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
- Draw the circuit diagram for a 4-bit Johnson counter.
- List the sequence of states for a 3-bit Johnson counter.
- Explain how a Johnson counter can be used as a timing or sequencing element in digital circuits.
References
- Digital Design by Morris Mano
- Johnson Counter Tutorial