18.2.18 For the Boolean function F=xy'z+x'y'z+w'xy+wx'y+wxy A. Obtain the truth table of F. B. Draw the logic diagram, using the original Boolean expression. C. * Use Boolean algebra to simplify the function to a minimum number of literals. D. Obtain the truth table of the function from the simplified expression and show that it is the same as the one in part (a). E. Draw the logic diagram from the simplified expression, and compare the total number of gates with the diagram of part (b).
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- Exercise 4.31 shows how to test whether a point is on the left side of a directed line, on the right, or on the same line. Write the following functions: # Return true if point (x2, y2) is on the left side of the# directed line from (x0, y0) to (x1, y1)def leftOfTheLine(x0, y0, x1, y1, x2, y2):# Return true if point (x2, y2) is on the same# line from (x0, y0) to (x1, y1)def onTheSameLine(x0, y0, x1, y1, x2, y2):# Return true if point (x2, y2) is on the# line segment from (x0, y0) to (x1, y1)def onTheLineSegment(x0, y0, x1, y1, x2, y2): Write a program that prompts the user to enter the three points for p0, p1, and p2 and displays whether p2 is on the left of the line from p0 to p1, on the right, on the same line, or on the line segment. The sample runs of this program are the same as in Exercise 4.31.1.1 Define a growth factor for the above difference equation (in the picture), also verify that your function is a growth factor for the above difference equation. ( Reccomend Use of Python3) 1.2 Determine all the equilibria of the above difference equation by solving an appropiate equation using simpy. 1.3 Use numpy and matplotlib to make a line plot of the graph of the growth factor g that you defined above on the interval 1.4 Use your plot to classify all determined equilibra as stable/unstable. Explain your reasoning..
- [Unbalanced Rod] Given a set of n weights {w₁,..., wn} and a rod of length n - 1 inches, we can attach the weights to the rod at hooks placed at one inch distances apart as shown in the figure below. -1". /10 2 3 12 2 4 We can attach a weight to any hook but no two weights can be attached to the same hook and we have to attach all the weights. For any given assignment of weights to hooks, we can compute the location of the center of mass of the rod and the weights according to the following equation (neglecting the weights of the rod and the hooks). where 0 ≤ Pi≤n-1 is the position of weight along the rod. For example, in the figure shown above, the center of mass is computed as C= C = i Wi Pi Σi Wi 10 0+2 1+3·2+4·3+12.4 +2.5 10+2+3+4+12+2 78 33 The problem is to find an assignment of weights to hooks that makes the center of mass as far as possible to the left, i.e., minimize the value of c. Answer the following questions. 1. Describe a greedy algorithm that finds the assignments that…4.4 Find all perfect squares of the form aaa . . . a | {z } n digits bbb . . . b | {z } n digits .Pb#1: For several values of x, confirm that eix = cos x + i sin x Pb#2: An object thrown vertically with a speed vo reaches a height h at time t, where h= vo*t - gt2 Write and test a function that computes the time t required to reach a specified height h, for a given value of vo. The function's inputs should be h, vo, and g. Test your function for the case where h=100 m, vo=50 m/s. and g=9.81 m/s2. Interpret both answers. (MATLAB)