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Transcript of Number systems
Brief history of number
Brief definition of numbers
The History Of Number System
The Ancient Babylonians
Aztecs, Eskimos, And Indian Merchants.
The Ancient Egyptians
Number System according to different civilizations
A number system defines a set of values used to represent a quantity. We talk about the number of people attending school, number of modules taken per student etc.
Quantifying items and values in relation to each other is helpful for us to make sense of our environment.
The study of numbers is not only related to computers. We apply numbers everyday, and knowing how numbers work, will give us an insight of how computers manipulate and store numbers.
A number is a mathematical object used in counting and measuring. It is used in counting and measuring. Numerals are often used for labels, for ordering serial numbers, and for codes like ISBNs. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers.
The number system with which we are most familiar is the decimal (base-10) system , but over time our ancestor have experimented with a wide range of alternatives, including duo-decimal (base-12), vigesimal (base-20), and sexagesimal (base-60)…
The Ancient Egyptians experimented with duo-decimal (base-12) system in which they counted finger-joints instead of finger . Each of our finger has three joints. In addition to their base-twelve system, the Egyptians also experimented with a sort –of-base-ten system. In this system , the number 1 through 9 were drawn using the appropriate number of vertical lines.
Babylonians, were famous for their astrological observations and calculations, and used a sexagesimal (base-60) numbering system. In addition to using base sixty, the babylonians also made use of six and ten as sub-bases. The babylonians sexagesimal system which first appeared around 1900 to 1800 BC, is also credited with being the first known place-value of a particular digit depends on both the digit itself and its position within the number . This as an extremely important development, because – prior to place-value system – people were obliged to use different symbol to represent different power of a base.
Other cultures such as the Aztecs, developed vigesimal (base-20) systems because they counted using both finger and toes. The Ainu of Japan and the Eskimos of Greenland are two of the peoples who make use of vigesimal systems of present day . Another system that is relatively easy to understand is quinary (base-5), which uses five digit : 0, 1, 2, 3, and 4. The system is particularly interesting , in that a quinary finger-counting scheme is still in use today by Indian merchant near Bombay . This allow them to perform calculations on one hand while serving their customers with the other
The Decimal Number System
The number system we use on day-to-day basis in the decimal system , which is based on ten digits: zero through nine. As the decimal system is based on ten digits, it is said to be base -10 or radix-10. Outside of specialized requirement such as computing , base-10 numbering system have been adopted almost universally. The decimal system with which we are fated is a place-value system, which means that the value of a particular digit depends both on the itself and on its position within the number.
Brief definition of numbers
History of number systems
Number system according to different civilizations
Types of numbers
Mayan number system
This system is unique to our current decimal system, as our current decimal system uses base -10 whereas, the Mayan Number System uses base- 20.
The Mayan system used a combination of two symbols. A dot (.) was used to represent the units and a dash (-) was used to represent five. The Mayan's wrote their numbers vertically as opposed to horizontally with the lowest denomination on the bottom.
Binary number system
The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2. Owing to its straight forward implementation in digital electronic circuitry using logic gates, the binary system is used internally by all modern computers. Counting in binary is similar to counting in any other number system. Beginning with a single digit, counting proceeds through each symbol, in increasing order. Decimal counting uses the symbols 0 through 9, while binary only uses the symbols 0 and 1.
Types of numbers
Real (rational and irrational)
Why do we need numbers?
Time and Date
Time and date uses multiple bases to express time and date in relation to the amount of time it takes the earth to revolve around the sun, and also with respect to the time it takes for the earth to make a complete revolution on its own rotation (around its axis).
Notice that for measuring a year in terms of seconds we have a 365:24:60:60 representation: a mixture of different basis that are optimized for a specific purpose of relating time and date to the revolutions of our earth and around our sun.
If we used base 10, then we would probably get some weird number and it wouldn't make as much sense as our current format.
If you ever do a computer degree (Computer Science, Computer Engineering, Electrical Engineering etc), you'll end up learning about logical gates. You'll also learn that using these gates you can do everything from arithmetic computations to logical computations and so on. The atomic version of information is the bit, and based on this we use any kind of analysis in the context of computer science and engineering to refer to bits or collections of bits.
Octal and hexadecimal representations just make it easier to deal with collections of bits. Instead of reading a sequence of 32 1's and 0's, it's a lot easier to read 8 hexadecimal digits.
These are just two examples, and I'm sure that there are more out there.
Tobias Dantzig, Number, the language of science; a critical survey written for the cultured non-mathematician, New York, The Macmillan company, 1930.
Erich Friedman, What's special about this number?
Steven Galovich, Introduction to Mathematical Structures, Harcourt Brace Javanovich, 23 January 1989, ISBN 0-15-543468-3
Paul Halmos, Naive Set Theory, Springer, 1974, ISBN 0-387-90092-6.
Morris Kline, Mathematical Thought from Ancient to Modern Times, Oxford University Press, 1972.
Alfred North Whitehead and Bertrand Russell, Principia Mathematica to *56, Cambridge University Press, 1910.
George I. Sanchez, Arithmetic in Maya,Austin-Texas, 1961.