n-bit Johnson Counter in Digital Logic

Prerequisite - Counters 

Johnson counter also known as creeping counter, is an example of synchronous counter. In Johnson counter, the complemented output of last flip flop is connected to input of first flip flop and to implement n-bit Johnson counter we require n flip-flop. It is one of the most important type of shift register counter. It is formed by the feedback of the output to its own input. Johnson counter is a ring with an inversion. Another name of Johnson counter are creeping counter, twisted ring counter, walking counter, mobile counter and switch tail counter. 

What is Johnson Counter?

A Johnson counter is a type of a synchronous counter with a special counting pattern in this case being Johnson counter. It operates by the complemented output of the last flip flop feed back into the input of the first flip flop. What results from this setup is a series of states which forms a sequence that is not characteristic of normal ring counters.

The Johnson counter can be implemented using n flip flops to count 2n distinct states – a feature that makes it better than a ring counter that uses an equal number of flip flops, as it serves twice the number of states. This counter is used in applications where the number of states is higher than the number of flip-flops; besides, it has a distinguishing feature of self-decodability.

Total number of used and unused states in n-bit Johnson counter: 
number of used states=2n 
number of unused states=2ⁿ - 2*n 
 
Example: 
If n=4 
4-bit Johnson counter 

Initially, suppose all flip-flops are reset. 

 

Truth Table

where, 
CP is clock pulse and 
Q1, Q2, Q3, Q4 are the states. 

Question: Determine the total number of used and unused states in 4-bit Johnson counter. 

Answer: Total number of used states= 2*n 
= 2*4 
= 8 
Total number of unused states= 2ⁿ - 2*n 
= 2⁴-2*4 
= 8 

Difference Between Ring Counter and Johnson Counter

Advantages of Johnson counter

• The Johnson counter has same number of flip flop but it can count twice the number of states the ring counter can count.
• It can be implemented using D and JK flip flop.
• Johnson ring counter is used to count the data in a continuous loop.
• Johnson counter is a self-decoding circuit.

Disadvantages of Johnson counter

• Johnson counter doesn't count in a binary sequence.
• In Johnson counter more number of states remain unutilized than the number of states being utilized.
• The number of flip flops needed is one half the number of timing signals.
• It can be constructed for any number of timing sequence.

Applications of Johnson counter

• Johnson counter is used as a synchronous decade counter or divider circuit.
• It is used in hardware logic design to create complicated Finite states machine. ex: ASIC and FPGA design.
• The 3 stage Johnson counter is used as a 3 phase square wave generator which produces 1200 phase shift.
• It is used to divide the frequency of the clock signal by varying their feedback.

Conclusion

This article has covered a number of aspects of Johnson counters ranging from how the system operates to the benefits of using the technology as well as shortcomings of the Johnson counters. Johnson counters are a subtype of shift register counter and they are capable of counting twice more states than a ring counter with similar flip flops. It can be seen that the fundamental differences between the ring counters and Johnson counters have been discussed above which can be used in selecting the proper counter circuits for certain digital circuit applications.