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Unformatted text preview: ains one of these is indistinguishable from one that contains another of a different type. The difference is not in the way the information is stored but in the way it is used. A computer data type can therefore be characterized by: the number of bits it requires; the ordering of those bits; the uses to which the group of bits is put. Some data types, such as addresses and instructions, exist principally to serve the purposes of the computer, whereas others exist to represent information in a way that is accessible to human users. The most basic of the latter category, in the context of computation, is the number. Numbers What started as a simple concept, presumably as a means of checking that no sheep had been stolen overnight, has evolved over the ages into a very complex mechanism capable of computing the behaviour of transistors a thousandth of a millimetre wide switching a hundred million times a second. Here is a number written by a human: MCMXCV Roman numerals Decimal numbers The interpretation of this Roman numeral is complex; the value of a symbol depends on the symbol and its positional relationship to its neighbours. This way of writing a number has largely (but not entirely; see the page numbers in the front matter of this book) been replaced by the decimal scheme where the same number appears as: 1995 Here we understand that the righthand digit represents the number of units, the digit to its left the number of tens, then hundreds, thousands, and so on. Each time we move left one place the value of the digit is increased by a factor of 10. 154 Architectural Support for HighLevel Languages Binary coded decimal To represent such a number as a group of Boolean variables, the simplest thing appears to be to find a representation for each digit and then use four of these to represent the whole number. We need four Boolean variables to be able to represent each digit from 0 to 9 differently, so the first form of this number that could easily be handled by logic gates...
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 Spring '09
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