**Design of synchronous counters**

Synchronous Counters is the important topic of the Digital Electronics. Moreover, freestudy9 has all kind of important information and topic related to it.

**Step 1. The number of flip-flops**

- Based on the description of the problem, determine the required number n of the FFs – the smallest value of n is such that the number of states N ≤ 2
^{n}and the desired counting sequence.

**Step 2. State diagram**

- Draw the state diagram showing all the possible states.

**Step 3. Choice of flip-flops and excitation table**

- Select the type of flip-flops to be used and write the excitation table.
- An excitation table is a table that lists the present state (PS), the next state (NS) and the required excitations.

**Step 4. Minimal expressions for excitations**

- Obtain the minimal expressions for the excitations of the FFs using K-maps for the excitations of the flip-flops in terms of the present states and inputs.

**Step 5. Logic Diagram: **

- Draw the logic diagram based on the minimal expressions.

**Excitation Tables**

**Design a counter to generate the repetitive sequence 0,1,2,4,3,6. **

Step 1. The number of flip-flops:

- A counter with repetitive sequence 0, 1, 2, 4, 3, 6 requires 3 flip-flops. The counting sequence is 000, 001, 010, 100, 011, 110, 000 …

Step 2. Moreover, Draw the state diagram

Step 3.Also, Select the type of flip-flops and draw the excitation table

- T flip-flops are selected and the excitation table of a given sequence counter using T flip-flops.

Step 4. So, Obtain the minimal expressions

- K – Maps for excitations T
_{3}, T_{2}, and T_{1}

**Design 3-bit synchronous up counter using T flip-flop**

Step 1. NThe number of flip-flops

- A 3 bit up counter requires 3 flip-flops. The counting sequence is 000, 001, 010, 011, 100, 101, 110, 111, 000 ..

Step 2. Moreover, Draw the state diagram

Step 3. So, Select the type of flip-flops and draw the excitation table

- T flip-flops are selected and the excitation table of a given sequence counter using T flip-flops.

Step 4. Also, Obtain the minimal expressions

- From excitation table, T
_{1}= 1. - K – Maps for excitations T
_{3}and T_{2.}

**Design a synchronous BCD counter with JK flip-flops**

Step 1. Number of flip-flops

- A BCD counter requires 4 flip-flops. The counting sequence is 0000, 0001, 0010, 0011, 0100, 0101, 0110, 0111, 1000, 1001, 0000…

Step 2.Now, Draw the state diagram

Step 3. Moreover, Select the type of flip-flops and draw the excitation table

- J-K flip-flops are selected and the excitation table of a given sequence counter using J-K flip-flops.

Step 4. Also, Obtain the minimal expressions

- Also, From excitation table, it is clear that J
_{1 }= K_{1}= 1 - K – Maps for excitations J
_{4}, K_{4}, J_{3}, K_{3}, J_{2}, K_{2}, J_{1}and K_{1}and their minimized form.

**Related Terms**

Digital Electronics, Full Subtractor Circuit, General model, Full Adder Circuit, **Design of synchronous counters**

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