please show your work

$2.$ Do the following.

$($a$)$ Provide the instructions for a URM program that computes the predicate function $\backslash ($ f$($x$)=\backslash )\backslash (3^\{$x$\}\backslash ).$ Enclose in a box the instructions for any while$-$loop that is used by your program. Hint: your program should make use of nested while$-$loops, and hence there should be at least one box drawn within another box. $(10$ pts $)$

$($b$)$ Write a paragraph that describes the logic of how your program computes $\backslash (3^\{$x$\}\backslash ).$ Include mention of the purpose of each register. $(10$ pts$)$