Use the knowledge (including finite field GF(28 ), extended Euclidean algorithm, polynomial division,

Apply R to simulate a set of 100 numbers with standard deviation of 2 and mean of 20. List out the set of numbers.

Stuck on this question. Please help. Thank you.

can this be proved mathematically?

Given an integer say 45, to find the sum of 45 with 8 in binary form (see the figure below), we can use the TM designed in slides 79-90 of the notes "Turing Machines and Equivalent Models I" twice to find the result. A more effective way is to design a TM to do the addition with 8 directly. 1000 101101 A + = ? Such a TM can be designed by extending the TM designed in slides 79-90 of the notes "Turing Machines and Equivalent Models I". The TM has 14 instructions and 6 states: 0, 1, 2, 3, 4, and halt. Six instructions of such a TM have been given in the first and the second tables below. Fill out the remaining blanks in the first and the second tables and also blanks in the third table to show the remaining instructions of the TM (you have to use your own text boxes here)

Using MATLAB : Please explain the process of how you constructed your code and provide screenshots of the output, pictures and graph