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”.
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)
(GATE 2003)
Answer: (C) (9, 10)
Explanation:
Sum-of-product (SOP) = WY + W'Y' + Z'WX' + XYZ'
Therefore, literal count = 10
Product-of-sum (POS) = (Y' + Z')(W' + Z')(Z' + Y)(X + Z + W)
Therefore, linteral count = 9
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