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# hw2 - Assignment#2 Number Representation Loss of...

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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 (32-bit 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 32-bit floating point machine number x that can be added to 256 using single precision arithmetic to produce a 32-bit 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 one-and-a-half precision floating point number representation in which 1 bit

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hw2 - Assignment#2 Number Representation Loss of...

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