Base Number Systems 

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The number system is the way we conceptualise the whole way we number things. For example, our general number system is of base 10. We count to 10 and then repeat the next ten and so on. It is a kind of a framework in which a set of numbers are expressed in a consistent way which also shows the structure of the system and of the numbers themselves. For example, if you write 11, that would not be sufficient for you to know what actuall number that represents: it can be three in the the binary system, or eleven in decimal system or four in ternary (base 3). Arabic numerals have a positional base 10 number system (this is the one we generally use). Babylonian numerals have a positional base 60 number system (this is the system comparable to our measurement of time). The binary numeral system has two numeric values and uses only two symbols, 1 and 0. It is also a positional notation and because it can be easily translated to the way electronic systems work (on and off) it has been widely applied to computing.
The first known description of a binary system comes from an Indian mathematician Pingala, from a period between 5th and 2nd century BC. The English scientist Francis Bacon (15611626) wrote about it in his essay on encryption and then Leibniz explained it more fully in his work Explication de l'Arithmétique Binaire in 1705. page from Leibniz' famous book in which he for the first time explained how binary system works There he explained the ideas about the system  how to write the numbers and how to compute using all operations that you would normally use in other systems. Although we mainly use decimal number system (with a base 10), we also make great use of the binary system through its application in computing. But how does it work? Well binary system has only two digits to represent all values: 0 and 1. (In computing this is used in such a way that 1 is produced when there is an electrical impulse and 0 when there isn't.) Binary number system really made it big through the work of a British mathematician, George Boole. Boole published a paper in 1854 in which he used only two values  true and false, and constructed a whole system of algebra and logic which are now known as Boolean algebra and Boolean logic.
Decimal The decimal system has a longer and richer history all round. It was known and possibly used as far back as 3500BC Iran. In 2600BC the Indian Valley Civilisation used it in the way of decimal fractions in their weight system. Chinese authors showed that they knew about it, and the Arabic mathematicans both used and wrote about it.

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