For each of the following circuits, determine the sum-of-products expression and simplify (reduce it to the minimal form) your result. A white circle represents a NOT. Attached is the image of the circuit.

Simplify the following Boolean functlons using four-variable maps.  d.  F(A, B, C, D) = ∑ (0, 2, 4, 5, 6, 7, 8, 10, 13, 15)

9. Give a truth table and a standard sum of products expressions form (min-terms) that describes F(A,B,C) = A OBOC

2. calculates the trajectory r(t) and stores the coordinates for time steps At as a nested list trajectory that contains [[xe, ye, ze], [x1, y1, z1], [x2, y2, z2], ...]. Start from time t = 0 and use a time step At = 0.01; the last data point in the trajectory should be the time when the oscillator "hits the ground", i.e., when z(t) ≤ 0; 3. stores the time for hitting the ground (i.e., the first time t when z(t) ≤ 0) in the variable t_contact and the corresponding positions in the variables x_contact, y_contact, and z_contact. Print t_contact = 1.430 X_contact = 0.755 y contact = -0.380 z_contact = (Output floating point numbers with 3 decimals using format (), e.g., "t_contact = {:.3f}" .format(t_contact).) The partial example output above is for ze = 10. 4. calculates the average x- and y-coordinates 1 y = Yi N where the x, y, are the x(t), y(t) in the trajectory and N is the number of data points that you calculated. Store the result as a list in the variable center = [x_avg, y_avg]…

Please make a k-map to simplify the given boolean equation (and list the final simplified expression)(((((Y AND (~Z)) OR ((~Y) AND Z)) OR (~Z)) AND (~(X OR Y))) OR  (~(((Y AND (~Z)) OR ((~Y) AND Z)) OR (~Z))) AND (X OR Y))