A Johnson ring counter with N states has _______ flip flops:a)Nb)2Nc)N...
n-bit Johnson ring counter has 2n states.
Thus, if a Johnson counter has n states then the number of flip flops required are N/2.
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A Johnson ring counter with N states has _______ flip flops:a)Nb)2Nc)N...
A Johnson ring counter is a type of shift register that cycles through a sequence of states. It is composed of a series of flip flops connected in a ring configuration, with the output of each flip flop connected to the input of the next flip flop. The counter advances one state at a time in response to a clock signal.
The number of flip flops required in a Johnson ring counter is determined by the number of states it needs to cycle through. Each flip flop represents one state in the counter.
To find the number of flip flops required, we can use the formula:
Number of flip flops = log2(N) + 1
Here, N represents the number of states in the counter.
Explanation:
1. Formula for calculating the number of flip flops:
- The formula for calculating the number of flip flops required in a Johnson ring counter is given by Number of flip flops = log2(N) + 1.
- This formula is derived from the fact that the number of flip flops required is equal to the number of bits needed to represent the maximum count value.
- The maximum count value in a Johnson ring counter is N, so the number of bits required is log2(N).
- Adding 1 to the number of bits accounts for the fact that an additional flip flop is needed to hold the initial state of the counter.
2. Example:
- Let's consider an example where the Johnson ring counter has 8 states.
- Using the formula, Number of flip flops = log2(8) + 1, we can calculate the number of flip flops required.
- log2(8) = 3, so the number of flip flops required is 3 + 1 = 4.
3. Applying the formula to the options:
- The options given are a) N, b) 2N, c) N-1, and d) N/2.
- Substituting N with the number of states in the formula, we can evaluate each option.
- Option a) N: This is not the correct formula for calculating the number of flip flops. It does not account for the additional flip flop needed to hold the initial state.
- Option b) 2N: This formula overestimates the number of flip flops required. It assumes that each state requires two flip flops, which is not the case in a Johnson ring counter.
- Option c) N-1: This formula underestimates the number of flip flops required. It assumes that one flip flop is shared between two states, which is not possible in a Johnson ring counter.
- Option d) N/2: This formula is incorrect. Dividing the number of states by 2 does not give the correct number of flip flops required.
4. Correct answer: Option d) N/2:
- Option d) N/2 is not the correct answer. It does not provide the correct formula for calculating the number of flip flops required in a Johnson ring counter.
- The correct answer is option c) N-1, which represents the formula log2(N) + 1 - 1, accounting for the additional flip flop needed to hold the initial state.
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