Exercises 7 (20 pts)

1. (2 pts) A sequential system has one input with values a, b, and c and one output with values p and q. The output is q whenever the input sequence has an even number of a's and an odd number of b's. Fill in the blanks to obtain a state high-level description of the system.

Input: x(t) element of
Output: z(t) element of

                                       |   q if x(         ) contains even number of       and          number of b's
          Function:       z(t) =|
                                       |   p otherwise

2. (2 pts) Determine the state table corresponding to the state diagram shown in Figure 7-18, page 189.

3. (4 pts) For the sequential system specified by the state diagram shown in Figure 7.19, give a code for the:

a.    input
b.    output
c.    state
d.    give the corresponding state table.

4. (2 pts) Reduce the number of states in the following state table and show the minimal table.

PS| x=0 x=1
A| F,0 C,0
B| H,1 A,1
C| H,0 D,1
D| B,0 H,0
E| G,0 C,0
F| C,1 E,1
G| H,1 E,1
H| C,0 A,1
| NS,z

5. (10 pts) For the following state table.

PS|    Input
| x=a   x=b   x=c
A | A,0   B,1   A,0
B | B,0   C,1   A,1
C | C,0   D,1   A,1
D | D,0   E,1   A,0
E | E,0   A,1   A,1
| NS, Output
a.    Determine the state diagram.
b.    Give the state table for a binary encoding.
c.    Give the state diagram for the state table using switching expressions.
d.    Give the VHDL for the state diagram.