Question $2$: $(30$ Points$)$

Given two processors where the first is a non$-$pipelined processor operating at its maximum frequency of $1$ GHz$,$ and

the second is a pipelined processor operating at its maximum frequency of $1\mathrm{.}635$ GHz$,$ and assuming that both

processors are to run the same instruction mix $($program$),$

a$)$ What would be the minimum size of that program, i$.$e$.,$ minimum number of instructions, beyond which the

pipelined processor starts outperforming the non$-$pipelined processor? $(15$ points$)$

b$)$ What is the maximum relative performance between these two processors, i$.$e$.,$ maximum speedup of the

pipelined processor over the non$-$pipelined processor? How significant is it$?(15$ points$)$

Hint $$ Assume the following when answering both parts $($a$)$ and $($b$)$:

$$ Program behavior: The program does not have any other types of hazards than the control hazard $($branch

hazard$)$ and $30\%$ of the program are branch instructions with an expected $30\%$ chance of the branch

conditions to be false.

$$ Pipeline $($Processor$)$ configuration: The pipelined processor consists of $5$ stages where the branch conditions

are evaluated in the $4$th stage, and is designed to use trivial $$not$-$taken$$ branch prediction.