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1. [6 points.] Consider the double-precision numbers in the IEEE-standard for binary floating-point arithmetic, that is, use values p = 53, Emin = -1022, Emaz = 1023 from Table 1 of the standard. (a) What is the largest positive number of this number system? What is the smallest positive normalized number? What is the smallest positive number overall, including de-normalized numbers? What is machine epsilon e? Machine epsilon e is defined as the smallest positive number such that 1.0+ would not round to 1.0 in computer arithmetic. Explain how you obtained your results. (b) Use Matlab to check your results. Use format hex to display the output. Look at its functions eps, realmin, and realmax, and determine if these give the results that you calculated by hand above. 1. [6 points.] Consider the double-precision numbers in the IEEE-standard for binary floating-point arithmetic, that is, use values p = 53, Emin = -1022, Emaz = 1023 from Table 1 of the standard. (a) What is the largest positive number of this number system? What is the smallest positive normalized number? What is the smallest positive number overall, including de-normalized numbers? What is machine epsilon e? Machine epsilon e is defined as the smallest positive number such that 1.0+ would not round to 1.0 in computer arithmetic. Explain how you obtained your results. (b) Use Matlab to check your results. Use format hex to display the output. Look at its functions eps, realmin, and realmax, and determine if these give the results that you calculated by hand above

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