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1 3 Computing System Fundamentals 3.5 Data Representation

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3.5.2 Number Systems

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3 Commonly used systems Decimal: base 10 Binary: base 2 Hexadecimal: base 16 Octal: base 8

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4 Hexadecimal In hex, we must invent some more digits to count above ten. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, then A (ten), B (eleven), C (twelve), D (thirteen), E (fourteen), F (fifteen) Only then do we start a new (sixteens) column: 10 (sixteen), 11 (seventeen)...

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5 Hexadecimal So = (1 sixteen and 9 ones), 1A 16 = 26 10, 1B 16 = 27 10, etc. As with all other systems, the LSD changes fastest. 1F 16 = 31 10, = The maximum 2 digit hex number is FF 16 =

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6 Hexadecimal Beyond FF 16 ( ), we need a 256s column ( = 16 2 ) So, FF 16 = , = , =

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7 Why hexadecimal? Computers cannot work in decimal. Humans find binary hard (long to write and difficult to remember and convert). Sixteen is two to the power of four. So to convert binary to hex is simple...

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8 Why hexadecimal? Take a long binary number, e.g Split it into groups of four: And convert each group to hex: 972DD9 So one hex digit represents half a byte (hex digits often occur in pairs to represent a whole byte).

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9 You already know hex Hex colour codes in HTML e.g. #FF0088 is full red ( ), no green and half blue ( ) IP addresses e.g is FF.FF.FF.00 in hex WiFi security keys e.g. 33E5A10DB96EF130.

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