324_Book

# Thus the rst blocks in the array would map to set 0

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Unformatted text preview: s to represent a number as a fraction of the form ¾Ü . We can write this in binary using the binary representation of Ü, with the binary point inserted 698 positions from the right. As an example, for positions from the right to get ½ ¼½½½¾ . Problem 2.24 Solution: [Pg. 68] APPENDIX B. SOLUTIONS TO PRACTICE PROBLEMS ¾¿ ½ , we have ¾¿½ ¼ ½¼½½½¾ . We then put the binary point 4 In most cases, the limited precision of ﬂoating-point numbers is not a major problem, because the relative error of the computation is still fairly low. In this example, however, the system was sensitive to the absolute error. A. We can see that Ü ¼ ½ has binary representation: ¼ ¼¼¼¼¼¼¼¼¼¼¼¼¼¼¼¼¼¼¼¼¼¼¼½½¼¼ ½½¼¼ ¡¡¡ ¾ ¾ Comparing this to the binary representation of around ¢ ½¼ . B. C. ½ ½¼ , we can see that it is simply ¾¼ ¢ ½ ½¼ , which is ¼¿ ¿ ¢ ¢ ½¼ ¢ ½¼¼ ¢¢¢ ¼ ¼ ½¼ ¼¿ ¿ . ¾¼¼¼ . Problem 2.25 Solution: [Pg. 73] Working through ﬂoating p...
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