# GATE | GATE CS Mock 2018 | Question 60

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

Explanation: Correct statements are :
S1 : The Hamming distance of an Overbeck counter is 2 and the Hamming distance of a Johnson counter is 1.
S2 : Output sequence 0, 8, 12, 14, 15, 7, 3, 1, 0, … is possible in Johnson counter and output sequence 2, 1, 8, 4, 2, 1, … is possible in Overbeck counter.
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.

So, option (A) is correct.

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