Solutions For Digital Design Chapter 5 Problem 19P

(a)

Draw the state table for D flip-flops. This is drawn with respect to the next state and the input or output given in the state diagram. If the present state is 000 makes a transition to 100,011 with a input 1, 0 and output 1, 0. Thus each and every state is tabulated as shown in Table 1.

The unused sates are don’t-cares conditions.

Draw the K-map for as shown in Figure 2.

Write the Boolean expression for .

Thus, the Boolean expression for A is,

.

Write the Boolean expression for .

Thus, the Boolean expression for B is,

.

Draw the K-map for as shown in Figure 4.

Write the Boolean expression for .

Thus, the Boolean expression for C is,

.

Draw the K-map for as shown in Figure 5.

Write the Boolean expression for .

Thus, the Boolean expression for y is,

.

The sequential circuit using three D flip-flops is shown in Figure 6.

Even though the circuit have unused states such as . It gets self-corrected as follows:

For unused present state ABC = 101, the next state for input is,

So, for the present state 101, the next state becomes 011 for .

Output.

For unused present state 110, the next state for input is,

So, for the present state 110, the next state becomes 010 for and 011 for. Output is

For unused present state 111, the next state for input is,

So, for the present state 111, the next state becomes 011 for or .

Output is.

The unused states make transitions to the new states as shown in Figure 7.

(b)

Design the sequential circuit using JK flip-flops.

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

The flip-flop inputs are derived from the state table in conjunction with the excitation table for the JK flip-flop.

Draw the state table for JK flip-flops.

Normally in a JK flip-flop in order to make transition of states from present state 0 to next state 0, requires that input J be 0 and input K be a don’t care so 0 and x can be entered in the first row under and . Thus, considering the states and its transition shown in Table 1, each row is tabulated as shown in Table 3.

Draw the K-map for as shown in Figure 8.

Write the Boolean expression for .

Thus, the Boolean expression for is:

.

Draw the K-map for as shown in Figure 9.

Thus, the Boolean expression for is:

.

Draw the K-map for as shown in Figure 10.

Write the Boolean expression for .

Thus, the Boolean expression for is:

.

Draw the K-map for as shown in Figure 11.

Write the Boolean expression for .

Thus, the Boolean expression for is:

.

Draw the K-map for as shown in Figure 12.

Write the Boolean expression for .

Thus, the Boolean expression for is:

.

Draw the K-map for as shown in Figure 13.

Write the Boolean expression for.

Thus, the Boolean expression for is:

.

Draw the K-map for as shown in Figure 5.

Write the Boolean expression for .

Thus, the Boolean expression for y is,

.

The design of sequential circuit using JK flip-flops is shown in Figure 14.

For unused present state ABC = 101, the next state for input is,

Use JK Excitation table to find the next state expressions.

So, for the present state 101, the next state becomes 011 for and 010Output.

For unused present state ABC = 110, the next state for input is,

Use JK Excitation table to find the next state expressions.

So, for the present state ABC = 110, the next state becomes 010 for and 001Output.

Similarly, for unused present state ABC = 111, the next state for input is,

So, for the present state 111, the next state becomes 001 for and 010Output.