A Johnson counter, also known as a twisted ring counter or a walking ring counter, is a type of digital sequential circuit used in digital electronics. It is a modification of the traditional ring counter, and its primary characteristic is that the pattern of shifting bits is such that only one bit changes its state at a time during each clock cycle.
In a Johnson counter, the output of each flip-flop is connected to both the clock input of the next flip-flop and the complement (inverted) input of the previous flip-flop in the sequence. This interconnection creates a shifting pattern that allows the counter to cycle through a sequence of states in a continuous loop.
The number of states in a Johnson counter is equal to twice the number of flip-flops used. For an 'n'-stage Johnson counter, there are '2n' states, and it requires 'n' flip-flops. The initial state can be set arbitrarily, but only half of the states (n) are unique, while the other half are simply the complements of the unique states.
For example, let's consider a 4-stage Johnson counter with flip-flops labeled A, B, C, and D. Initially, the counter might be set to a specific state, say A=0, B=0, C=0, D=1. The shifting pattern in this case would be as follows:
State: A=0, B=0, C=0, D=1
State: A=1, B=0, C=0, D=1
State: A=1, B=1, C=0, D=1
State: A=1, B=1, C=1, D=1
State: A=1, B=1, C=1, D=0
State: A=1, B=1, C=0, D=0
State: A=1, B=0, C=0, D=0
State: A=0, B=0, C=0, D=0
The shifting pattern continues to cycle through these eight states repeatedly. As you can see, at each clock pulse, only one bit changes its state, making it a "1" or a "0" as it moves through the sequence.
Johnson counters find applications in various areas, such as frequency division, generating timing signals, or providing control signals for sequential logic circuits. They are particularly useful in situations where a low-speed division of clock frequency is required and where the one-bit shift at a time pattern is advantageous.