# HW1 - COT4501 Spring 2012 Homework I This assignment has...

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COT4501 Spring 2012 Homework I This assignment has seven problems and they are equally weighted. The assignment is due in class on Tuesday, January 31, 2012. Problem 1 Provide short answers to the following questions: True or false: Floating-point numbers are distributed uniformly throughout their range. True or false: In a floating-point number system, the underflow level is the smallest positive number that perturbs the number 1 when added to it. Suppose you are solving a given problem using a given algorithm. For each of the following, state whether it is affected by the stability of the algorithm, and why. 1. Propagated data error, 2. Accuracy of the computed result, 3. Conditioning of problem. Give two reasons why floating-point number systems are usually normalized. In a p -digit binary floating-point system with rounding to nearest, what is the value of the unit roundoff mach ? Give an example of a number whose decimal representation is finite (i.e., it has only a finite number of nonzero digits) but whose binary representation is not.

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