A program with the instruction mix given in the table below is executed on a computer.

Instruction class

Clock Cycles per Instruction

Number of Instructions

Branch

$3$

$18\%$

Store

$4$

$23\%$

Load

$5$

$32\%$

ALU$/$R$-$Type

$4$

$27\%$

a$)$ If the program execution time is $2$ s$,$ and that the number of Load instructions is $130,000$ what is the clock cycle of the computer? At what frequency does the computer run?

b$)$ How much does the CPI for the Store instructions have to be reduced to gain $30\%$ reduction in execution time?

c$)$ Assume that a computer system has a processor with $16$ cores that can be used to solve a problem in parallel. $96\%$ of the code is parallelizable. Can the system achieve a speedup of $10?$ How many cores are needed for this performance?