Dale - Computer Science Illuminated 84

Dale - Computer Science Illuminated 84 - 3.2 Representing...

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Sign-magnitude repre- sentation Number representation in which the sign represents the ordering of the number (negative and positive) and the value represents the magnitude 3.2 Representing Numeric Data 57 In general, n bits can represent 2 n things because there are 2 n combina- tions of 0 and 1 that can be made from n bits. Note that every time we increase the number of available bits by 1, we double the number of things we can represent. Let’s turn the question around. How many bits do you need to repre- sent, say, 25 unique things? Well, four bits wouldn’t be enough because four bits can represent only 16 things. We would have to use at least five bits, which would allow us to represent 32 things. Since we only need to represent 25 things, some of the bit combinations would not have a valid interpretation. Keep in mind that even though we may technically need only a certain minimum number of bits to represent a set of items, we may allocate more than that for the storage of that data. There is a minimum number of bits
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