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GATE 2012 CS (CS1) – Question 40

Digital Logic · Boolean Algebra and Minimization · 2 marks · Multiple choice

Minimize the shown four-variable Karnaugh map. X marks don’t-care cells; blank cells are zeros.

Diagram for GATE 2012 CS (CS1) question 40
  1. $\bar b\bar d$
  2. $\bar b\bar d+\bar b\bar c$
  3. $\bar b\bar d+a\bar b\bar c d$
  4. $\bar b\bar d+\bar b\bar c+\bar c\bar d$

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Show answer and explanation

Correct answer: (B) $\bar b\bar d+\bar b\bar c$

Explanation

Use the wraparound group over columns ab=00,10 and rows cd=00,10, including a don’t-care, to obtain b̄d̄. The remaining one at ab=10,cd=01 joins the top-left wraparound group across rows 00,01, giving b̄c̄. The cover is $\bar b\bar d+\bar b\bar c$, B.

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