fri 31 Oct 14)

  
  Encyclopedia :: encyclopedia : Modular arithmetic   (Site not responding. Last check: 2007-11-01)
The notion of modular arithmetic is related to that of the remainder in division.
In cryptography, modular arithmetic directly underpins public key systems such as RSA and Diffie-Hellman, as well as providing finite fields which underlie elliptic curves, and is used in and a variety of symmetric key algorithms including IDEA and RC4.
In music, modular arithmetic is used in the consideration of the twelve tone equally tempered scale, where octave and enharmonic equivalency occurs (that is, pitches in a 1∶2 or 2∶1 ratio are equivalent, and C-sharp is the same as D-flat).
www.hallencyclopedia.com /Modular_arithmetic   (872 words)

  
 modular arithmetic - Article and Reference from OnPedia.com
Modular arithmetic is a modified system of arithmetic for integers, sometimes referred to as "clock arithmetic", where numbers "wrap around" after they reach a certain value (the modulus).
For example, whilst 8 + 6 equals 14 in conventional arithmetic, in modulo 12 arithmetic the answer is two, as two is the remainder after dividing 14 by the modulus 12.
In music, because of octave and enharmonic equivalency (that is, pitches in a 1/2 or 2/1 ratio are equivalent, and C# is the same as Db), modular arithmetic is used in the consideration of the twelve tone equally tempered scale, especially in twelve tone music.
www.onpedia.com /encyclopedia/modular-arithmetic   (418 words)

  
 Modular arithmetic - Wikipedia, the free encyclopedia
One way to understand modular arithmetic is to consider "24-hour clock arithmetic": the arithmetic of time-keeping in which the day runs from midnight to midnight and is divided into 24 hours, numbered from 0 to 23.
In cryptography, modular arithmetic directly underpins public key systems such as RSA and Diffie-Hellman, as well as providing finite fields which underlie elliptic curves, and is used in and a variety of symmetric key algorithms including AES, IDEA, and RC4.
More generally, modular arithmetic also has application in disciplines such as law (see e.g., apportionment), economics, (see e.g., game theory) and other areas of the social sciences, where proportional division and allocation of resources plays a central part of the analysis.
en.wikipedia.org /wiki/Modular_arithmetic   (1034 words)

  
 Modular arithmetic
For example, whilst 8 + 6 equals 14 in conventional arithmetic, in modulo 12 arithmetic the answer is 2, as 2 is the remainder after dividing 14 by the modulus 12.
Modular arithmetic, first systematically studied by Carl Friedrich Gauss at the end of the eighteenth century, is applied in number theory, abstract algebra and cryptography.
In abstract algebra, it is realized that modulo arithmetic is a special case of forming the factor ring of a ring modulo an ideal.
www.ebroadcast.com.au /lookup/encyclopedia/mo/Modulo.html   (756 words)

  
 Image reader with image point data averaging - Patent 4866290
The arithmetic mean circuit 120 averages in an arithmetic manner the output from the arithmetic mean circuit 119 and the output from the 1-clock delay circuit 120.
The arithmetic mean circuit 119 averages in an arithmetic manner the output from the arithmetic mean circuit 109 and the output from the 1-row delay circuit 118, this averaging corresponding to the scanning clock signal.
The output from the arithmetic mean circuit 119 and the output from the 1-row delay circuit 120 is averaged in an arithmetic manner by the arithmetic mean circuit 121.
www.freepatentsonline.com /4866290.html   (4710 words)

  
 Modular Arithmetic
Clock (or modular) arithmetic is arithmetic you do on a clock instead of a number line.
Clock arithmetic has negative numbers, but each negative number has a positive number name.
To subtract on a clock, first find standard (positive) names for the two numbers, count clockwise for the first one, and count counterclockwise for the second.
www.math.csusb.edu /faculty/susan/number_bracelets/mod_arith.html   (585 words)

  
 Modular arithmetic
Likewise, if the clock starts at noon and 7 hours elapses three times (3 × 7), then the time will be 9 o'clock (rather than 21).
Since the time starts over at 1 after passing 12, this is similar to arithmetic modulo 12, except that normal modular arithmetic would begin at 0 and "roll over" after 11.
The 24 hour clock, which goes from 00:00 to 23:59, is a closer approximation to modular arithmetic, using a modulus of 24.
www.brainyencyclopedia.com /encyclopedia/m/mo/modular_arithmetic.html   (977 words)

  
 Tcl Built-In Commands - clock manual page   (Site not responding. Last check: 2007-11-01)
Specifies that clock arithmetic, formatting, and scanning are to be done according to the rules for the time zone specified by zoneName.
Most of the subcommands supported by the clock command deal with times represented as a count of seconds from the epoch time, and this is the representation that clock seconds returns.
Unlike clock seconds and clock milliseconds, the value of clock clicks is not guaranteed to be tied to any fixed epoch; it is simply intended to be the most precise interval timer available, and is intended only for relative timing studies such as benchmarks.
www.tcl.tk /man/tcl8.5/TclCmd/clock.htm   (5511 words)

  
 Clock Arithmetic
It could be very embarassing if we were doing clock arithmetic and someone looked at our work and, thinking that we were doing regular arithmetic, said, "Oh no! Most of your answers are wrong!" In order to prevent that from happening, we write clock arithmetic expressions in a special way.
In regular arithmetic, there is only one number that you could add or subtract from another number and leave that other number unchanged...
For this reason, we usually write 0 for the number of hours in the clock and change the way the clock looks so that instead of having the number of hours in the clock at the top, we put a 0 there and think of the clock as starting there instead of ending there.
www-math.cudenver.edu /~wcherowi/clockar.html   (932 words)

  
 Modular arithmetic
In mathematics, modular arithmetic is a system of arithmetic for certain equivalence classes of integers, called congruence classes.
Modular arithmetic, first systematically studied by Carl Friedrich Gauss at the end of the eighteenth century, is applied in number theory, abstract algebra, cryptography, and visual and musical art.
In abstract algebra, it is realized that modular arithmetic is a special case of forming the factor ring of a ring modulo an ideal.
www.knowledgefun.com /book/m/mo/modular_arithmetic.html   (1888 words)

  
 Modular Art
Modular or "clock" arithmetic is arithmetic on a circle instead of a number line.
In ordinary arithmetic, the additive inverse of 4 is -4.
In mod 12 arithmetic, the additive inverse of 4 is 8.
britton.disted.camosun.bc.ca /modart/jbmodart.htm   (680 words)

  
 Tcl Reference Manual: clock   (Site not responding. Last check: 2007-11-01)
On clock scan, the lack of a -format option indicates that a "free format scan" is requested; see FREE FORM SCAN for a description of what happens.
The effect of locale on clock arithmetic is discussed under CLOCK ARITHMETIC.
clock command deal with times represented as a count of seconds from the epoch time, and this is the representation that clock seconds returns.
tmml.sourceforge.net /doc/tcl/clock.html   (5575 words)

  
 [No title]   (Site not responding. Last check: 2007-11-01)
Clock arithmetic means that you imagine a clock having 26 hours on its face.
Another way to do clock arithmetic is to do the addition, multiplication, or subtraction the way you normally would and then divide by 26.
But remember, in clock arithmetic, 28 = 2 (since 28/26 has remainder 2), so we look at what letter corresponds to 2 on the chart and it is C. So Z gets encoded as C. Using the equation y = x + 3, write the coded letters for the entire alphabet.
www.math.columbia.edu /~phan/browse/museum/Cryptography.doc   (966 words)

  
 rec.puzzles Archive (arithmetic), part 03 of 35
Since the clock was not adjusted since the last visit, it's also possible that the radio time shifted by one hour due to a change to or from summer daylight saving time.
Without even considering the rules for when in the month the clock is changed, these possible solutions are ruled out because we know that both visits were in the evening ("I spent a second evening with him").
Digital clocks may run from (a) 1:00 to 12:59 (b) 01:00 to 12:59 (c) 0:00 to 23:59 (d) 00:00 to 23:59 (e-h) any of the above with seconds appended, :00 to :59.
www.faqs.org /faqs/puzzles/archive/arithmetic/part1   (6923 words)

  
 Modular Arithmetic Index   (Site not responding. Last check: 2007-11-01)
A calculator for renaming numbers on a clock.
A calculator for arithmetic (+, -, x) on a clock.
Number bracelets: a game/activity that is based on clock arithemtic.
www.math.csusb.edu /faculty/susan/modular/modular.html   (295 words)

  
 Cryptography Tutorial - Modular Arithmetic
Figure 1: Arithmetic MOD 3 can be performed on a clock with 3 different times: 0, 1 and 2.
and p.m., we are performing mod arithmetic on the clock.
However, performing modular arithmetic using the modulus m=1234569 we are able to compute the answer 64.
www.antilles.k12.vi.us /math/cryptotut/mod_arithmetic.htm   (2634 words)

  
 LESSON PLANET - Many 'Arithmetic' related lesson plans reviewed by teachers.
Arithmetic Sequence - Students think about the concept of arithmetic sequence and learn to find the sum of arithmetic sequence.
Clock Arithmetic - Students work with modular arithmetic and work with their ability to express time on both a 12 and a 24 hour clock system.
The Clock Game - One of the ideas often developed in elementary school is the idea of converting base 10 numbers to base 2 numbers (often called binary numbers).
www.lessonplanet.com /search/Math/Arithmetic   (392 words)

  
 Number Bracelets: Clock Arithmetic   (Site not responding. Last check: 2007-11-01)
By dropping all but the ones digit of the numbers, you are really doing arithmetic on a clock with 10 hours instead of on a number line.
The Fibonacci sequence is the sequence of whole numbers you get starting with 1 and 1 and adding the last two numbers to get the next number of the sequence.
Fibonacci, also known as Leonardo of Pisa, was a medieval mathematician who worked in the field of algebra (that's high school algebra, which was hot stuff then, not abstract algebra).
www.geom.uiuc.edu /~addingto/number_bracelets/clock.html   (498 words)

  
 Mathematics for the Liberal Arts Chapter 10 -- Outline   (Site not responding. Last check: 2007-11-01)
This chapter might be called "counting around a circle" as opposed to "counting on a line." Ordinary counting can be viewed as moving a marker one unit along the number line for each object counted.
We can do the same thing on a circle instead, and that is precisely the principle underlying the clock, where the hour marker moves one unit around the circle for each hour that passes.
Hence the phrase "clock arithmetic." The material in this chapter relates to some basic ideas of abstract mathematics: algebraic structures, generalization, conjecture and proof, the pigeonhole principle, etc.
www.math.fau.edu /richman/mla/chapter10.html   (127 words)

  
 Modular Arithmetic — An Introduction
As shown by the preceding examples, one of the powers of modular arithmetic is the ability to show, often very simply, that certain equations and systems of equations have no integer solutions.
Without modular arithmetic, we would have to find all of the solutions and then see if any turned out to be integers.
Of course, we don't need the formality of modular arithmetic in order to compute this, but when we do this kind of computation in our heads, this is really what we are doing.
www.math.rutgers.edu /~erowland/modulararithmetic.html   (1827 words)

  
 Read This: Arithmetic for Teachers
On the one hand, it is important to emphasize the ways in which the basic ideas of numbers, arithmetic, and elementary geometry form a logically consistent fabric.
On the other hand, it is equally important to recognize that a disproportionately large percentage of prospective elementary teachers are math-averse in one way or another, and the presentation should seek to lessen the aversion so that it is not passed along to another generation of students.
In particular, Chapter 8 on clock arithmetic is good, within the parameters of the book's overall style, and Chapter 9 on RSA Encryption is novel and interesting.
www.maa.org /reviews/arithmeticforteachers.html   (1395 words)

  
 nrich.maths.org::Mathematics Enrichment::Modulus Arithmetic and a Solution to Dirisibly Yours
For example, the hours on a clock face can be considered as a modulo 12 system, with only the numbers from 1 to 12 being possible.
The difference between clock arithmetic and modulo arithmetic is that in modulo arithmetic the numbers begin at 0.
One crucial feature of the modulo arithmetic system (as regards this problem) is that if a number can be written as 0 under modulo n arithmetic, then the number is divisible by n.
nrich.maths.org.uk /public/viewer.php?obj_id=1346&part=index&refpage=monthindex.php   (495 words)

  
 [No title]   (Site not responding. Last check: 2007-11-01)
Successive releases of the Pentium processor added multimedia instructions (MMX) and boosted the clock speed, but the internal architecture remained unchanged until the Pentium® Pro processor was introduced in 1995.
The Pentium Pro processor architecture was tweaked here and there in subsequent releases (the Pentium® II processor and Pentium® III processor), but advances consisted primarily of accelerating the clock speed past 1GHz and expanding cache sizes-the basic micro-architecture inherited from the Pentium Pro processor remained fundamentally the same.
Arithmetic Logical Units (ALUs) are the computational heart of most microprocessors.
www.intel.com /cd/ids/developer/asmo-na/eng/44004.htm?prn=Y   (1861 words)

  
 Clock Arithmetic.
Clock arithmetic is an example of what is called a "modular system." Have a look at a normal 12-hour clock, with numbers from "0" to "11" (we usually start at zero, hence "0" would be "noon" or "midnight" at the top of the clock).
There are many different types of clocks, and hence many different types of clock arithmetic.
Suppose you have a 24-hour clock (as it is common in Europe, for example).
mathcentral.uregina.ca /qq/database/QQ.09.97/dixon3.html   (215 words)

  
 Clock Arithmetic 2
Going ahead 6 hours on this clock will bring us back to where we started, so if we start at 0, every time we go ahead 6 hours, we are back at 0.
So, to use this division method for doing clock arithmetic we follow these steps: first we add (or subtract) the numbers in the usual w ay, then we divide the result by the modulus and take the remainder of this division as our answer.
Having the division method for doing clock arithmetic means that we can do more complicated things than just addition and subtraction.
www-math.cudenver.edu /~wcherowi/clockar2.html   (1075 words)

  
 Modular Arithmetic   (Site not responding. Last check: 2007-11-01)
Modular arithmetic is arithmetic you do on a clock instead of a number line.
One way to find a standard name for a number on the clock is to count around the clock.
This is not the same a clock arithmetic, but it is related.
pages.sbcglobal.net /george.bunson/Programming/modularArithmetic.htm   (515 words)

  
 Motivate : Mathematics Videoconferences for Schools.
= 4, since if we count round a clock to 16, it's the same as counting to 4 (as in the diagram on the right - 4pm is the same as 16.00 on the 24-hour clock).
Since we are only interested in whether 12 divides into the final answer exactly or not, we don't need to know that the answer is 341 remainder 4, only that there is a remainder of 4, and clock arithmetic will tell us what our remainders are.
So using clock arithmetic can help you check this method for numbers which are too big for your spreadsheet or calculator.
www.motivate.maths.org /conferences/conf59/c59_generating_primes.shtml   (978 words)

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