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and double precision representations of are would require writing out the
binary representations and converting these to decimal.
Exercise 7 What is the gap between 2 and the rst IEEE single precision number larger than 2? What is the gap between 1024 and the rst IEEE
single precision number larger than 1024? What is the gap between 2 and the
rst IEEE double precision number larger than 2? x = m 2E be a normalized single precision number, with
1 m < 2. Show that the gap between x and the next largest single precision Exercise 8 Let number is 2E :
(It may be helpful to recall the discussion following Figure 1.) 3 Rounding and Correctly Rounded Arithmetic
We use the terminology \ oating point numbers" to mean all acceptable numbers in a given IEEE oating point arithmetic format. This set consists of
0, subnormal and normalized numbers, and 1, but not NaN values, and
11 is a nite subset of the reals. We have seen that most real numbers, such as
1=10 and , cannot be represented exactly as oating point numbers. For
ease of expression...
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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.
 Spring '09
 LIE

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