$20pts$ Problems in this question refer to a clock cycle in which the processor fetches the following instruction:

sw $$r0,20($$$r1)$

Assume that data memory is all zeros and that the processor's registers have the following values at the beginning of the cycle in which the above instruction word is fetched:

$\backslash$table$[[10,r,12,r,14,rs,r8,rB,12,31],[0,-1,2,-3,-4,10,6,8,2,-16]]$

$($Let the content of PC be $010000000)$

I. $[4$pts$+4$pts$]$ What are the outputs of the sign$-$extend and the jump "Shift left $2"$ unit $($near the top of Figure $1)$ for this instruction word?

II$.[4$ pts$]$ For each Mux $($Four Mux in Figure $1),$ show the values of its data output during the execution of this instruction. $($If the output of the MUX does not matter for the instruction, you can write the output as 'don't care'$)$

III. $[4$pts$]$ What are the values of these registers after the execution of this instruction

$\backslash$table$[[$r$0,$r$1,$r$2,$r$3,$r$4,$r$5,$r$6,$r$8,$r$12,$r$31],[,,,,,,,,,]]$

IV$.[4$pts$]$ What is the new PC address after this instruction is executed?