Question 1 [40 points]: Consider a heterogeneous computer architecture that has two types of processors: a powerful processor (of which there is only one) and p small capacity processors (called small processors heretofore). Consider that a program P can be broken down into two parts: a sequential part (which is executed by the powerful processor) and a parallelizable part that is processed in parallel by the p small processors. The sequential and parallel parts of the computation start at the same time and the program ends when both parts end (i.e., when the part that takes the longest time ends) Assume the following notation T: total CPU time of the program P (assume the program does not do any I/0) I: total number of instructions executed by P f: fraction of the instructions of P that have to be executed by the powerful processor, i.e., the sequential part of P's instructions CPls: average CPI of the part of the program executed on the powerful processor CPlp: average CPI of the part of the program executed on each small processor fs: clock frequency of the powerful processor jp : clock frequency of each small processor (a) [6 points] Give an expression for the CPU time of the sequential part of the progranm (b) [6 points] Give an expression for the CPU time of the parallel part of the program (c) [8 points] Give an expression for the total CPU time T (d) [2 points] Give an expression for Twhen f- 0 (e) [2 points] Give an expression for T when f-1 (f) [12 points] Assume that I 2 *1010, fs 3.5 GHz, fp -1.8 GHz, CPls 1.5, CPIp 3.0. Use Excel to draw a graph of T vs p. Your graph should show 5 curves for the following values of f 0, 0.15, 0.25, 0.5, and 1. The values of p should go from 1 to 50 in increments of 5. Use a x-y scatter plottype in Excel. Make sure to properly label the y and x axes. (g) [4 points] What conclusions do you draw from the graph? Question 1 [40 points]: Consider a heterogeneous computer architecture that has two types of processors: a powerful processor (of which there is only one) and p small capacity processors (called small processors heretofore). Consider that a program P can be broken down into two parts: a sequential part (which is executed by the powerful processor) and a parallelizable part that is processed in parallel by the p small processors. The sequential and parallel parts of the computation start at the same time and the program ends when both parts end (i.e., when the part that takes the longest time ends) Assume the following notation T: total CPU time of the program P (assume the program does not do any I/0) I: total number of instructions executed by P f: fraction of the instructions of P that have to be executed by the powerful processor, i.e., the sequential part of P's instructions CPls: average CPI of the part of the program executed on the powerful processor CPlp: average CPI of the part of the program executed on each small processor fs: clock frequency of the powerful processor jp : clock frequency of each small processor (a) [6 points] Give an expression for the CPU time of the sequential part of the progranm (b) [6 points] Give an expression for the CPU time of the parallel part of the program (c) [8 points] Give an expression for the total CPU time T (d) [2 points] Give an expression for Twhen f- 0 (e) [2 points] Give an expression for T when f-1 (f) [12 points] Assume that I 2 *1010, fs 3.5 GHz, fp -1.8 GHz, CPls 1.5, CPIp 3.0. Use Excel to draw a graph of T vs p. Your graph should show 5 curves for the following values of f 0, 0.15, 0.25, 0.5, and 1. The values of p should go from 1 to 50 in increments of 5. Use a x-y scatter plottype in Excel. Make sure to properly label the y and x axes. (g) [4 points] What conclusions do you draw from the graph