A Johnson counter, also known as a Möbius counter, is a type of digital counter circuit that operates by sequentially shifting a single "1" bit (high voltage level) through a series of flip-flops or shift registers. Unlike traditional binary counters where each stage represents a binary digit (0 or 1), the Johnson counter's stages represent a sequence of states that are cyclically shifted. This results in a circular pattern of high and low states as the counter progresses.
The shifting pattern of a Johnson counter follows a distinct sequence, also known as a "Johnson sequence" or "Möbius sequence." For an n-stage Johnson counter, there are 2^n possible states. The pattern is designed in such a way that only one bit changes its state at a time, and it repeats after every n clock cycles.
Here's a step-by-step explanation of the shifting pattern for a 4-stage Johnson counter (also called a 4-bit Johnson counter):
Initial State: All stages are set to low (0): 0000.
First Shift: The rightmost stage (LSB) is set to high (1), and all other stages are low: 0001.
Second Shift: The previous high bit shifts one position to the left, and the LSB becomes low: 0010.
Third Shift: The previous high bit shifts again, and the LSB becomes high: 0110.
Fourth Shift: The previous high bit shifts, and the LSB becomes low: 0100.
Fifth Shift: The previous high bit shifts, and the LSB becomes high again: 1100.
Sixth Shift: The previous high bit shifts, and the LSB becomes low: 1000.
Seventh Shift: The previous high bit shifts, and the LSB becomes high again, completing the cycle: 0001.
The above sequence illustrates the shifting pattern of a 4-stage Johnson counter. As you can see, only one bit changes its state in each shift, and the pattern repeats after every 4 shifts (since it's a 4-stage counter). This pattern is widely used in various applications such as frequency division, digital displays, and generating pseudo-random sequences.
It's important to note that the shifting pattern described here is for a specific counter size (4-stage). The pattern varies based on the number of stages in the Johnson counter. For an n-stage counter, the sequence will repeat after every n shifts.