A Johnson counter, also known as a twisted-ring counter or Möbius counter, is a type of digital sequential circuit used in digital electronics and digital signal processing. It's a modification of a traditional ring counter, where the output of each flip-flop is connected to the input of the next flip-flop in a circular manner. The unique feature of a Johnson counter is its shifting pattern, which creates a continuous and cyclic sequence of 0s and 1s.
In a Johnson counter, the outputs of the flip-flops are combined in such a way that only one flip-flop changes state at a time, creating a shifting or rotating effect. This results in a distinctive sequence of binary values, either in a clockwise or counter-clockwise direction. The shifting pattern for a 4-bit Johnson counter, for instance, can be as follows:
Clockwise shifting:
0000
1000
1100
1110
1111
0111
0011
0001
Counter-clockwise shifting:
0000
0001
0011
0111
1111
1110
1100
1000
As you can see, in the clockwise shifting pattern, the sequence moves from all 0s to all 1s, while in the counter-clockwise shifting pattern, it moves from all 0s to a single 1 and then back to all 0s.
Johnson counters find applications in various areas such as shift register implementations, frequency dividers, ring oscillators, and some types of rotating displays. The unique shifting pattern makes them useful for generating patterns that can be used for synchronization, pattern recognition, and other sequential logic operations.