GATE CS Mock 2018 | Question 60 | GFG

Question

Consider the following statements regarding counters:

S1 : The Hamming distance of an Overbeck counter is $1$. and the Hamming distance of a Johnson counter is $2$.

S2 : Only output sequence $0, 8, 12, 14, 15, 7, 3, 1, 0, ...$ is possible  in Overbeck counter but not output sequence $2, 1, 8, 4, 2, 1, …$

S3 : A binary counter can represent $2^N$ states, where $N$ is the number of bits in the code, whereas an Overbeck counter can represent only $N$ states  and a Johnson counter can represent only $2N$ states.

(A) Only S1, S2 are false and S3 is true

(B) Only S2, S3 are false and S1 is true

(C) Only S1, S3 are false and S2 is true

(D) All S1, S2, and S3 are true

Answer 1

The answer is (A) Only S1, S2 are false and S3 is true.

S1 (False):

• The Hamming distance of an Overbeck counter is $2$, not $1$.
• This means that each successive state in the counter's sequence differs by $2$ bits, not $1$.
• The Hamming distance of a Johnson counter is $1$, not $2$.
• Adjacent states in a Johnson counter differ by only $1$ bit.

S2 (False):

• Both output sequences mentioned ($0, 8, 12, ...$ and $2, 1, 8, ...$) are possible in an Overbeck counter.
• The specific sequence depends on the initial state of the counter.

S3 (True):

• A binary counter with $N$ bits can represent $2^N$ unique states.
• An Overbeck counter with $N$ flip-flops can represent only $N$ distinct states.
• This is because it doesn't utilize all possible $2^N$ combinations of states.
• A Johnson counter with $N$ flip-flops can represent $2N$ states.
• It uses a unique feedback configuration to achieve this.