Two improvements are considered to a base machine with a load/store ISA and in which floatingpoint arithmetic instructions are implemented by software handlers. The first improvement is to add hardware floating-point arithmetic units to speed up floating-point Arithmetic instructions. It is estimated that the time taken by each floating-point instruction can be reduced by a factor of 12 with the new hardware. The second improvement is to add more first-level data cache to speed up the execution of loads and stores. It is estimated that, with the same amount of additional on-chip cache real-estate as for the floating-point units, loads and stores can be speeded up by a factor of 3 over the base machine. Let Ffp and Fls be the fraction of execution time spent in floating-point and load/store instructions respectively. The executions of these two sets of instructions are nonoverlapping in time. a) Using Amdahls speedup, what should the relation be between the fractions Ffp and Fls such that the addition of the floating-point units is better than the addition of cache space? b) Suppose that, instead of being given the values of fractions Ffp and Fls, you are given the fraction of floating-point instructions and the fraction of loads and stores. You are also given the average number of cycles taken by floating-point operations and loads/stores. Can you still find out which improvement is better based on these numbers? Explain why and how. Can you still estimate the maximum speedups for each improvement using Amdahls law? Why? c) What are fractions Ffp and Fls such that a speedup of 40% (or 1.4) is achieved for each improvement deployed separately? d) It is decided to deploy the floating-point unit first and to add cache space later on. In the original workload, fractions Ffp and Fls are 40% and 10%, respectively. What is the maximum speedup obtained by upgrading to the floating-point units? Assuming that this maximum speedup is achieved by the floating-point unit upgrade, what is t