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For ease of expression we will say a general real

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Unformatted text preview: we will say a general real number is \normalized" if its modulus lies between the smallest and largest positive normalized oating point numbers, with a corresponding use of the word \subnormal". In both cases the representations we give for these numbers will parallel the oating point number representations in that b0 = 1 for normalized numbers, and b0 = 0 with E = ;126 for subnormal numbers. For any number x which is not a oating point number, there are two obvious choices for the oating point approximation to x: the closest oating point number less than x, and the closest oating point number greater than x. Let us denote these x; and x+ respectively. For example, consider the toy oating point number system illustrated in Figures 1 and 2. If x = 1:7, for example, then we have x; = 1:5 and x+ = 1:75, as shown in Figure 3. : : :: : : 0 1 x2 3 Figure 3: Rounding in the Toy System Now let us assume that the oating point system we are using is IEEE single precision. Then if our genera...
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