Solutions For Digital Design Chapter 5 Problem 16P

To design a sequential circuit, find the Boolean expression.

Draw the K-map to obtain the Boolean expression.

The K-map for output is shown in Figure 1.

Note: Clearly, from the state table, we get the output at

Write the Boolean expression for Figure 1.

Thus, the Boolean expression for A is,

.

The K-map for outputis shown in Figure 2.

Note: Clearly, from the state table, we get the output at

Write the Boolean expression for Figure 2.

Thus, the Boolean expression for B is,

.

Draw the sequential circuit from the Boolean expressions for A and B as shown in

Figure 3.

Thus, sequential circuit has been implemented.

The circuit remains in the same state, if and the circuit goes through the state transitions from 00 to 11, to 01, to 10, back to 00, and repeats if .

Draw the state table from this data.

To design a sequential circuit, need Boolean expression.

Draw the K-map to obtain the Boolean expression.

The K-map for output is shown in Figure 4.

Note: Clearly, from the state table, we get the output at

Clearly, find the Boolean expression for .

Thus, the Boolean expression for A is,

.

The K-map for outputis shown in Figure 5.

Note: Clearly, from the state table, we get the output at .

Clearly, from Figure 5:

Thus, the Boolean expression for B is,

.

Draw the sequential circuit from the Boolean expressions for A and B as shown in

Figure 6.

Thus, sequential circuit has been implemented.