A Johnson counter is a type of digital circuit that acts as a shift register, capable of generating a unique shifting pattern of its output states. It is a modification of the more common ring counter, with the key difference being that in a Johnson counter, every flip-flop (stage) is complemented (negated) and connected to the next stage's complement input, creating a circular pattern of complemented outputs.
The unique shifting pattern of a Johnson counter is achieved by its inherent characteristic of toggling through all possible states before returning to its initial state. The pattern generated by a Johnson counter has the property that only one bit changes at a time, creating a sequence that can be useful in various applications such as frequency division, LED display scanning, and generating pseudo-random patterns.
For example, let's consider a 4-bit Johnson counter. The counter will go through the following sequence of states:
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0000 -> 1000 -> 1100 -> 1110 -> 1111 -> 0111 -> 0011 -> 0001 -> 0000
As you can see, only one bit changes at a time in the sequence, and it eventually returns to its initial state after cycling through all possible states.
Johnson counters can be constructed using D-type flip-flops or other types of sequential logic elements. They find applications in various digital systems where controlled and cyclic pattern generation is required. The unique shifting pattern of a Johnson counter makes it a valuable tool in designing circuits for purposes like display multiplexing, frequency division, or generating special control signals.