Solutions For Digital Design Chapter 5 Problem 9P

(a)

Write the expression of the output of the J-K flipflop for the first flip-flop.

…… (1)

Substitute for , for , and for for the first flip flop in equation (1).

Write the expression of the output of the J-K flipflop for the second flip-flop.

…… (2)

Substitute for , for , and for for the second flip flop in equation (1).

NOTE: Here, is input not the don’t care.

The state table for the sequential circuit is shown in Table 1.

The next state can also be determined from the characteristic table of J-K flipflop.

The JK flip-flop characteristic table is shown in Table 2.

From the state table of Table 1, the next state of the JK flip-flop A is,

The next state of the JK flip-flop B is,

Therefore, the state equations and are and.

Draw the corresponding state diagram is shown in Figure 2.

Thus, state diagram of the circuit is implemented.