FloatingPointRepresentation

142 which is closer to than the truncated result 3141

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Unformatted text preview: .142, which is closer to than the truncated result 3.141. Exercise 9 What is the rounded value of 1=10 for each of the four rounding modes? Give the answer in terms of the binary representation of the number, not the decimal equivalent. The (absolute value of the) di erence between round(x) and x is called the absolute rounding error associated with x, and its value depends on the rounding mode in e ect. In toy precision, when round down or round towards zero is in e ect, the absolute rounding error for x = 1:7 is 0:2 (since round(x) = 1:5), but if round up or round to nearest is in e ect, the absolute 13 rounding error for x = 1:7 is 0:05 (since round(x) = 1:75). For all rounding modes, it is clear that the absolute rounding error associated with x is less than the gap between x; and x+ , while in the case of round to nearest, the absolute rounding error can be no more than half the gap between x; and x+ . Now let x be a normalized IEEE single precision number, and suppose that x > 0, so that x = (b0:b1b2 : : :b23b24b25 : : :)2 2E with b0 = 1...
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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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