Essay about Number System in Mathematics

2773 Words Apr 21st, 2011 12 Pages
Introduction I. Number Systems in Mathematics:
A Number system (or system of numeration) is a writing system for expressing numbers, that is a mathematical notation for representing number of a given set, using graphemes or symbols in a consistent manner. It can be seen as the context that allows the symbols "11" to be interpreted as the binary symbol for three, the decimal symbol for eleven, or a symbol for other numbers in different bases.
Ideally, a number system will: * Represent a useful set of numbers (e.g. all integers, or rational 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,
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The word “decimal” describes a system that has ten possible digits. These are the digits 0 through 9. Every number expressed in the decimal system is a combination of these ten digits. You use the decimal system every day, it comes naturally, we all have 10 fingers and 10 toes (unless your family tree doesn’t fork, but let’s not go there), and some of us use those 10 fingers and toes extensively to help with every day addition and subtraction.
The binary system works essentially the same way, with the only difference that it only has two digits. These are visually expressed by the digits 0 and 1. Every number expressed in the binary system is a combination of these two digits. b. History
The Indian scholar Pingala (circa 5th–2nd centuries BC) developed mathematical concepts for describing prosody, and in so doing presented the first known description of a binary numeral system. He used binary numbers in the form of short and long syllables (the latter equal in length to two short syllables), making it similar to Morse code. In the 11th century, scholar and philosopher Shao Yong developed a method for arranging the hexagrams which corresponds to the sequence 0 to 63, as represented in binary, with yin as 0, yang as 1 and the least significant bit on top.
Similar sets of binary combinations have also been used in traditional African divination systems such as Ifá as well as in

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