A Johnson counter, also known as a rotating or circular shift register, is a digital sequential logic circuit used for generating a continuous cyclic sequence of binary values. It's a type of shift register that has a feedback loop, allowing the shifted data to be cycled back to the input. Johnson counters are often used in various applications like LED displays, frequency dividers, and pseudorandom number generators.
The basic principle behind a Johnson counter's shifting pattern is that it follows a cyclic pattern of states where only one bit changes at a time, resulting in a smooth transition from one state to another. This cyclic behavior is achieved through a combination of flip-flops and feedback connections.
Here's a simple explanation of how a 4-bit Johnson counter (also known as a 4-bit ring counter) works:
Initialization: At the beginning, all the flip-flops are set to a specific state, either all 0s or all 1s.
Shifting Pattern: Each clock pulse shifts the entire sequence by one bit position in a circular manner, with the last bit looping back to the first bit. This creates a smooth transition from one state to the next.
Feedback: The key aspect that enables the cyclic behavior is the feedback connection. The output of the last flip-flop is connected to the input of the first flip-flop. This ensures that the shifted-out bit is fed back into the input, creating a circular loop.
Pattern Sequence: The sequence of states created by a Johnson counter is a binary sequence where each bit is the complement of the previous bit. For example, if the initial state is 0000, the next state will be 1000, then 1100, 1110, and so on. The pattern loops after reaching the final state.
Here's the shifting pattern for a 4-bit Johnson counter with an initial state of 0000:
Clock Cycle State
1 0000
2 1000
3 1100
4 1110
5 1111
6 0111