Unformatted text preview: ion or extended precision signi cands is not so straightforward, however, since dropping bits may, as in addition, lead to incorrectly
rounded results. The actual multiplication and division implementation may
or may not use the standard \long multiplication" and \long division" algorithms which we learned in school. One alternative for division will be
mentioned in a later section. Multiplication and division are much more
complicated operations than addition and subtraction, and consequently they
may require more execution time on the computer this is the case for PC's.
However, this is not necessarily true on faster supercomputers since it is possible, by using enough space on the chip, to design the microcode for the
instructions so that they are all equally fast.
Exercise 16 Assume that x and y are normalized numbers, i.e. 1 m < 2,
1 p < 2. How many bits may it be necessary to shift the signi cand product
m p left or right to normalize the result? 4 Exceptional Situations
One of the most di cult things about programming is the need to anticipate
exceptional situations. In as much as it...
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 Spring '09
 LIE
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