Exercises 5 (14 pts)

1. (2 pts) Represent on K-maps the functions described by the following table:

     x y   z |   f1 f0
     0 0   0 |    0   -
     0 0   1 |    1   0
     0 1   0 |    1   1
     0 1   1 |    0   1
     1 0   0 |    0   -
     1 0   1 |    1   0
     1 1   0 |    0   1
     1 1   1 |    0   0

2. (2 pts) Represent on K-maps the functions described by the following expressions:

a. E(x,y,z) = Sm(2,4,7)
b. E(w,x,y,z) = w'x'y+y'z+xz'

3. (3 pts) Represent on K-maps the functions described by the following expressions:

a.    E(w,x,y,z) = PM(1,3,4,7,10,13,14,15)
b.    E(w,x,y,z) = Sm(0,4,5,9,11,14,15), dc(w,x,y,z)=Sm(2,8)
c.    E(x,y,z) = Sm(0,1,4,6)

4. (3 pts) Using the K-maps of Exercise 3, find the minimal sum of products and product of sums.

5. (4 pts) A combinational system has four inputs, a, b, c, and d, and one output y. The output y is 1 if and only if the number represented by (a,b,c,d) in binary code is prime. Note that 0 and 1 are not prime.

a.    Give the switching function (truth table).
b.    Using K-maps, find the minimal sum of products or product of sums switching expression.
c.    Give a graphical representation of a minimal, two-level network to implement this system using AND, OR, and NOT gates.
d.    Give a graphical representation of a minimal, two-level network to implement this system using NAND gates.