CS E6831 HW 5 04f  Due 10/13/04

1. Consider the flow table below.

         X
       0   1
       -----
   1   5   3
   2   6   4
   3   2   1
   4   1   2
   4   5   4
   6   2   4
       -----
(a) Is it strongly connected?

(b) For this table, find a closed 2-block partition that equates 1 and
    2 (1~2).

2. (a) For the table of the previous question, find a 4-subset closed
cover that includes 12 as one of the subsets.  (Recall that a closed
cover consists of a collection of subsets whose union consists of the
set of all states, and such that if a and b are in one of the subsets,
then, for any input, the next-states from a and b are also in one of
the subsets.)

(b) Use the closed cover found in part-a, along with the partition
(135, 246), to generate a state assignment for the table, and then find
minimal SOP expressions for Y1, Y2, and Y3.

3. For the flow table below, find an optimum state assignment using
the Armstrong method, whereby we try to maximize the number of
adjacencies (00 and 11 points) in the functions.  In compiling the
scores, include the output function.  After finding the assignment,
generate the Y and Z logic expressions (SOP), and count the gate
inputs, gi, (assuming double-rail inputs for both the X's and y's).  Next,
find the state assignment with the LOWEST score, generate the logic
and compare the costs in gi.

                 AB
        00    01    11   10
       --------------------
   1   2,0   3,0   4,1   2,0
   2   3,0   3,0   2,0   3,1
   3   4,0   2,1   3,1   2,0
   4   1,0   1,1   2,0   4,1
       ---------------------

4. Split the flow table shown below into two tables corresponding to
the states 1, 2, and 4 for M1, and 3, 5, and 6 for M2.  Show the
complete flow tables of M1 and M2.  Use state assignments 00, 01, 11,
and 10 for both machines and generate logic expressions (SOP) for the
Y's, and V's.

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