Johnson Counter

Johnson Counter

Overview

The Johnson counter, also known as the twisted ring counter, is a type of shift register with a feedback loop that produces a unique counting sequence. For an n-bit counter, it cycles through 2n distinct states. Johnson counters are used for digital timing, state machine design, and as sequence generators in digital systems.

Detailed Explanation

Principle of Operation

- A standard n-bit shift register is modified so that the complement of the last flip-flop’s output is fed back to the input.
- This “twisted” configuration produces a sequence that is twice the number of bits.

Example (4-bit Johnson Counter):
States: 0000, 1000, 1100, 1110, 1111, 0111, 0011, 0001 then back to 0000.

Circuit Implementation

1. Construct a 4-bit shift register with D flip-flops.
2. Connect Q' (complement) of the last flip-flop to the D input of the first flip-flop.
3. All flip-flops are clocked simultaneously.

Timing and State Transition

A state table:
State (Q3 Q2 Q1 Q0) | Next State
--------------------|-----------
0000                | 1000
1000                | 1100
1100                | 1110
1110                | 1111
1111                | 0111
0111                | 0011
0011                | 0001
0001                | 0000

Practice Problems

  1. Draw the circuit diagram for a 4-bit Johnson counter.
  2. List the sequence of states for a 3-bit Johnson counter.
  3. Explain how a Johnson counter can be used as a timing or sequencing element in digital circuits.

References

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