thanks An automobile manufacturer is automating the placemen

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An automobile manufacturer is automating the placement of certain components on the bumpers of a limited-edition line of sports cars. The components are color coordinated, so the robots need to know the color of each car in order to select the appropriate bumper component. Models come in only four colors: blue, green, red, and white. You are hired to propose a solution based on imaging. How would you solve the problem of automatically determining the color of each car, keeping in mind that cost is the most important consideration in your choice of components? Show how Shannon\'s expansion can be used to create a BDD for the function. f= x_1x_3 + x_2 x_4, with the input order x_1, x_2, x_3, x_4.

Solution

Answer:

p13)

Shannon Expansion fix a variable

f = xi f|xi=1(x1, …, xn) + x’i f|xi=0(x1, …, xn)

f = x1 x3 + x2 x4

ordering 1 : x1 x2 x3 x4(linear result)

=> If (x1 x2)= 1, f = 1 no need to read

=>Otherwise we can “forget about x1 x2”

=>The “memoryless effect” makes BDD small

=A node in a BDD is a memory cell to

the intermediate results during the computation
of the function

ordering 2 : x1 x3 x2 x4 (exponential result)

=>If (x1=x3=x2=1) we need to remember them all.

=>Because nothing can be decided based upon the
information we have