Unformatted text preview: 0) 2;123 =
(0:11001100 : : :)2 2;126 is stored as
0 00000000 11001100110011001100110
while (1=10) 2;133 = (0:11001100 : : :)2 2;136 is stored as
0 00000000 00000000001100110011001 :
Exercise 4 Determine the IEEE single precision oating point representation of the following numbers: 2, 1000, 23/4, (23=4) 2100, (23=4) 2;100,
(23=4) 2;135, 1=5, 1024=5, (1=10) 2;140.
Exercise 5 Write down an algorithm that tests whether a oating point number x is less than, equal to or greater than another oating point number y , by simply comparing their oating point representations bitwise from
left to right, stopping as soon as the rst di ering bit is encountered. The
fact that this can be done easily is the main motivation for biased exponent
notation.
Exercise 6 Suppose x and y are single precision oating point numbers. Is
it true 4 that round(x ; y ) = 0 only when x = y ? Illustrate your answer with some examples. Do you get the same answer if subnormal numbers are not
allowed, i.e. subnormal results are rounded to zero? Again, illu...
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 Spring '09
 LIE
 oating point

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