You are expected to develop two simulators mimicking the behavior and analyze the performance of iterative multiplication algorithm and add-and-shift multiplication algorithm. You are free to use any programming language as you are familiar and comfortable with. Two binary unsigned numbers of 4 ≤ length ≤ 16 bits are the input to the simulators (operands are of the same length). For each pair of given test data, your simulators should generate the multiplication result in binary and hexadecimal, record the execution time of the multiplication algorithms in term of Delta t, where Delta t is the delay of a basic logic gate (AND or OR). a technical paper. It should be typed and contain: 

1) A detail discussion about your simulators, their implementations, and the generic equations for calculating the execution times. Make sure to include pseudo codes for your simulators, 

2) Simulation results and analysis of the results, including: a. A table showing the inputs in binary, multiplication results (both in binary and hexadecimal), execution time for both algorithms, b. Detail analysis of the results, c. Two overlapping plots showing the overall execution time vs. the length of operands, 

3) A copy of well documented simulator as an appendix Note: You are using carry select adder to perform additions (refer to the class notes for its timing), Shift operation is 3Deltat, and You have 4 basic building blocks of 4 * 4 multiplier units with the execution time of 21Delta t (in case of iterative multiplication algorithm).

Use c++ for coding and attached the full code with detailed discretion.