Consider the normalized floating-point system R3(3, 1) with exponent range -1 e 1. (a)...

 

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Consider the normalized floating-point system R3(3, 1) with exponent range -1 ≤ e ≤ 1. (a) What is the smallest positive (nonzero) number representable? Give your answer in both base-3 and base-10. (b) What is the largest positive number representable? Give your answer in both base-3 and base-10. (c) Assuming round-to-nearest, what is the tightest upper bound on the relative error [f(x) - x\/|x| when x ER is stored as fl(x) in this floating-point system? Give your answer in base-10. (d) Assuming round-to-nearest, what is the exact relative error in the floating-point representation of (407) 10 in this system? Give your answer in base-10. (e) Assuming round-to-nearest, what is the exact absolute error f(x) - r in the floating-point representation of (0.567) 10 in this system? Give your answer in base-3. (f) On the base-10 real axis, plot all of the numbers that can be expressed exactly (i.e., with no round-off error) in this system. Comment on the distribution of these numbers and on how well these numbers represent the real number system. Consider the normalized floating-point system R3(3, 1) with exponent range -1 ≤ e ≤ 1. (a) What is the smallest positive (nonzero) number representable? Give your answer in both base-3 and base-10. (b) What is the largest positive number representable? Give your answer in both base-3 and base-10. (c) Assuming round-to-nearest, what is the tightest upper bound on the relative error [f(x) - x\/|x| when x ER is stored as fl(x) in this floating-point system? Give your answer in base-10. (d) Assuming round-to-nearest, what is the exact relative error in the floating-point representation of (407) 10 in this system? Give your answer in base-10. (e) Assuming round-to-nearest, what is the exact absolute error f(x) - r in the floating-point representation of (0.567) 10 in this system? Give your answer in base-3. (f) On the base-10 real axis, plot all of the numbers that can be expressed exactly (i.e., with no round-off error) in this system. Comment on the distribution of these numbers and on how well these numbers represent the real number system.

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a The smallest positive number in base 3 is 0 001 and ... View the full answer