A $32-$bit machine has all the registers and instructions shown in Figure $1($the addresses and opcodes shown are in hexadecimal format$)$: a$)$ How many bits are required for PC and IR$?(4$ marks$)$ b$)$ Draw the program execution of the instructions. Remember, the figure shows that there are $6$ instructions need to be executed. Thus, your answer should have exactly $12$ steps $(2$ steps per instruction$).$