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8.28 Binary & Representation Of Numbers

Analogordigital numberrepresentations

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Unformatted text preview: ent things. different '''The question is,' said Humpty 'The Dumpty, 'which is to be master - that's all.' master Analog or Digital? Analog or Digital? Number Representations Number Representations 1/2 + 1/6 + 1/9 5137 01100010100 0 Analog Digital are analogous not necessarily analogous can be continuous discrete symbols precision a problem add extra digits errors hard to detect errors easier to detect requires little decoding requires some decoding Why Binary? Why Binary? Because 2 is special! It’s the smallest number that’s not 1. So simple a computer could do it! Why Binary? Why Binary? So simple a computer could do it! Bits, Bytes, Words Bits, Bytes, Words Bit = 0 or 1. One character of information Byte = 8 bits. Example: 01101101 Word = some number of bytes, depending on computer. Typical = 4 bytes = 32 bits “A 32­bit machine” Word size limits what can be represented easily (more on this later) 1 100 10 1000 Decimal Numbers…. 5137 Binary Numbers…. 02 1 4 37 9 58 6 decimal digits 0 1 b its binary digits bits 16 8 4 (2^1) (2^0) 1 1 1 1 0 2 1 16 + 4 + 2 + 1 = 23 16 8 4 2 1 01110 8 + 4 + 2 = 14 16 8 4 2 1 11101 16 + 8 + 4 + 1 = 29 16 8 4...
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