Solutions For Digital Design Chapter 5 Problem 13P

From Table 1, at the present state a, when the input is 0, then the next state goes to the state f and the output will be 0.

At the state f, when the input is 1, then the next state goes to the state b and the output will be 1.

Similarly, the whole output sequence traverse thorough different states for the given input sequence.

The output sequence for the original state table shown in Table 1 is shown in Table 1.1

Reduction of state table, a state can be replaced with an another in the state table if and only if the states and the outputs are exactly equal.

In the provided state table h and d have the same next states and outputs; So, the state h can be replaced with d. Replace all h’s with d.

Similarly b and e are equal states; So, remove e state and replace e with b in the rest of the states. The above replacement leads to equal states in a and c, remove the state c from the state table and replace all c’s with a.

Draw the reduced state table.

From Table 2, at the present state a, when the input is 0, then the next state goes to the state f and the output will be 0.

At the state f, when the input is 1, then the next state goes to the state d and the output will be 1.

Similarly, the whole output sequence traverse thorough different states for the given input sequence.

The output sequence for the reduced state table shown in Table 2 is shown in Table 2.1

Therefore, from the tables Table 1.1 and Table 2.1, the output sequence obtained from the original and reduced state tables are same.

The so obtained output sequence is.