6831 04f HW 2

READ: Text: Finish 6.6 (on clocking schemes.)  Read notes, p. MS-1.
      (I will eventually make available--via the class website--more
      complete notes on the partition material, perhaps by Monday.)

Problems: in text 6/(49, 50)

Non Text Problems:
NT1. For each of the flow tables shown below, determine if it is
strongly connected (i.e., if every state is reachable from every other
state.)

a. 

    A   B   C
    ---------
1   5   1   5
2   6   4   2
3   5   4   1
4   3   6   2
5   1   3   3
6   2   4   2
    ---------
b.
    A   B   C
    ---------
1   3   1   4
2   2   5   5
3   4   1   3
4   3   6   6
5   6   2   6
6   2   6   5
    ---------

NT2. Find output consistent partitions for each of the flow tables
below.  (These are partitions such that given the block in which a
state resides, and the input, we can determine the output.)

a. 
        X
     0     1
    --------
1   3,0   2,1
2   1,1   4,0
3   1,0   2,1
4   2,1   4,0
    ---------
b.

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

NT3. Find a partition for the flow table below that is input
     consistent (i.e., given the current state, the block in which the
     next state lies is independent of the inputs.)

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

NT4. For the flow table below, y1 is assigned.  Complete the state
assignment by finding an input consistent partition, and then generate
logic expressions for Y1 and Y2.  (Y2, of course, should be independent
of X.)

         X
       0   1  y1
       -----
   1   4   2   0
   2   2   4   0
   3   1   3   1
   4   3   1   1
       -----

NT5. For the flow table below, find a partition that is input
consistent with respect to input variable A.  (i.e., for every state,
it is possible to determine which block of the partition the next
state will be in, without knowing the value of A.)

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

NT6. For the flow table below, find a closed partition with 2 blocks.
     (A partition P is closed if, given the block of P containing the
     present state, and the input state, the block of P containing the
     next state can always be determined.)

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