1.1 1. The natural exponent \( e = 2.71828182459 \ldots \) Answer the following questions: a. Assuming we follow the standard rules for representing floating point numbers, what is the exponent required to represent \( e \) as a floating point binary number? Report your answer in both the base-2 and base-10 representations. b. How many bits of data are necessary to represent the decimal portion (i.e., mantissa) of \( \sqrt{e} \) to the fifth decimal place (1.64872)? c. Suppose you have a calculator that stores floating point numbers using a six-bit mantissa. What is the machine precision, “eps” for this calculator? d. If the calculator employs rounding, what is the largest possible relative round-off error introduced by a single calculation with the calculator from part ‘c’? e. Suppose instead that this calculator uses the following number format: \[ FL(x) = S|E|E|E|M|M|M \] - **Bit 1:** Sign of the number. - **Bits 2-4:** Biased exponent – subtract 4 to achieve the final exponent value. - **Bits 5-8:** Mantissa. Assuming that the calculator uses exact rounding, what is the expected relative error produced when performing the calculation \( \sqrt{e} \)?

Answered: Image /qna-images/answer/100db944-0cba-468d-9b0a-1cbe064ca126.jpg

Answered: 1. The natural exponent e =…

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

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