CS E6831 04f  HWK #3 
<PRE>
Due 9/29/04

Read the posted notes.

PROBLEMS:

1. For the flow matrix below, generate minimal SOP logic expressions
for Y1 and Y2.

                 AB
         00   01   11   10  y1  y2
         ----------------
    1    1    4    3    2   0   0
    2    1    4    3    1   0   1
    3    1    4    1    2   1   1
    4    1    1    3    2   1   0
         ----------------

2. Consider a synchronous sequential machine of the type we have been
   discussing.  Assume 3 state variables were used and that the logic
   for one of them is described by
     Y2=X1X2y2'y3 + X1'X2'y1.
   Now suppose that the state assignment is changed by complementing
   both the y1 and y2 columns.  Specify the new expression for Y2.

3. For the flow table of problem 1, generate the complete lattice of
   closed partitions.

4. For the flow table below, find a partition that is both input
   consistent and closed.  Then find one more closed partition.  Using
   these partitions, generate a state assignment that leads to a very
   economical set of SOP expressions for the Y's.  Hint: You will find
   that there are very few closed partitions, so your choice will be
   simple.  Also, only 3 y-variables are used in the solution.

         X
       0   1
       -----
   1   6   4
   2   5   3
   3   2   6
   4   1   5
   5   4   2
   6   3   1
       -----

5. Use the lattice generated in problem 3 to find a good state
   assignment.  Then generate minimal SOP expressions for the Y's.
   Note that you will have to use more than the minimum number of
   y-variables if you are to take full advantage of the closed
   partitions.  How does the logic complexity compare with that of the
   assignment used in problem 1?

..............
</PRE>