# 18.6 The Procedure to Design Counters – Pulse and Digital Circuits

##### 18.6 THE PROCEDURE TO DESIGN COUNTERS

The major in the design of counters is briefly described here:

• The statement of the problem or the state diagram will be given.
• Identify the number of flip-flops required.
• Choose the type of flip-flop needed.
• Assign variable names to the flip-flops.
• Draw the state table.
• Develop the excitation table.
• Use a K-map to derive the logic equations.
• Implement a counter to produce the specified sequence of states.

This design procedure can be further understood with the help of the following example.

FIGURE 18.24 A state diagram

##### EXAMPLE

Example 18.4: Design a 3-bit binary counter whose state diagram is shown in Fig. 18.25.

FIGURE 18.25 The state diagram of a 3-bit binary counter

Solution:

Step 1: Since it is a 3-bit counter, the number of flip-flops required is 3.

Step 2: Let the type of the flip-flop be JK flip-flop.

Step 3: Let the three flip-flops be A, B, C

Step 4: The state table is as shown in Table 18.26.

Step 5: The next step is to develop an excitation table from the state table, which is shown in Table 18.27.

Step 6: Now transfer the JK states of the flip-flop inputs from the excitation table to Karnaugh maps (K-maps) given in Tables 18.28(a)(f) to derive a simplified Boolean expression for each flip-flop input.

TABLE 18.26 The state table

TABLE 18.27 The state table

TABLE 18.28 (a) The K-map for JA; (b) the K-map for KA

TABLE 18.28 (c) The K-map for JB; (d) the K-map for KB

From the K-maps, the following expressions for the J and K inputs of each of the flip-flops are obtained:

JC = KC = 1 JB = KB = C JA = KA = B.C

Step 7: The final step is to implement the combinational logic from the equations and connect the flip-flops to form the sequential circuit. The complete logic of a 3-bit binary counter is shown in Fig. 18.26.

TABLE 18.28 (e) The K-map for JC; (f) the K-map for KC

FIGURE 18.26 The logic diagram of a 3-bit binary counter