Question 3: Given m = 0110 and n = 1100 in two's complement notation (ie., m = 6 and n = - - 4). Show your working on computation of the product p = m n using Booth's algorithm. Also, verify your answer. Solving an initial value problem on a computer using the Euler method produces solutions that are not exactly correct because the change in the solution from tn to tn+1 is only approximated using a tangent line, assuming the value at t was exact except at to, the change in the solution from tn to tn+1 is estimated using an inaccurate value of the solution at tn round-off error in computer calculations accumulates over many calculations all three of the above Write a well-commented program that (a) Creates two vectors 92D and E where the energy (E) is the mid- point value for each range. Using units of Eo, E-=[250, 750, 1250,...,9750] . etc. (b) Determines the total degeneracy (density of states=92D) in the energy ranges: (n+n) < 499, 500 < (n+n) < 999,..., 9500 < (n+ n) < 10000 (c) Assumes that 92D(E) = CE, and finds a and C using curve fitting routines. (d) Plots 92D vs E as well as the curve of best fit on a single graph. (e) Calculate 92D(E) theoretically using the technique used in class and compare to your computer calculation. Consider a free electron gas inside a three dimensional box of side L. This time, the energy states are E = E.(n+n+ n) where n, I. Write a well-commented program that (a) Creates two vectors 93D and E where the energy (E) is the mid- point value for each range, that is when using units of Eo, E=[250, 750, 1250,...,9750] . etc. (b) Determines the total degeneracy (density of states=93D) in the energy ranges: (n +n + n) < 499, 500 < (n+ n+ n) < 999, ..., 9500 < (n +n + n) < 10000 (c) Assumes that 93D(E) = CE and finds a and C. (d) Plots 93D vs E as well as the curve of best fit on a single graph. (e) Calculate 93D(E) theoretically using the technique used in class and compare to your computer calculation.