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Topic: Positional notation


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In the News (Thu 18 Apr 19)

  
  Definition of Positional notation
Positional notation is a system in which each position has a value represented by a unique symbol or character.
For each position, the resultant value of each position is the value of that character multiplied by a power of the base number for that numeral system.
The position of each character or symbol (usually called a digit) counting from the right determines the power of the base that is to be multiplied by that digit.
www.wordiq.com /definition/Positional_notation   (306 words)

  
 Zero
Of course their notation for numbers was quite different from ours (and not based on 10 but on 60) but to translate into our notation they would not distinguish between 2106 and 216 (the context would have to show which was intended).
A negative number subtracted from zero is positive, a positive number subtracted from zero is negative, zero subtracted from a negative number is negative, zero subtracted from a positive number is positive, zero subtracted from zero is zero.
Zero divided by a negative or positive number is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator.
www-groups.dcs.st-and.ac.uk /~history/HistTopics/Zero.html   (2872 words)

  
 Positional notation - Definition, explanation
Positional notation is a numeral system in which each position is related to the next by a constant multiplier called the base of that numeral system.
The idea of indicating magnitude by means of position was embodied long ago by the use of the abacus in all its various forms.
A key argument against the positional system was its susceptibility to easy fraud by simply putting a number at the beginning or end of a quantity, thereby changing (e.g.) 100 into 5100, or 100 into 1000.
www.calsky.com /lexikon/en/txt/p/po/positional_notation.php   (917 words)

  
 Positional notation
Positional notation or place-value notation is a numeral system in which each position is related to the next by a constant multiplier called the base (or radix) of that numeral system.
For a positional system up to ten the ubiquitous digits 0,1,2,3,4,5,6,7,8 and 9 are used, for octal only eight digits up to 7 and for binary only two digits 0 and 1 are needed.
In the 1930s, Otto Neugebauer introduced a modern notational system for Babylonian and Hellenistic numbers that substitutes modern decimal notation from 0 to 59 in each position, while using a semicolon (;) to separate the integral and fractional portions of the number and using a comma (,) to separate the positions within each portion.
www.dejavu.org /cgi-bin/get.cgi?ver=93&url=http://articles.gourt.com/%22http%3A%2F%2Farticles.gourt.com%2F%3Farticle%3Dplace-value   (1067 words)

  
 positional notation@Everything2.com
Our decimal positional system is base ten, that is, we use ten symbols (which vary from culture to culture) to represent numbers.
A crude form of positional notation was in use by preliterate people who, when counting objects using their fingers, ran out of fingers on one hand and used each finger on the other hand to represent a whole hands' worth of objects.
Two cultures later developed positional notations involving true zeroes: The Mayans who had a base 20 system, and Hindus who began using a base 10 system in the early centuries of the Common Era (to be more precise, the earliest archaeological evidence for decimal numbers in India comes from that time).
everything2.com /index.pl?node_id=1365630   (1232 words)

  
 numeration and numbers, Roman, binary, positional, additive
These two numbers are pointed out with the V signs and X and the single unity, suitable with the sign I, additions were considered or subtracted one had positioned to their right or left.
The invention and introduction of the zero is the end of the additives numerations and the beginning of the positional notation.
The positional notation with him uses of the figures, is from India, where the first traces of such system go up again the VI sec.
www.themeter.net /numerazioni_e.htm   (1106 words)

  
 Positional notation - Wikipedia, the free encyclopedia
A positional notation or place-value notation system is a numeral system in which each position is related to the next by a constant multiplier, a common ratio, called the base (or radix) of that numeral system.
Before positional notation became standard, simple additive systems (sign-value notation) were used such as Roman Numerals.
For a positional system up to ten the ubiquitous digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are used, for octal only eight digits up to 7 and for binary only two digits 0 and 1 are needed.
en.wikipedia.org /wiki/Positional_notation   (1187 words)

  
 Sexual Paradox: Undecidability
Zero thus only came to be recognized indirectly, through a long, tortuous route, which first led to positional notation for numbers and then to the need for a mark for a space For example in counting a hundred and one objects by writing 101, the zero (sunya) is needed to indicate there are no tens.
Zero and with it positional notation was transmitted in the Middle ages from India, through the Arabs, to Europe.
It is thus to Fibonnaci all merchants owe the Arabic-Indic positional notation which has made numerical calculation so natural and made both science and the precipitous rise and fall of stock markets in their triple witching hour possible.
www.dhushara.com /paradoxhtm/paradoxs.htm   (2205 words)

  
 ANSDIT - The letter "P"   (Site not responding. Last check: 2007-11-06)
A pose is characterized in terms of six degrees of freedom to specify position and orientation.
In a subprogram call, the correspondence of an actual parameter with a formal parameter in the same position in the declaration of the subprogram.
A rotating disk that presents all the characters of the set at a single print position A daisywheel is a type of print wheel.
www.ncits.org /tc_home/k5htm/p2.htm   (2747 words)

  
 Autonomy » Community Standard Sexagesimal
It is a numerical system that employs sixty unique numerals and a positional notation using powers of sixty to express larger numbers.
In contrast, binary employs two numerals (0 and 1) and a positional notation using powers of two to express larger numbers.
The Sumerians used a sexagesimal numerical system, which the Babylonians refined with a “positional” notation (”Positional Notation” is explained in the “Primer: Positional and Integer Base Notation.” The system all of us have grown up with is a decimal, or base-10, positional notation system).
autonomyseries.com /sexagesimal-numerals   (844 words)

  
 Uri's page-Arabic Numeral System
The important innovation in the Arabic system was the use of positional notation, in which individual number symbols assume different values according to their position in the written numeral.
Positional notation is made possible by the use of a symbol for zero.
Positional notation also greatly simplifies all forms of written numerical calculation.
www.geocities.com /uripi/arabic_numbers.html   (354 words)

  
 Representing Data   (Site not responding. Last check: 2007-11-06)
In an eight bit pattern, the most significant bit is the sign bit, followed by a 3-bit exponent (expressed in excess notation) followed by a 4-bit mantissa.
Note: in a normalized floating point notation, the mantissa must begin with a "1"; the radix point is assumed to be at the left of the mantissa.
the number 101 in excess (4) notation is 5-4 that is +1; a positive exponent moves the radix to the right and a negative exponent moves the radix to the left.
www.cse.yorku.ca /course/1520/binaryRep.htm   (622 words)

  
 Nothing Changes - Alternative History - A Wikia wiki
In our time line, the Greek system for notating numbers was quite awkward This made doing math very difficult and ultimately limited their progress in the sciences.
Together the two philosophers learned much of Babylonian science, astronomy, mysticism, and mathematics -- including their method of positional notation for numbers and of their use of ":" as a place holder for numbers which are not there (the zero).
He used positional notation and the ":" in his calculations which made it much easier for him to advance his own studies.
althistory.wikia.com /wiki/Nothing_Changes   (1041 words)

  
 Historical Notes: Mathematical notation
Particularly from working with computers it is often now assumed that base-2 positional notation is somehow the most natural and fundamental.
The idea of having notation for operators emerged in the early 1600s, and by the end of the 1600s, notably with the work of Gottfried Leibniz, essentially all the basic notation now used in algebra and calculus had been established.
Notation for mathematical logic began to emerge in the 1880s, notably with the work of Giuseppe Peano, and by the 1930s it was widely used as the basis for notation in pure mathematics.
www.wolframscience.com /reference/notes/1182a   (498 words)

  
 Base-n Concepts   (Site not responding. Last check: 2007-11-06)
The Tally number notation is actually a primitive precursor of base-5 notation, but it is not a positional notation.
A positional number notation makes the value contributed by a numeric symbol depend on its position, so that the same symbol can be used over and over for different values.
All these notations use the same system based on the value of n - which is called the radix of the number notation.
core.ecu.edu /math/wirthj/tutor/basen2.html   (1042 words)

  
 Mathematical Notation: Past and Future
By the way, even though math notation hadn't gotten going very well by their time, the kind of symbolic notation used in alchemy, astrology, and music pretty much had been developed.
Actually, he thought that having the right notation was somehow the secret to a lot of issues of human affairs in general.
In particular, it emphasized using notation whenever one could, and somehow minimizing the amount of potentially imprecise text that had to be written.
www.stephenwolfram.com /publications/talks/mathml/mathml2.html   (4335 words)

  
 Notes from week 3   (Site not responding. Last check: 2007-11-06)
You may not be familiar with the term, but you have used positional notation ever since you learned to count.
  In the string "230" the "0" is in position zero, the "3" is in position one, and the "2" is in position two.
A third common number system used in computers is Base 8 positional notation, also known as "Octal".
spot.pcc.edu /~rchriste/121/n3.html   (3613 words)

  
 Special Variable Types
One way to prevent this is to append an extra character to both sides of the assignment statement using the expected positional parameter.
command reassigns the positional parameters, in effect shifting them to the left one notch.
If you use a large number of positional parameters to a script,
www.tldp.org /LDP/abs/html/othertypesv.html   (725 words)

  
 Binary - LQWiki
To express higher numbers, a "positional notation" is used.
In two's complement notation, getting the complement of a number requires putting ones where the zeros are and zeros where the ones are, and then adding 1 to the result.
This should be slightly confusing because, as I mentioned earlier, binary numbers are represented in positional notation.
wiki.linuxquestions.org /wiki/Binary   (924 words)

  
 The Binary System
The notation is read from right to left, instead of the left to right system offered by the implied progression of powers.
The binary notation signifies the presence/absence of either a one (1) or a zero (0), which represents the presence/absence of its corresponding figure on the previous progression of constant numbers.
In contemporary math, then, the binary notation is presented as only relating to the possibility of the constant number series 1, 2, 4, 8, 16, 32, 64...n, as we have seen.
www.earthmatrix.com /binary/system.htm   (2706 words)

  
 3.1.2 Array aggregate values   (Site not responding. Last check: 2007-11-06)
As with record aggregates or subprogram calls, an array aggregate can use named or positional notation to specify which components of the array are being given which values.
The positional notation supplies a list of values which are associated with elements in the array, starting with the first element of the array and not all values need to be stated.
Named notation uses the index value of the element to be initialised to associate an element of the array with a value.
www.scism.sbu.ac.uk /law/Section3/chapter1/s3c1p2.html   (291 words)

  
 Telstra ClassRoom - The Story of Digital Transmission and Data Communication - Section 3   (Site not responding. Last check: 2007-11-06)
We do this by using a system called "positional notation", which means that the value of a particular digit depends on its position.
This system of positional notation is by far the easiest we have been able to devise for representing numbers.
In the binary system, positional notation works just as it does in the decimal system, except that the columns to the left of the units column represent increasing powers of two instead of ten.
www.telstra.com.au /classroom/sec_1_3.htm   (974 words)

  
 conversionmath
First consider what is known as positional notation.
Positional notation means that the value of a digit in a number depends not only on its own intrinsic value but also on its location in the number.
Once you understand the expanded notation, the rest is easy: You expand the number just as in base 10, but use the appropriate base of the number.
condor.depaul.edu /~psisul/conversionmath.html   (831 words)

  
 Notes - Week 2
Since the binary system is positional we may incorporate the idea of fractional values as we do for the decimal system.
That is, if the exponent is positive then we move the decimal point to the right and if it is negative we move it to the left.
Again, the first significant digit is adjacent to the binary point and the exponent tells us the direction and number of positions to move the decimal point to obtain the original number.
condor.depaul.edu /~jmorgan1/255.lecture2.html   (875 words)

  
 Binary Numbers
But the decimal system is only one of many possible notations that can be used to represent numbers.
The Roman numeral notation lacks the capability of representing 0, negative numbers, and fractions.
The decimal positional notation is so second nature to us that we seldom give a thought to such expansions.
cs.furman.edu /digitaldomain/more/binary/bin1.html   (600 words)

  
 Positional Notation   (Site not responding. Last check: 2007-11-06)
The decimal system is a positional notation for representing numbers.
The position of each digit in the string is significant.
Think of each position as a numbered slot where a digit can go.
chortle.ccsu.edu /AssemblyTutorial/Chapter-06/ass06_5.html   (89 words)

  
 Notation - Wikipedia, the free encyclopedia
Octal notation, a positional notation in base eight, used in some computers
Decimal notation, a positional notation in base ten
Hexadecimal notation, a positional notation in base sixteen, commonly used in computers
en.wikipedia.org /wiki/Notation   (328 words)

  
 Procedure Calls
(These two forms are sometimes referred to as "positional notation" and "named notation," respectively.) Another example is given in the next section, where the understandability advantage of named association is made very evident.
When a formal parameter of mode in has a default value or expression, the actual parameter may be omitted in the call.
When the position of a parameter follows that of an omitted parameter, named association must be used.
www.cs.uni.edu /~mccormic/AdaEssentials/procedure_calls.htm   (380 words)

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