Design counter for given sequence
Last Updated : 13 Sep, 2024
A Counter is a device which stores (and sometimes displays) the number of times a particular event or process has occurred, often in relationship to a clock signal. Counters are used in digital electronics for counting purpose, they can count specific event happening in the circuit. For example, in UP counter a counter increases count for every rising edge of clock.
What is Counter?
Counter is a sequential circuit implemented via flip flops. They are used to count the number of clock signals or pulse. A mod n counter will count from 0 to n-1.
Counters can be synchronous or unsynchronous. In synchronous counter, a single common clock is used for all the flip flops. Whereas in asynchronous counter, only a clock is given as input for first flip flop. For an intermediate or final flip flops, its clock pulse will be the output of previous flip flop.
Problem - Design synchronous counter for sequence: 0 → 1 → 3 → 4 → 5 → 7 → 0, using T flip-flop. Explanation - For given sequence, state transition diagram as following below: 
State transition Table logic
| Present State | Next State |
|---|
| 0 | 1 |
| 1 | 3 |
| 3 | 4 |
| 4 | 5 |
| 5 | 7 |
| 7 | 0 |
State transition table for given sequence
| Present State | Next State |
|---|
| Q3 | Q2 | Q1 | Q3(t+1) | Q2(t+1) | Q1(t+1) |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 1 | 0 | 0 |
| 1 | 0 | 0 | 1 | 0 | 1 |
| 1 | 0 | 1 | 1 | 1 | 1 |
| 1 | 1 | 1 | 0 | 0 | 0 |
T flip-flop - If value of Q changes either from 0 to 1 or from 1 to 0 then input for T flip-flop is 1 else input value is 0.
Draw input table of all T flip-flops by using the excitation table of T flip-flop. As nature of T flip-flop is toggle in nature. Here, Q3 as Most significant bit and Q1 as least significant bit.
| Input table of Flip-Flops |
|---|
| T3 | T2 | T1 | |
| 0 | 0 | 1 | |
| 0 | 1 | 0 | |
| 1 | 1 | 1 | |
| 0 | 0 | 1 | |
| 0 | 1 | 0 | |
| 1 | 1 | 1 | |
Find value of T3, T2, T1 in terms of Q3, Q2, Q1 using K-Map (Karnaugh Map): 
Therefore,
T3 = Q2
Therefore,
T2 = Q1
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K map
Therefore,
T1 = Q2+Q1'
Now, you can design required circuit using expressions of K-maps: 
Advantages of Counters
- Counters can be use for measuring time. E.g. Elapsed time, Response time, etc.
- They can be used in real time system
- They are easy to implement and cost effective
Disadvantages of Counters
- The hazards and delay in flip-flop can create error
- Different digital circuit are to be realized for different value of n and type of flip flop used in n-mod counter
Conclusion
To design a counter for given sequence, we must first design the state transition diagram and table. And then we have to chose the type and number of flip flops. We have to find the excitation table for the same. And we have to simply the equation using K-map or Quine McCluskey (tabular) Method.
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