Design of Synchronous Counters

Design of Synchronous Counters

AU: Dec.-03, 07, 09, 11, 12, 14, 15, 16,19, May-03, 04, 05, 10, 11, 14, 15, 16, 17

1. Determine the number of flip-flops needed. If n represents number of flip-flops 2ⁿ≥ number of states in the counter.

2. Choose the type of flip-flops to be used.

3. Using excitation table for selected flip-flop determine the excitation table for the

counter.

4. Use K-map or any other simplification method to derive the flip-flop input functions.

5. Draw the logic diagram.

Example 5.5.1 Design a MOD-5 synchronous counter using JK flip-flops and implement it.Also draw the timing diagram.  AU May-16, 17, Marks 16

Solution:

Step 1: Determine the number of flip-flop needed

Flip-flops required are

2ⁿ≥ N

Here N = 5  n = 3 i.e. three flip-flops are required.

Step 2: Type of flip-flop to be used: JK

Step 3:Determine the excitation table for the counter.

Step 4:K-Map simplification

Step 5:Draw the logic diagram

Example 5.5.2 Design divide by 6 counter using T-flip-flops. Write state table and reduce the expression using K-map.

Solution :

Step 1: Determine the number of flip-flops needed.

For designing mod 6 counter using the formula

2ⁿ≥ N

Here N = 6     n = 3 i.e. 3 flip-flops are required.

Step 2:Type of flip-flops to be used: T

Step 3:Determine the excitation table for counter.

Step 4: K-map simplification.

Step 5: Draw the logic diagram.

Example 5.5.3 Using positive edge triggering SR flip-flops design a counter which counts in the following sequence:

000, 111, 110, 101, 100, 011, 010, 001, 000,…..

Solution :

Step 1:Determine the number of flip-flops needed

We know that2ⁿ≥ N. Here, N = 8     therefore n = 3

Step 2: Type of flip-flop to be used: SR

Step 3: Determine the excitation table for counter.

Here, the next state for each present state is written according to given sequence. For example, the next state for the present state 000 is 111.

Step 4: K-map simplification.

Step 5: Draw logic diagram

Example 5.5.4 Design a synchronous decade counter using D flip-flop.  AU May-15, Marks 16

Solution: The decade counter is a mod-10 counter. It has ten states: 0 - 9.

Step 1: Determine the number of flip-flops needed.

We know that 2ⁿ ≥ N. Here, N = 10  therefore n = 4 i.e. 4 flip-flops needed.

Step 2: Type of flip-flops to be used: D

Step 3:Determine the excitation table for counter.

Step 4: K-map simplification

Step 5: Draw the logic diagram.

Example 5.5.5 Design a MOD-10 synchrnous counter using JK flip-flops. Write execution table and state table.  AU: Dec.-14, 16, Marks 10

Solution : Flip-Flops required = 4

Execution Table

K-map simplification

Implementation

Example 5.5.6 Design a counter with the sequence 0, 1, 3, 7, 6, 4, 0.

Solution :

Step 1:Determine the number of flip-flops needed. Here, counter should count maximum count = 7 = (111)₂, which is 3-bit. Thus, we need 3-flip-flops.

Step 2: Flip-flops to be used: JK.

Step 3:Determine the excitation table for counter. Here, the next state for each present state is written according to given sequence. For example, the next state for the present state 3 (011) is 7 (111). The counts which are not in sequence are treated as don't cares.

Step 4: K-map simplification

Step 5: Draw logic diagram.

Example 5.5.7 Design a BCD up/down counter using SR flip-flops.

Solution :

Step 1: Number of flip-flops needed = 4

Step 2: Flip-flops to be used = SR

Step 3: Excitation table for counter

Step 4: K-map simplification

Step 5:Logic diagram

Example 5.5.8 Design a synchronous counter using JK flip-flop to count the following sequence 7, 4, 3, 1, 5, 0, 7 ....  AU: Dec.-14, Marks 16

Solution :

Step 1: Since 2³ > 7, three flip-flops are required

Step 2: Flip-flops to be used: JK

Step 3: Excitation table for counter

Example 5.5.9 Design and implement a synchronous decade counter using T flip-flop. Draw the timing diagram.

Solution :

Step 1: Since N = 10, n = 4 i.e. flip-flops needed

Step 2: Flip-flops to be used: T

Step 3: Determine excitation table for counter

Step 4: K-map simplification

Step 5: Logic diagram

Step 6: Timing diagram

Fig. 5.5.18 shows the timing diagram for the synchronous decade counter.

Example 5.5.10 Design a 3-bit synchronous updown counter using T flip-flops.

Solution :Table 5.5.12 shows the excitation table for 3-bit up/down synchronous counter using T flip-flops.

Excitation table

K-map simplification

Logic diagram

Example 5.5.11 Design a three bit binary counter using T flip-flops and draw the diagram.  AU: Dec.-09, 11, 12, 15, 19, May-16, Marks 16

Solution : Table 5.5.13 shows the excitation table for 3-bit binary counter.

K-map simplification

Logic diagram

Example 5.5.12 Design and explain the working of a synchronous mod-3 counter.  AU: May-03, Marks 16

Solution: N = 3 and

Step 1: Since 2²> 3, n = 2 i.e. flip-flops needed = 2.

Step 2: Flip-Flops used : JK

Step 3: Transition table

Step 4: K-map simplification

Step 5: Logic diagram

Example 5.5.13 Design and explain the working of mod-7 counter.  AU: Dec.-03, Marks 8

Solution :

Step 1: N = 7, and since 2³>7, n = 3 i.e. Flip-Flops needed = 3

Step 2: Flip-Flops used : JK

Step 3: Transition table

Step 4: K-map simplification

Step 5: Logic diagram

Example 5.5.14 Design a synchronous counter with states 0, 1, 2, 3, 0, 1…………. using JK FFs.  AU: May-04, Marks 16

Solution :

Step 1: Here, N = 4 and since 2² ≥ 4 we need 2 Flip-Flops

Step 2: Flip-Flops to be used : JK

Step 3: Transition table

Step 4: K-map simplification

Step 5: Logic diagram

Example 5.5.15 Design a 3-bit binary counter using T flip-flop that has a repeated sequence of six states. 000-001-010-100-101-110. Give the state table, state diagram and logic diagram. Next states for unused states should be 000.  AU: Dec.-07, Marks 16

Step 3: K-map simplification

Step 4: Logic diagram

Example 5.5.16 Design a synchronous up/down counter that will count up from zero to one to two to three and will repeat whenever an external input x is logic 0, and will count down from three to two to one to zero and will repeat whenever the external input x is logic 1. Implement your circuit with one TTL SN74LS76 device and one TTL SN74LS00 device.  AU May-10, Marks 12

Solution: Step 1: Excitation table

Step 2: K-map simplification

Step 3:Logic diagram

We can implement combinational logic circuit for JA and KA input using NAND-NAND logic, as shown in the Fig. 5.5.27.

Example 5.5.17 Design a synchronous counter using JK flip-flop to count the following sequence : "1-3-15-5-8-2-0-12-6-9".  AU May-11, Marks 16

Solution: Since counter has 0-15 states we need 4 flip-flops.

Excitation table

K-map simplification

Logic diagram

Examples for Practice

Example 5.5.18 Design a Mod-6 synchronous counter using JK flip-flops.

Example 5.5.19 Find a modulo-6 gray code using K-map and design the correspondingcounter.

Example 5.5.20 Design and explain the working of a mod-11 counter.  AU May-05, Marks 8

Example 5.5.21 Using D flip-flops, design a synchronous counter which counts in the sequence, 000, 001, 010,011, 100, 101, 110, 111, 000.  AU May-14, Marks 8

Example 5.5.22 Design a modulo-12 up synchronous counter using T flip-flops and draw the circuit diagram.