Let ݇\(k = 2^n\). A circuit is built by giving the output of an ݊\(n\)-bit…

2014

Let ݇\(k = 2^n\). A circuit is built by giving the output of an ݊\(n\)-bit binary counter as input to an ݊\(n\)-to-\(2^n\) bit decoder. This circuit is equivalent to a

  1. A.

    \(k\)݇-bit binary up counter.

  2. B.

    \(k\)݇-bit binary down counter.

  3. C.

    \(k\)݇-bit ring counter.

  4. D.

    \(k\)݇-bit Johnson counter.

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Correct answer: C

Key insight: the n-bit counter cycles through 2^n binary values and the decoder converts each binary value into a single active output (one-hot).

  • The n-bit binary counter generates the sequence of binary numbers 0 to 2^n - 1.

  • The n-to-2^n decoder maps each binary number to exactly one of k = 2^n outputs being high (one-hot encoding).

  • As the counter increments, the single high output moves through the k outputs in a repeating sequence, which is the defining behaviour of a k-bit ring counter.

Short elimination of other choices:

  • A binary up or down counter outputs n-bit binary codes, not a one-hot 2^n-line sequence.

  • A Johnson counter produces 2n states with characteristic multi-bit patterns, not the 2^n one-hot rotation produced here.

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