$2.$ This exercise examines the accuracy of various branch predictors for the following repeating pattern e$.$g$.,$ in a loop$)$ of branch outcomes: T$,$ NT$,$ T$,$ T$,$ NT$,$ T$,$ NT$.$

a$)$ What is the accuracy of always$-$taken and always$-$not$-$taken predictors for this sequence of branch outcomes? $(10$pts$)$

b$)$ What is the accuracy of the two$-$bit predictor for the first $4$ branches in this pattern and why, assuming that the predictor starts off in the bottom left state $($predict not taken$)$ from the figure below: $(20$ pts$)$

c$)$ What is the accuracy of the two$-$bit predictor if this pattern is repeated forever? and explain why $($explain every occurrence of the pattern will helpful$).(20$ pts$)$