1. Numeral System - Wikipedia, The Free Encyclopedia This article is about different methods of expressing numbers with symbols. For completely different sets of numbers, see number system. http://en.wikipedia.org/wiki/Numeral_system

Numeral system From Wikipedia, the free encyclopedia Jump to: navigation search This article is about different methods of expressing numbers with symbols. For completely different sets of numbers, see number system Numeral systems by culture Hindu-Arabic numerals Indian Eastern Arabic Khmer ... Thai East Asian numerals Chinese Counting rods Japanese Korean Alphabetic numerals Abjad Armenian Cyrillic Ge'ez ... Āryabhaṭa Other systems Attic Babylonian Egyptian Etruscan ... Positional systems by base Decimal more… v ... e A numeral system (or system of numeration ) is a mathematical notation for representing a set of numbers by symbols in a consistent manner. It can be seen as the context that allows the numeral "11" to be interpreted as the binary numeral for three , the decimal numeral for eleven , or other numbers in different bases Ideally, a numeral system will: Represent a useful set of numbers (e.g. all whole numbers integers , or real numbers Give every number represented a unique representation (or at least a standard representation) Reflect the algebraic and arithmetic structure of the numbers. For example, the usual

2. Number Systems Harder A number system is the set of symbols used to express quantities as the basis for counting, determining order, comparing amounts, http://42explore.com/number.htm

3. The Real Number System The real number system evolved over time by expanding the notion of what we mean by the word “number.” At first, “number” meant something you could count, http://www.jamesbrennan.org/algebra/numbers/real_number_system.htm

The Real Number System The real number system evolved over time by expanding the notion of what we mean by the word “number.” At first, “number” meant something you could count, like how many sheep a farmer owns. These are called the natural numbers , or sometimes the counting numbers Natural Numbers or “Counting Numbers” The use of three dots at the end of the list is a common mathematical notation to indicate that the list keeps going forever. At some point, the idea of “zero” came to be considered as a number. If the farmer does not have any sheep, then the number of sheep that the farmer owns is zero. We call the set of natural numbers plus the number zero the whole numbers Whole Numbers Natural Numbers together with “zero” About the Number Zero What is zero? Is it a number? How can the number of nothing be a number? Is zero nothing, or is it something? Well, before this starts to sound like a Zen koan, let’s look at how we use the numeral “0.” Arab and Indian scholars were the first to use zero to develop the place-value number system that we use today. When we write a number, we use only the ten numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. These numerals can stand for ones, tens, hundreds, or whatever depending on their position in the number. In order for this to work, we have to have a way to mark an empty place in a number, or the place values won’t come out right. This is what the numeral “0” does. Think of it as an empty container, signifying that that place is empty. For example, the number 302 has 3 hundreds, no tens, and 2 ones.

4. Number Systems The Mayan number system dates back to the fourth century and was approximately 1000 years more advanced than the Europeans of that time. http://www.math.wichita.edu/history/topics/num-sys.html

Number Systems Topic Tree Home Following are some of the different number systems discussed in the history of mathematics. Contents of this Page The Number Sense Quipu - An Inca Counting System Fractions of Ancient Egypt The Mayan Number System ... Where Did Numbers Originate? The Number Sense The number sense is not the ability to count, but the ability to recognize that something has changes in a small collection. Some animal species are capable of this. The number of young that the mother animal has, if changed, will be noticed by all mammals and most birds. Mammals have more developed brains and raise fewer young than other species, but take better care of their young for a much longer period of time. Many birds have a good number sense. If a nest contains four eggs, one can safely be taken, but when two are removed the bird generally deserts. The bird can distinguish two from three. An experiment done with a goldfinch showed the ability to distinguish piles of seed: three from one, three from two, four from two, four from three, and six from three. The goldfinch almost always confused five and four, seven and five, eight and six, and ten and six. Another experiment involved a squire who was trying to shoot a crow which made its nest in the watchtower of his estate. The squire tried to surprise the crow, but at his approach, the crow would leave, watch from a distance, and not come back until the man left the tower. The squire then took another man with him to the tower. One man left and the other stayed to get the crow when it returned to the nest, but the crow was not deceived. The crow stayed away until the other man came out. The experiment was repeated the next day with three men, but the crow would not return to the nest. The following day, four men tried, but it was not until that next day with five men that the crow returned to the nest with one man still in the tower.

5. Number System Conversion - Explanation Our decimal number system is known as a positional number system, because the value of the number depends on the position of the digits. http://www.cstc.org/data/resources/60/convexp.html

CSTC home browse resources cover page content Conversion Between Different Number Systems Positional number systems Our decimal number system is known as a positional number system, because the value of the number depends on the position of the digits. For example, the number has a very different value than the number , although the same digits are used in both numbers. (Although we are accustomed to our decimal number system, which is positional, other ancient number systems, such as the Egyptian number system were not positional, but rather used many additional symbols to represent larger values.) In a positional number system, the value of each digit is determined by which place it appears in the full number. The lowest place value is the rightmost position, and each successive position to the left has a higher place value. In our decimal number system, the rightmost position represents the "ones" column, the next position represents the "tens" column, the next position represents "hundreds", etc. Therefore, the number represents hundred and tens and ones, whereas the number

6. Number System Bit Byte; K M; number system; Convert From Any Base To Decimal; Convert From Decimal to Any Base; Addition and Multiplication Tables http://www.eng.umd.edu/~nsw/ench250/number.htm

Number System Computer Methods in Chemical Engineering Table of Contents Number System Convert From Any Base To Decimal Convert From Decimal to Any Base Addition and Multiplication Tables ... Comments Computer uses the binary system. Any physical system that can exist in two distinct states (e.g., 0-1, on-off, hi-lo, yes-no, up-down, north-south, etc.) has the potential of being used to represent numbers or characters. A binary digit is called a bit . There are two possible states in a bit, usually expressed as and 1. A series of eight bits strung together makes a byte , much as 12 makes a dozen. With 8 bits, or 8 binary digits, there exist 2^ =256 possible combinations. The following table shows some of these combinations. (The number enclosed in parentheses represents the decimal equivalent.) =1024 is commonly referred to as a "K". It is approximately equal to one thousand. Thus, 1 Kbyte is 1024 bytes. Likewise, 1024K is referred to as a "Meg". It is approximately equal to a million. 1 Mega byte is 1024*1024=1,048,576 bytes. If you remember that 1 byte equals one alphabetical letter, you can develop a good feel for size. Number System You may regard each digit as a box that can hold a number. In the binary system, there can be only two choices for this number either a "0" or a "1". In the octal system, there can be eight possibilities:

7. Links To Information On Number Systems Babylonian. Babylonia Babylonian Mathematics Dr. Ramsey Babylonian Mathematics Babylonian number system Sumerian and Babylonian Numerals http://mathforum.org/alejandre/numerals.html

Suzanne Alejandre Information Links Links to Information on Number Systems Suzanne's Math Lessons Suzanne's Workshop Ideas Arabic Arabic Mathematics Arabic mathematics: forgotten brilliance? Arabic Numbers ... Arabic Numeral System Babylonian Babylonia Babylonian Mathematics - Dr. Ramsey Babylonian Mathematics Babylonian Number System ... Sumerian and Babylonian Numerals Chinese The Abacus Abacus in Various Number Systems The Chinese Calendar Chinese Numbers ... Mathematics in China India Ancient India - Mathematics History of Ganit (Mathematics) History Topics: Index of Ancient Indian mathematics Indian mathematics ... The Kerala School, European Mathematics and Navigation Egyptian Egypt Egyptian Mathematics Egyptian Mathematics - Mark Millmore Egyptian Numerals ... Egyptology Resources Greek Ancient Greek Number Codes Mathematics in Ancient Greece Greek Mathematics Greek Numbers and Arithmetic ... Greek Number Systems Mayan Mayan Arithmetic by Steven Fought Maya Civilization Mayan Mathematics Mayan Numbers ... Mayan Number System Roman Decipher Roman Numeral Dr. Math FAQ on Roman Numerals Evolution of Arabic Numerals from India Roman Numeral Clock ... Help http://mathforum.org/ The Math Forum is a research and educational enterprise of the Drexel School of Education Send comments to: Suzanne Alejandre

8. The Number System Department of Mathematics, University of Utah. The number system. This page contains concise explanations of commonly used types of numbers. http://www.math.utah.edu/~pa/math/numbers.html

Understanding Mathematics by Peter Alfeld, Department of Mathematics, University of Utah The Number System This page contains concise explanations of commonly used types of numbers. Natural Numbers Natural numbers are the numbers 1, 2, 3, ... . Integers All natural numbers are integers, but also 0, -1, -2, ... . Rational numbers Rational numbers are fractions p/q where q is non-zero and p and q are both integer. For example, all integers are rational (pick q =1). Other examples of rational numbers are Real numbers Without getting technical, real numbers are all numbers that can be written as a possibly never repeating decimal fraction. For example, all rational numbers are real. Their decimal representations do repeat. Decimal fractions whose representation do not repeat are irrational.

9. California Articulation Number System (CAN) Neither the California Articulation number system nor the institutions of California s postsecondary system participating in CAN are held liable for errors http://www.cansystem.org/

CAN Online Welcome to the New CAN Website. Your cornerstone to the transfer process! Online CAN Guide CAN Catalog of Courses I-CAN CAN Information ... New CAN Model Featured College Send mail to info@cansystem.org with questions or comments about this web site. © 2003 California Articulation Number System. "CAN" is the official mark of the California Articulation Number System Every reasonable effort is made to keep the information provided here accurate and up-to-date. Neither the California Articulation Number System nor the institutions of California's post-secondary system participating in CAN are held liable for errors in or omissions. All final decisions regarding the transferability of courses should be confirmed with the institutions involved.

10. Greek Numbers The first Greek number system we examine is their acrophonic system which was use We now look at a second ancient Greek number system, the alphabetical http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Greek_numbers.html

Greek number systems Greek index History Topics Index Version for printing There were no single Greek national standards in the first millennium BC. since the various island states prided themselves on their independence. This meant that they each had their own currency, weights and measures etc. These in turn led to small differences in the number system between different states since a major function of a number system in ancient times was to handle business transactions. However we will not go into sufficient detail in this article to examine the small differences between the system in separate states but rather we will look at its general structure. We should say immediately that the ancient Greeks had different systems for cardinal numbers and ordinal numbers so we must look carefully at what we mean by Greek number systems. Also we shall look briefly at some systems proposed by various Greek mathematicians but not widely adopted. The first Greek number system we examine is their acrophonic system which was use in the first millennium BC. 'Acrophonic' means that the symbols for the numerals come from the first letter of the number name, so the symbol has come from an abreviation of the word which is used for the number. Here are the symbols for the numbers 5, 10, 100, 1000, 10000.

11. Abacus In Various Number Systems Each wire corresponded to a digit in a positional number system, commonly in base 10. A very curious state of affairs was mentioned by M. Gardner with a http://www.cut-the-knot.org/blue/Abacus.shtml

var MyPageLoc = document.location; var MyPageTitle = document.title; G o o g ... e Web CTK Sites for teachers Sites for parents Awards Interactive Activities ... Sites for parents Abacus in Various Number Systems Abacus abacus to the Phoenician abak (sand). American Heritage Dictionary points to the Greek word abax , which might have originated from Hebrew avak (dust). There is little doubt that Ancients used a flat surface with sand strewn evenly over it as a disposable tool for writing and counting. It's said that the great Archimedes was slain by a Roman soldier while concentrating on figures drawn in sand. Later day abaci had grooves for small pebbles and later yet wires or rods on which counters could freely move back and forth. Each wire corresponded to a digit in a positional number system , commonly in base 10. A very curious state of affairs was mentioned by M. Gardner with a reference to K.Menninger. For more than 15 centuries the Greek and Romans and then Europeans in the Middle Ages and early Renaissance calculated on devices with authentic place-value system in which zero was represented by an empty line, wire or groove. Yet the written notations did not have a symbol for zero until it was borrowed by Arabs from Hindus and eventually introduced into Europe in 1202 by Leonardo Fibonacci of Piza in his Liber Abaci The Book of Abacus ). According to D. Knuth, counting with abaci was so convenient and easy that, at the time when only few knew how to write, it might have seemed preposterous to scribble some symbols on expensive papyrus when an excellent calculating device was readily available.

12. Number Systems Placevalue and the decimal system. Our decimal or base ten number system is a place-value system. This means that the place or location where you put a http://www.dotlessbraille.org/numbersystems.htm

Introduction to the Binary and Other Number Systems Note to persons reading this in Braille. This section contains some mathematical notation which may not display correctly when transcribed to Braille 2. We would appreciate feedback on any problems. Place-value and the decimal system. Our decimal or base ten number system is a place-value system. This means that the place or location where you put a numeral determines its corresponding numerical value. (This is analogous to braille codes in that the place you put a cell sometimes determines its meaning.) A two in the one's place means two times one or two. A two in the one-thousand's place means two times one thousand or two thousand. Figure 1 shows the place values for the first six whole number places in the decimal system. Whole number places: Place values: 100000 10000 1000 100 10 1 Fig. 1. Place values (in decimal) for the decimal number system. The place-value of the place immediately to the left of the "decimal" point is one in all place-value number systems. (The point itself should have different names in different number systems but this distinction isn't usually made.)

13. Binary Number System Since there is a correspondence between the logic levels used by the computer and the two digits used in the binary numbering system, it should come as no http://www.danbbs.dk/~erikoest/binary.htm

My Home Page has moved to... / Min Hjemmeside er flyttet til... http://www.erikoest.dk Please amend your bookmarks accordingly. / Please wait a moment and the browser will automatically redirect to your requested page... / http://www.erikoest.dk/binary.htm Bottom of This Page Binary Number System The Binary Number Base Systems Most modern computer systems (including the IBM PC) operate using binary logic. The computer represents values using two voltage levels (usually 0V for logic and either +3.3 V or +5V for logic 1). With two levels we can represent exactly two different values. These could be any two different values, but by convention we use the values zero and one. These two values, coincidentally, correspond to the two digits used by the binary number system. Since there is a correspondence between the logic levels used by the computer and the two digits used in the binary numbering system, it should come as no surprise that computers employ the binary system. The binary number system works like the decimal number system except the Binary Number System: uses base 2 includes only the digits and 1 (any other digit would make the number an invalid binary number) The weighted values for each position is determined as follows: In the United States among other countries, every three decimal digits is separated with a comma to make larger numbers easier to read. For example, 123,456,789 is much easier to read and comprehend than 123456789. We will adopt a similar convention for binary numbers. To make binary numbers more readable, we will add a space every four digits starting from the least significant digit on the left of the decimal point. For example, the binary value 1010111110110010 will be written 1010 1111 1011 0010.

14. ::The Nashville Number System In the late 50 s, Neil Matthews devised a musical number system for the Jordanaires to use in the studio. Charlie McCoy and fellow studio musicians began http://www.nashvillenumbersystem.com/

The Nashville Number System (7th Edition) comes with a copy of Chas Williams' latest cd, "String of Pearls". BUY IT NOW! THE NASHVILLE NUMBER SYSTEM In the late 50's, Neil Matthews devised a musical number system for the Jordanaires to use in the studio. Charlie McCoy and fellow studio musicians began adapting Matthews' number system into chord charts. The Nashville Number System has evolved into a complete method of writing chord charts and melodies-combining Nashville shorthand with formal notation standards. The Nashville Number System is 130 pages with a step by step method of how to write a Nashville number chart for any song. Included with each NNS book in Edition 7 is the cd, "String Of Pearls" . This is a 10 song cd of instrumentals, including, Amazing Grace. I walk you through the details of each song and explain the Number System tools used to write the charts. Now, while listening to the cd, you can see and hear how Nashville number charts work. 7th EDTION NOW AVAILABLE AT A GREAT PRICE! The 7th Edition of the "Nashville Number System" by Chas Williams is now available! More great charts, an Interactive CD, updated content!

15. Ancient Number Systems Project To begin with students had to research into the number systems of the ancient Egyptians Egyptians 2, Babylonians Babylonians 2, Greeks, Romans, Romans 2, http://www.internet-at-work.com/hos_mcgrane/ancient_numbers/maths_menu.html

[Grade 5 Projects] [Ancient History Projects] This project was a joint social studies and maths activity. To begin with students had to research into the number systems of the ancient Egyptians Egyptians 2 Babylonians Babylonians 2 ... Arabs , and Hindus . There is also an article History of Numbers from The Encyclopedia Britannica This research was done during the library periods, and students continued to work on the project during their maths lessons where they were able to access the Internet from the classroom computer. Students had to explain how the systems are similar and how they differ. As well as the compulsory number systems, some students chose to research origins of their own number systems and many of them also chose to look at the Mayan system , as the Maya is a topic we study during social studies later in the year. Following on from this, students had to create their own number systems, showing symbols up to 1.000,000 and explaining the advantages and disadvantages of their systems. Here is a selection of the students' projects which they have recently completed. Click on the name of the students to visit their pages or follow the arrow for a "guided tour" of our projects. Pages created: Wednesday, 19-November-97 11:35:12 EST

16. Online CS Modules: Number Systems The following lessons introduce the topic of number systems with a focus on binary numbers and binary arithmetic. Each lesson includes a set of review http://courses.cs.vt.edu/csonline/NumberSystems/Lessons/index.html

17. Phi Number System -- From Wolfram MathWorld Bergman, G. A number system with an Irrational Base. Math. Mag. 31, 98110, 1957. Rousseau, C. The Phi number system Revisited. Math. Mag. http://mathworld.wolfram.com/PhiNumberSystem.html

Search Site Algebra Applied Mathematics Calculus and Analysis ... Levasseur Phi Number System For every positive integer , there is a unique finite sequence of distinct nonconsecutive (not necessarily positive) integers such that where is the golden ratio For example, for the first few positive integers, (Sloane's The numbers of terms needed to represent for , 2, ... are given by 1, 2, 2, 3, 3, 3, 2, 3, 4, 4, 5, 4, ... (Sloane's ), which are also the numbers of 1s in the base- representation of The following tables summarizes the values of that require exactly powers of in their representations. Sloane numbers requiring exactly powers SEE ALSO: Base Golden Ratio [Pages Linking Here] REFERENCES: Bergman, G. "A Number System with an Irrational Base." Math. Mag. Knott, R. "Using Powers of Phi to represent Integers (Base Phi)." http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/phigits.html Knuth, D. The Art of Computer Programming, Vol. 1: Fundamental Algorithms, 3rd ed. Reading, MA: Addison-Wesley, 1997. Levasseur, K. "The Phi Number System."

18. Egypt: The Ancient Egyptian Number System (Math), A Feature Tour Egypt Story Egypt The Ancient Egyptian number system (Math), A Feature Tour Egypt Story. http://www.touregypt.net/featurestories/numbers.htm

Egypt Home Ancient Egypt Shop Request Tour ... Message The Ancient Egyptian Number System By Caroline Seawright In ancient Egypt mathematics was used for measuring time, straight lines, the level of the Nile floodings, calculating areas of land, counting money, working out taxes and cooking. Maths was even used in mythology - the Egyptians figured out the numbers of days in the year with their calendar . They were one of the ancient peoples who got it closest to the 'true year', though their mathematical skills. Maths was also used with fantastic results for building tombs, pyramids and other architectural marvels. A part of the largest surviving mathematical scroll, the Rhind Papyrus (written in hieratic script), asks questions about the geometry of triangles. It is, in essence, a mathematical text book. The surviving parts of the papyrus show how the Egyptian engineers calculated the proportions of pyramids as well as other structures. Originally, this papyrus was five meters long and thirty three centimeters high. It is again to the Nile Valley that we must look for evidence of the early influence on Greek mathematics. With respect to geometry, the commentators are unanimous: the mathematician-priests of the Nile Valley knew no peer. The geometry of Pythagoras, Eudoxus, Plato, and Euclid was learned in Nile Valley temples. Four mathematical papyri still survive, most importantly the Rhind mathematical papyrus dating to 1832 B.C. Not only do these papyri show that the priests had mastered all the processes of arithmetic, including a theory of number, but had developed formulas enabling them to find solutions of problems with one and two unknowns, along with "think of a number problems." With all of this plus the arithmetic and geometric progressions they discovered, it is evident that by 1832 B.C., algebra was in place in the Nile Valley.

19. Frank's Electron Tube Pages - Tube Number Systems Final number distinguishes between different valves in the same class. MAZDA NUMBERING SYSTEM Power rectifier valves http://www.tubedata.org/tubnum.html

Frank's Electron tube Pages Tube Number Systems European system after 1934 Philips system before 1934 Mazda numbering system Russian numbering system ... Brimar type designation code European system after 1934 (pro-electron) 1st letter heater indication tubes without filament A 4 V AC parallel connection B 180 mA DC C 200 mA AC/DC series or parallel connection D <= 1.4 V DC dry-battery, parallel connection E 6.3 V AC or carbattery, parallel connection F 13 V carbattery G 5V AC parallel connection H early: 4V DC battery. later: 150mA AC/DC series connection I 20V AC/DC parallel connection K 2 V battery O 150 mA AC/DC series connection P 300 mA AC/DC series connection U 100 mA AC/DC series connection V 50mA AC/DC series connection X 600 mA AC/DC series connection Y 450 mA AC/DC series connection 2nd+next letters tube systems A single detection diode B double detection diode C small-signal triode D power triode E small-signal tetrode (or 2nd emmission tube EE1) F small-signal pentode H hexode or heptode K octode L power pentode or power tetrode M indicator tube N thyratron Q enneode W single gasfilled rectifier diode

20. Maya Mathematics Because the base of the number system was 20, larger numbers were written down in powers of 20. We do that in our decimal system too for example 32 is http://www.michielb.nl/maya/math.html

michielb.nl projects maya astronomy / geographical orientation Maya Mathematics Instead of ten digits like we have today, the Maya used a base number of 20. (Base 20 is vigesimal.) They also used a system of bar and dot as "shorthand" for counting. A dot stood for one and a bar stood for five. In the following table, you can see how this works. Because the base of the number system was 20, larger numbers were written down in powers of 20. We do that in our decimal system too: for example 32 is 3*10+2. In the Maya system, this would be 1*20+12, because they used 20 as base. Numbers were written from bottom to top. Below you can see how the number 32 was written: 20's 1's It was very easy to add and subtract using this number system, but they did not use fractions. Here's an example of a simple addition: 8000's 400's 20's 1's As you can see, adding is just a matter of adding up dots and bars! Maya merchants often used cocoa beans, which they layed out on the ground, to do these calculations. If you have a Java-enabled browser, you will see an interactive number converter below. Fill in the a number in the top field, and press return to find its Maya equivalent.. Press +1 and -1 to change the number by one.

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