A certain direct mapped cache is size $2$KB and has $16$B Frames. This cache is associated with a $16$ GB RAM $($here$,$ G is $2^30)$ that is addressed with $64$ bit addressing.

a$.$ Discuss the beekeeping "overhead" necessary to maintain cache entries. Both list and explain in full the details, including all assumptions. Quantify anything quantifiable about this overhead.

b$.$ Compute the number of frames in this cache. Show all work.

c$.$ A floating$-$point variable at address $0$x$0..\mathrm{.}0$f$044$ needs to be placed in the cache. Where $($all$)$ it can be placed $?$ Explain showing all work.

d$.$ For the situation described in $($c$),$ what is the exact bookkeeping overhead that will be maintained for this entry in the cache?

You must identity and give specifics for all aspects of this items bookkeeping overhead.