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GATE | GATE-CS-2003 | Question 90

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  • Difficulty Level : Medium
  • Last Updated : 22 Feb, 2022
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The literal count of a boolean expression is the sum of the number of times each literal appears in the expression. For example, the literal count of (xy + xz’) is 4. What are the minimum possible literal counts of the product-of-sum and sum-of-product representations respectively of the function given by the following Karnaugh map ? Here, X denotes “don’t care”

(A) (11, 9)
(B) (9, 13)
(C) (9, 10)
(D) (11, 11)

Answer: (C)

Explanation: Analyzing both POS as well as SOP


Sop- wy+w’y’+z’wx’+xyz’

Literal count=10

Pos— (w’+z’)(x’+y)(z+w+x)(z’+y’)

Literal count=9

So, option (C) is correct.

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