Suppose in the IEEE single format, the width of the exponent field is 4, not 8, and the width of the fraction field is 6, not 23. What should the exponent bias be? (b) What is the machine epsilon of this system? (c) What are the smallest and largest positive normal floating point numbers in this system? (d) Can any integer number between the smallest and largest positive normal floating point numbers be stored exactly in this floating point system? Either prove it or give a counterexample. (e) What are the largest and smallest nonnegative subnormal floating point numbers in this system? (f) What are the two floating point numbers (neither is equal to 5) closest to 5? (g) Given number -(11.1001011) 2. Round it using the four rounding modes.
Suppose in the IEEE single format, the width of the exponent field is 4, not 8, and the width of the fraction field is 6, not 23. What should the exponent bias be? (b) What is the machine epsilon of this system? (c) What are the smallest and largest positive normal floating point numbers in this system? (d) Can any integer number between the smallest and largest positive normal floating point numbers be stored exactly in this floating point system? Either prove it or give a counterexample. (e) What are the largest and smallest nonnegative subnormal floating point numbers in this system? (f) What are the two floating point numbers (neither is equal to 5) closest to 5? (g) Given number -(11.1001011) 2. Round it using the four rounding modes.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Only for d,e,f,g no
Transcribed Image Text:Suppose in the IEEE single format, the width of the exponent field is 4, not 8, and the width of the fraction field is 6, not 23.
What should the exponent bias be?
(b)
What is the machine epsilon of this system?
(c)
What are the smallest and largest positive normal floating point numbers in this system?
(d)
Can any integer number between the smallest and largest positive normal floating point numbers be stored exactly in
this floating point system? Either prove it or give a counterexample.
(e)
What are the largest and smallest nonnegative subnormal floating point numbers in this system?
(f)
What are the two floating point numbers (neither is equal to 5) closest to 5?
(g)
Given number -(11.1001011) 2. Round it using the four rounding modes.
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