45. Ring Counters and Johnson Counters

These are specialized types of shift registers configured to act as sequence generators, often used in control systems.

1. Ring Counter (Circular Shift Register)

• Structure: An N-bit shift register where the output of the last FF ($Q_{N-1}$) is fed back to the input of the first FF ($D_0$).
• Operation: Requires initialization (e.g., 1000).
• Sequence: The single '1' bit circulates around the ring (1000, 0100, 0010, 0001, repeat).
• Modulus: MOD-N (N distinct states).
• Advantage: Self-decoding. The state is read directly from $Q_i$, eliminating the need for an external decoder.

2. Johnson Counter (Twisted Ring Counter)

• Structure: Similar to a ring counter, but the complement of the last output ($\overline{Q_{N-1}}$) is fed back to the input of the first FF ($D_0$).
• Sequence (4-bit example): 0000, 1000, 1100, 1110, 1111, 0111, 0011, 0001, 0000.
• Modulus: MOD-2N (Twice the number of states as a simple ring counter).

Johnson counters are also self-decoding and offer a greater sequence length than ring counters for the same number of FFs.