$2.[10$ points$]$ There is an old CPU running a program in which memory operations currently take $\backslash (30\backslash \%\backslash )$ of its execution time. Scientists find that adding a cache memory speeds up $\backslash (80\backslash \%\backslash )$ of memory operations by a factor of $6.$ Adding a second level of cache speeds up half of the remaining $\backslash (20\backslash \%\backslash )$ by a factor of $3.$ By how much does the overall speed increase using these optimizations? $3.[10$ points$]$ Frank is designing the memory system for a new processor to be launched next year. If the current version of his processor expends $35\backslash \%$ of its time processing memory references, by how much must Frank increase the speed of the memory system to get a total speedup of $1\mathrm{.}7?$ What about a speedup of $1\mathrm{.}9?1.[10$ points$]$ Convert the following floating point numbers to binary. You must use upto $3$ binary digits after the decimal point. Also write down their representations in IEEE single precision floating point. A$.14\mathrm{.}79$ B$.6\mathrm{.}783$ C$.3\mathrm{.}211$