Poincar (product of spheres) polynomial: f(Sm x Sm? x Sn3 x . . x Sm) [ LUT design | [ ROM design [MIPS Assembly implementation] Given: The Poincar (product of spheres) polynomial: 1. Design a digital logic circuit (all steps are required), using minimal amount of gates, that will realize a digital LookUp Table (LUT) corresponding to the following Poincar polynomial: (a) Set-up the truth-table Binary input: (z); Binary output: f(SmI x Sm2 x Sms) (b) Derive the output expressions (c) Simplify the derived expressions (d) Implement the simplified digital logic circuit, using LogiSim. 2. Design a Read Only Memory (ROM) to implement the following Poincar polynomial: f(Sm x Sma x Sm*) - (112)(1), with input (a) What is the size of the initial (unsimplified) ROM? (b) What is the size of the final (simplified) ROM? (c) Show in detail the final ROM layout, using LogiSim. 0s()s3 3. Using MIPS Assembly evaluate the following Poincar polynomial (a) The program should be simple modularized and well-documented (b) Appropriate comments are necessary (c) Place the result (decimal number) into register: [ Sto]. 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 result (decimal number) Poincar (product of spheres) polynomial: f(Sm x Sm? x Sn3 x . . x Sm) [ LUT design | [ ROM design [MIPS Assembly implementation] Given: The Poincar (product of spheres) polynomial: 1. Design a digital logic circuit (all steps are required), using minimal amount of gates, that will realize a digital LookUp Table (LUT) corresponding to the following Poincar polynomial: (a) Set-up the truth-table Binary input: (z); Binary output: f(SmI x Sm2 x Sms) (b) Derive the output expressions (c) Simplify the derived expressions (d) Implement the simplified digital logic circuit, using LogiSim. 2. Design a Read Only Memory (ROM) to implement the following Poincar polynomial: f(Sm x Sma x Sm*) - (112)(1), with input (a) What is the size of the initial (unsimplified) ROM? (b) What is the size of the final (simplified) ROM? (c) Show in detail the final ROM layout, using LogiSim. 0s()s3 3. Using MIPS Assembly evaluate the following Poincar polynomial (a) The program should be simple modularized and well-documented (b) Appropriate comments are necessary (c) Place the result (decimal number) into register: [ Sto]. 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 result (decimal number)