Assignment #2: Number Representation, Loss of Significance and Range Reduction
Due date: Wednesday, September 22, 2010 (10:10am)
For full credit you must show all of your work.
1.
Show how the following numbers would be represented using the IEEE standard single
precision (32bit floating point) machine representation:
a.
2
b.
1
2
c.
1
10
d.
+
∞
2.
Which of the following quantities
cannot
be represented exactly using the IEEE standard
single precision (32 bit) floating point number representation, and why not?
a.
1
2
b.
1
3
c.
1
5
d.
2 x 10
128
3.
What is the smallest positive 32bit floating point machine number
x
that can be added to
256 using single precision arithmetic to produce a 32bit floating point machine number
y
where
y
> 256?
Is this number the same as the machine epsilon?
Why or why not?
4.
What are the smallest and largest machine numbers that can be represented using a
hypothetical
oneandahalf precision
floating point number representation in which 1 bit
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 Spring '08
 MEYER
 5 bits, 7 bits, 16 bits, 1 bit, 18 bits

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