FloatingPointRepresentation

In this example using any of round towards zero round

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Unformatted text preview: g any of round towards zero, round to nearest, or round down as the rounding mode, the correctly rounded result is 215. If round up is used, the correctly rounded result is (1:00000000000000000000001)2 215. Exercise 14 In IEEE single precision, using round to nearest, what are the correctly rounded values for: 64 + 220, 64 + 2;20, 32 + 2;20, 16 + 2;20 , 8 + 2;20. Give the binary representations, not the decimal equivalent. What are the results if the rounding mode is changed to round up? 18 Exercise 15 Recalling how many decimal digits correspond to the 23 bit fraction in an IEEE single precision number, which of the following numbers do you think round exactly to the number 1, using round to nearest: 1+10;5, 1 + 10;10, 1 + 10;15? Although the operations of addition and subtraction are conceptually much simpler than multiplication and division and are much easier to carry out by hand, the implementation of correctly rounded oating point addition and subtraction is not trivial, even for the case when the result is a oating point number and therefore does not require rounding. For example, consider co...
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This note was uploaded on 02/12/2014 for the course MATH 4800 taught by Professor Lie during the Spring '09 term at Rensselaer Polytechnic Institute.

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