Define a Johnson counter and its unique shifting pattern.
1 Answer
A Johnson counter, also known as a twisted ring counter or walking ring counter, is a type of digital counter circuit used in digital electronics and sequential logic circuits. It is designed to cycle through a predetermined sequence of binary states, making it useful for applications like generating repetitive patterns, controlling LED displays, or generating clock signals with specific phase relationships.
The unique shifting pattern of a Johnson counter involves shifting the "1" bit in a cyclic manner through a series of flip-flops or other bistable elements. The sequence is designed in such a way that only one flip-flop is set to "1" at any given time, while the others are set to "0." When the counter progresses, the "1" bit moves to the next flip-flop, creating a circular motion.
The most common type of Johnson counter is the 4-bit Johnson counter, also known as a 4-bit twisted ring counter. It has four flip-flops, and its unique shifting pattern follows the sequence: 0001, 0010, 0100, 1000, and then back to 0001. This shifting pattern can be visualized as follows:
yaml
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Cycle: 0001 -> 0010 -> 0100 -> 1000 -> 0001
Bit #: 1 2 3 4 1
Each step of the cycle shifts the "1" bit to the next position, forming a circular movement. This pattern is created by using exclusive OR (XOR) gates to connect the outputs of the flip-flops to each other in a way that implements this cyclic shift behavior.
Johnson counters can be implemented with different numbers of flip-flops to create longer or shorter shifting patterns, but the key characteristic remains the same: a cyclic progression of the "1" bit through the flip-flops.
The unique shifting pattern of a Johnson counter involves shifting the "1" bit in a cyclic manner through a series of flip-flops or other bistable elements. The sequence is designed in such a way that only one flip-flop is set to "1" at any given time, while the others are set to "0." When the counter progresses, the "1" bit moves to the next flip-flop, creating a circular motion.
The most common type of Johnson counter is the 4-bit Johnson counter, also known as a 4-bit twisted ring counter. It has four flip-flops, and its unique shifting pattern follows the sequence: 0001, 0010, 0100, 1000, and then back to 0001. This shifting pattern can be visualized as follows:
yaml
Copy code
Cycle: 0001 -> 0010 -> 0100 -> 1000 -> 0001
Bit #: 1 2 3 4 1
Each step of the cycle shifts the "1" bit to the next position, forming a circular movement. This pattern is created by using exclusive OR (XOR) gates to connect the outputs of the flip-flops to each other in a way that implements this cyclic shift behavior.
Johnson counters can be implemented with different numbers of flip-flops to create longer or shorter shifting patterns, but the key characteristic remains the same: a cyclic progression of the "1" bit through the flip-flops.