In an 8 -bit Johnson counter sequence, how many states orbit patterns ...
Explanation:
To calculate the number of states or bit patterns in an 8-bit Johnson counter sequence, we need to understand the concept of a Johnson counter and its sequence.
A Johnson counter is a modified version of a ring counter. It is a sequential circuit that cycles through a fixed sequence of states. In an 8-bit Johnson counter, there are 8 flip-flops connected in a ring, forming a circular shift register.
Johnson Counter Sequence:
The sequence of states in a Johnson counter follows a specific pattern. It starts with all bits set to 0 and then cycles through a sequence of 2^n - 1 states, where n is the number of bits in the counter.
In an 8-bit Johnson counter, the sequence will have 2^8 - 1 = 255 states. However, we need to exclude the initial state (all bits set to 0) from the count.
Therefore, the number of states in the Johnson counter sequence is 255 - 1 = 254.
Orbit Patterns:
An orbit pattern is a subset of the Johnson counter sequence that represents a complete cycle or loop. It starts and ends at the same state.
To calculate the number of orbit patterns, we need to find the number of states in each orbit pattern. In an 8-bit Johnson counter, each orbit pattern will have 8 states, as it takes 8 clock cycles for the counter to return to its initial state.
The total number of possible orbit patterns can be calculated by dividing the total number of states in the Johnson counter sequence by the number of states in each orbit pattern.
Total number of states = 254
Number of states in each orbit pattern = 8
Number of orbit patterns = Total number of states / Number of states in each orbit pattern
= 254 / 8
= 31.75
Since the number of orbit patterns cannot be a fraction, we round it down to the nearest whole number.
Therefore, the number of orbit patterns in an 8-bit Johnson counter sequence is 31.
Conclusion:
The correct answer is option A) 240.
In an 8 -bit Johnson counter sequence, how many states orbit patterns ...
As we know, the total number of states in the Jhonson counter is determined by the given formula
2N = 2 8= 256
Now,
the total number of used states = 2N = 2* 8 = 16
therefore, the total number of unused states = 256-16 = 240