FloatingPointRepresentation

1 2 2e 2e 1 2 x is subnormal ie e 126 and b0

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Unformatted text preview: E 2E =1: 2 x is subnormal, i.e. E = ;126 and b0 = 0? Now another way to write the de nition of is round(x) = x(1 + ) so we have the following result: the rounded value of a normalized number x is, when not exactly equal to x, equal to x(1 + ), where, regardless of the rounding mode, j j< : Here, as before, is the machine precision. In the case of round to nearest, we have 1 jj 2: This result is very important, because it shows that, no matter how x is displayed, for example either in binary format or in a converted decimal format, you can think of the value shown as not exact, but as exact within a factor of 1 + . Using Table 3 we see, for example, that IEEE single precision numbers are good to a factor of about 1 + 10;7, which means that they have about 7 accurate decimal digits. Numbers are normally input to the computer using some kind of highlevel programming language, to be processed by a compiler or an interpreter. There are two di erent ways that a number such as 1=10 might be input. One way wo...
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