In this assignment, you are required to design a fully dedicated architecture $($FDA$)$ to implement the following algorithms:

xlarre$(a+b+c)$

ylarr$(a+c)(c+d)$

$(1)$ Apply coarse$-$level restructuring on the equation of $"x"($e$.$g$.,$ factoring, operator grouping, removing common sub$-$expressions, etc.$)$ to allow for minimal hardware implementation. Then, derive the data flow graph $($DFG$)$ for your design.

$(2)$ Design the corresponding datapath, applying the constrained resource allocation of one multiplier and one adder. Also apply as$-$late$-$as possible $($ALAP$)$ register allocation.