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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,*…show more content…*

In 1605 Francis Bacon discussed a system whereby letters of the alphabet could be reduced to sequences of binary digits, which could then be encoded as scarcely visible variations in the font in any random text. The modern binary number system was studied by Gottfried Leibniz in 1679. See his article:Explication de l'Arithmétique Binaire (1703). Leibniz's system uses 0 and 1, like the modern binary numeral system. In 1854, British mathematician George Boole published a landmark paper detailing an algebraic system of logic that would become known as Boolean algebra. In 1937, Claude Shannon produced his master's thesis at MIT that implemented Boolean algebra and binary arithmetic using electronic relays and switches for the first time in history In November 1937, George Stibitz, then working at Bell Labs, completed a relay-based computer he dubbed the "Model K" (for "Kitchen", where he had assembled it), which calculated using binary addition. c. Advantage 1) The advantage of using binary system is that the system counts by 2 digits only i.e. ‘0’ & ‘1’. Binary allows digital systems to operate. In a digital system a data line is either ‘ON’ or ‘OFF’ and the system counts ‘0’ as ‘OFF’ and ‘1’ as ‘ON’. 2) As it is not used in every counting so it was formerly used for transmitting codes during the war time. However now a days it is not used for this purpose. II. Decimal a. What is the decimal Number system? The decimal number

In 1605 Francis Bacon discussed a system whereby letters of the alphabet could be reduced to sequences of binary digits, which could then be encoded as scarcely visible variations in the font in any random text. The modern binary number system was studied by Gottfried Leibniz in 1679. See his article:Explication de l'Arithmétique Binaire (1703). Leibniz's system uses 0 and 1, like the modern binary numeral system. In 1854, British mathematician George Boole published a landmark paper detailing an algebraic system of logic that would become known as Boolean algebra. In 1937, Claude Shannon produced his master's thesis at MIT that implemented Boolean algebra and binary arithmetic using electronic relays and switches for the first time in history In November 1937, George Stibitz, then working at Bell Labs, completed a relay-based computer he dubbed the "Model K" (for "Kitchen", where he had assembled it), which calculated using binary addition. c. Advantage 1) The advantage of using binary system is that the system counts by 2 digits only i.e. ‘0’ & ‘1’. Binary allows digital systems to operate. In a digital system a data line is either ‘ON’ or ‘OFF’ and the system counts ‘0’ as ‘OFF’ and ‘1’ as ‘ON’. 2) As it is not used in every counting so it was formerly used for transmitting codes during the war time. However now a days it is not used for this purpose. II. Decimal a. What is the decimal Number system? The decimal number

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