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GATE CS 2011 · Digital Logic

Question 15

MCQPrinted as CS Q.151 markWrong answer: −1/3Easy (estimate)

Question

The minimum number of D flip-flops needed to design a mod-258 counter is

Choose one option
Official answer and solution
Official answer
A
From
Official GATE 2011 answer key

Solution

Determine the minimum number of binary state elements required to represent 258 distinct counter states.

  1. A modulo-NN counter must sequence through NN unique internal states.
  1. A counter constructed from nn flip-flops can represent at most 2n2^n distinct states.
  1. For N=258N = 258, we need 2n−1<258≤2n2^{n-1} < 258 \le 2^n.
  1. Since 28=256<2582^8 = 256 < 258 and 29=512≥2582^9 = 512 \ge 258, 8 flip-flops are insufficient to represent 258 states. Therefore, a minimum of 9 flip-flops is required.
Final answer

A

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper
GATE 2011 Computer Science and Information Technology (CS)
Question
15 of 65, printed as CS Q.15
Section
Computer Science and Information Technology

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