Please answer the third question and follow the instructions Euler's prime generating polynomial: f(x) x(x 1)+41 LUT design ] [ ROM design ] [ MIPS Assembly implementation ] 1. Design a digital logie circuit (all steps are required), using minimal amount of gates, that will realize a digital LookUp Table (LUT) corresponding to the following Euler's polynomial: x)-x(x-1)+41, with input (x): 0S(X)S7 (a) Set-up the truth-table Binary input: (2X); Binary output: f(Xx) (b) Derive the output expressions (e) Simplify the derived expressions (d) Implement the simplified digital logic circuit, using LogiSim 2. Design a Read Only Memory (ROM) to implement the following Euler's polynomial: x)-x(x-1)+41, with input (X): 0s (x)s7 (a) What is the size of the initial (unsimplified) ROM (b) What is the size of the final (simplified) ROM (e) Show in detail the final ROM layout, using Log Sim 3. Using MIPS Assembly evaluate the following Euler's polynomial: f(x)=x(X-1)+41, Y X = 1,2,3,5 (a) The program (ONLY one program for the 4-numbers X] should be simple mod- ularized and well-documented (b) Appropriate comments in the program are necessary (e) Place the 4-results (decimal numbers), [V X], into registers [Sa0, $a1, $82, Sa3]. In the report include a clear screenshot of the result (MARS) (d) Indicate if the program runs successfully according to specifications and clearly state the results (decimal numbers)