$[15/20/10]<5\mathrm{.}1>$ In this exercise, we examine the effect of the interconnection network topology on the CPI of programs running on a $64-$processor distributed$-$memory multiprocessor. The processor clock rate is $2\mathrm{.}0$ GHz$,$ and the base CPI of an application with all references hitting in the cache is $0\mathrm{.}75.$ Assume that $0\mathrm{.}2\%$ of the instructions involve a remote communication reference. The cost of a remote communication reference is $(100+10$ h$)$ ns$,$ h being the num$$ ber of communication network hops that a remote reference has to make to the remote processor memory and back. Assume all communication links are bidirectional. a$.[15]<5\mathrm{.}1>$ Calculate the worst$-$case remote communication cost when the $64$ processors are arranged as a ring, as an $8$ x $8$ processor grid, or as a hypercube $($hint: longest communication path on a $2"$ hypercube has n links$).$ Fraction of T $20\%20\%10\%5\%15\%20\%10\%$ Processors $($P$)1246816128$ b$.[20]<5\mathrm{.}1>$ Compare the base CPI of the application with no remote commu$$ nication to the CPI achieved with each of the three topologies in part $($a$).$