Problem $03$: $(30$ points$)$ This exercise examines the accuracy of various branch predictors for the following repeating pattern $($e$.$g$.,$ in a loop$)$ of branch outcomes: NT$,$ T$,$ T$,$ NT$,$ T

a$)$ What is the accuracy of always$-$taken and always$-$not$-$taken predictors for this sequence of branch outcomes?

b$)$ What is the accuracy of the two$-$bit predictor for the $5$ branches in this pattern, assuming that the predictor starts off in the bottom right state from Figure $4\mathrm{.}63($predict not taken$)?$

c$)$ What is the accuracy of the two$-$bit predictor if this pattern is repeated forever?