Floating Point Lab

# Floating Point Lab - of 16 values on the left corresponds...

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Floating Point Denormalized Numbers J. Stanley Warford Computer Science Department Pepperdine University Malibu, CA 90263 The following figure is a scale drawing of the ﬂoating point values for normalized num- bers (top) and denormalized numbers (bottom). The representation is identical to that of the IEEE 754 ﬂoating point standard except that the exponent field is three bits and the sig- nificand field is four bits, which corresponds to the example in Figure 3.32 of Computer Systems , fourth edition. For both number lines, the leftmost value is + 0 . 0 and the rightmost value is + 1 . 0 . The figure shows three complete sequences of values for exponent fields of 000, 001, and 010 (excess 3), which represent - 3 , - 2 , and - 1 (dec) respectively. For normalized numbers in general, the gap between successive values doubles with each unit increase of the exponent. For example, in the number line on the top the group
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Unformatted text preview: of 16 values on the left corresponds to numbers written in binary scienti±c notation with a multiplier of 2-3 . The next group of 16 numbers to the right are spaced twice as far apart and corresponds to numbers written in binary scienti±c notation with a multiplier of 2-2 . Without denormalization, the gap between + . and the smallest positive value is ex-cessive compared to the gaps in the smallest sequence. Denormalization makes the gap between successive values for the ±rst sequence equal to the gap between successive val-ues for the second sequence. It spreads these values out evenly as they approach + . from the right. On the left half of the number line, not shown in the ±gure, the largest negative values are spread out evenly as they approach-. from the left. . . . . . . 1...
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