1. (5 points) A 64-bit binary digit representation represents real numbers in the following way: the first bit indicates the sign s, the next 11 bits is the exponent c, followed by 52 bits describing a fraction f (0,1). The system gives a floating-point number of the form (-1)*22-1023 (1 + $). (a) (2 points) In this system, the largest number possible is represented by a single 0 followed by 51 63 1's. Denote the number it represent by Pmar and the second largest number this system can represent by pmar. What are the absolute error \Pmar - Pmax) and the relative error Pmax-Pmaz ? Pmax (b) (2 points) The smallest positive number it can represent starts with 51 63 0's and ends with a single 1. Denote the number by Pmin and the second smallest positive number by pmin. Calculate the absolute error and relative error between the two. (c) (1 point) For any real number in (Pmin, Pmax), we can approximate it with some element in the system. Judging from the previous two questions, is the system trying to maintain low absolute error or relative error? 1. (5 points) A 64-bit binary digit representation represents real numbers in the following way: the first bit indicates the sign s, the next 11 bits is the exponent c, followed by 52 bits describing a fraction f (0,1). The system gives a floating-point number of the form (-1)*22-1023 (1 + $). (a) (2 points) In this system, the largest number possible is represented by a single 0 followed by 51 63 1's. Denote the number it represent by Pmar and the second largest number this system can represent by pmar. What are the absolute error \Pmar - Pmax) and the relative error Pmax-Pmaz ? Pmax (b) (2 points) The smallest positive number it can represent starts with 51 63 0's and ends with a single 1. Denote the number by Pmin and the second smallest positive number by pmin. Calculate the absolute error and relative error between the two. (c) (1 point) For any real number in (Pmin, Pmax), we can approximate it with some element in the system. Judging from the previous two questions, is the system trying to maintain low absolute error or relative error