Say you have an LC$2$K program with the following characteristics:

$-\backslash (35\backslash \%\backslash )$ Iw

$-\backslash (20\backslash \%\backslash )$ sw

$-\backslash (15\backslash \%\backslash )$ add$/$nor

$-\backslash (30\backslash \%\backslash )$ beq

$-\backslash (25\backslash \%\backslash )$ of register$-$writing instructions are immediately followed by an instruction dependent on it$.$ You may assume that it is true no matter what instructions are involved.

$-\backslash (70\backslash \%\backslash )$ of branches are not taken

$1.$ What would be the expected CPI of your program using detect$-$and$-$stall to resolve data hazards and detect$-$and$-$stall for control hazards? Assume we are using the $5-$stage pipeline described in class and the stalling is handled by the pipeline. Clearly show your work. $[7]$

$2.$ What would be the expected CPI of your program using detect$-$and$-$forward to resolve data hazards and predict$-$not$-$taken for control hazards? Assume we are using the $5-$stage pipeline described in class. Clearly show your work. $[8]$