Solutions For Digital Design Chapter 5 Problem 12P

(a)

Draw the corresponding state diagram of the state table shown in Table 1 is shown in Figure 1.

Hence, the state diagram has been drawn.

(b)

The reduced state table is obtained as shown in Table1.2 through Table 1.4.

From Table 1, the present state b and e denoted in bold green are equivalent states because they both have the same next states, d (when x = 0) and c (when x = 1) as well as same output logic. Remove one of these two states from the original state table.

Remove row e from the Table 1 and replace all e’s by b.

The first stage modified state table is shown in Table 1.1.

From Table 1.1, the present state a and c denoted in bold red are equivalent states because they both have the same next states, f (when x = 0) and b (when x = 1) as well as same output logic. Remove one of these two states from the modified state table.

Remove row c from the Table 1.1 and replace all c’s by a.

The second stage modified state table is shown in Table 1.2.

Table 1.2 Second stage modified state table

From Table 1.2, the present state d and h denoted in bold blue are equivalent states because they both have the same next states, g (when x = 0) and a (when x = 1) as well as same output logic.

Remove one of these two states from the modified state table.

Remove row h from the Table 1.2 and replace all h’s by d.

The third (final) stage modified state table is shown in Table 1.3.

Table 1.3 Third (final) stage modified state table

Hence. The reduced state table has been drawn.

(c)

The corresponding state diagram of the reduced state table in Table 4 is shown in Figure 2.

Hence. The reduced state diagram has been drawn.