A simple RISC CPU is implemented with a single scalar instruction processing pipeline. Instructions are always executed sequentially except in the case of branch instructions. Given that p_b is the probability of a given instruction being a branch, p_t is the probability of a branch being taken, pc is the probability of a correct prediction, b is the branch penalty in clock cycles, and c is the penalty for a correctly predicted branch:

a. Calculate the throughput for this instruction pipeline if no branch prediction is made given that p_b = 0.16, p_t = 0.3, and b = 3.

b. Assume that we use a branch prediction technique to try to improve the pipeline’s performance. What would be the throughput if c = 1, p_c = 0.8, and the other values are the same as above?