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Вы можете ознакомиться и скачать презентацию на тему Numeral system. Доклад-сообщение содержит 9 слайдов. Презентации для любого класса можно скачать бесплатно. Если материал и наш сайт презентаций Mypresentation Вам понравились – поделитесь им с друзьями с помощью социальных кнопок и добавьте в закладки в своем браузере.

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Numeral systems. Transfer numeral from one numeral system to another. Arithmetic in the numeral systems.

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Numeral system Numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner

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The number the numeral represents is called its value. The number the numeral represents is called its value. Ideally, a numeral 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

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Main numeral systems The most commonly used system of numerals is the Hindu–Arabic numeral system. Two Indian mathematicians are credited with developing it. Aryabhata of Kusumapura developed the place-value notation in the 5th century and a century later Brahmagupta introduced the symbol for zero.

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Decimal Numbers Decimal numbers (base 10) Represented using 10 numerals: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Each position represents a power of 10: 401= 4*102+ 0*101 + 1*100 = 400+ 1 130= 1*102 + 3*101+0*100 = 100 + 30 9786= 9*103 + 7*102 + 8*101 + 6*100= = 9*1000 +7*100 + 8*10 + 6*1

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Binary Numeral System Binary numbers are represented by sequence of bits (smallest unit of information – 0 or 1) Bits are easy to represent in electronics 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 0

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Binary Numbers Binary numbers (base 2) Represented by 2numerals: 0and 1 Each position represents a power of 2: 101b= 1*22 + 0*21 + 1*20 = 100b + 1b = 4+1= 5 110b = 1*22 + 1*21 + 0*20 = 100b + 10b = 4+2=6 110101b= 1*25 + 1*24 + 0*23 + 1*22 + 0*21+ 1*20= = 32 + 16 + 4 + 1= = 53

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How ComputersRepresent Text Data? A text encoding is a system that uses binary numbers (1and 0) torepresent characters Letters, numerals, etc. In the ASCII encoding each character consists of 8 bits (one byte) of data ASCII is used in nearly all personal computers In the Unicode(UTF-16) encoding each character consists of 16 bits (two bytes) Can represent many alphabets