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GATE IT 2006 | Question: 35

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The boolean function for a combinational circuit with four inputs is represented by the following Karnaugh map.

Which of the product terms given below is an essential prime implicant of the function?

  1. $\text{QRS}$
  2. $\text{PQS}$
  3. $\text{PQ'S'}$
  4. $\text{Q'S'}$
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Only the top leftmost and bottom rightmost $1s$ have no alternate groupings. So, they form the essential prime implicants.

Answer is D. $Q'S'$

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Essential prime implicants which $r$ grouped only by only one method or way,

So, in above question cornor's ones r grouped by only one method,

d ) will be the answer.

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