A ring counter circulates a bit pattern, often one hot bit, around a register. A Johnson counter feeds the inverse of the last stage back to the first. With a suitable initialized cycle, n stages provide n one-hot ring states or 2n Johnson states.
Worked example
For four stages, a ring cycle is 0001 → 0010 → 0100 → 1000 → 0001. A Johnson cycle using left shift and inverted old MSB is 0000 → 0001 → 0011 → 0111 → 1111 → 1110 → 1100 → 1000 → 0000.
What to watch for
A one-hot ring initialized to all zeros stays at zero. Johnson counters also have states outside the intended cycle, so initialization and recovery matter.
Try it yourself
How many states are in the intended cycle of a three-stage Johnson counter?
Answer: Six. Its ordinary initialized cycle is 000, 001, 011, 111, 110, 100, then back to 000.
How to study this topic
Define the reset state and update rule before tracing a sequence. List several successive states by hand and check the wraparound. Bit direction, enable behavior and illegal-state handling are part of the specification.
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Digital Electronics