GATE EC 2018 Set 1 — Question 19
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Digital Circuits → Combinational Logic → Canonical SOP & POS
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Question
A function
F(A, B, C) defined by three Boolean variables , and when expressed as sum of products is given bywhere, , , and are the complements of the respective variables. The product of sums (POS) form of the function isCorrect answer
(C) F = (A + B + C) · (A + B + C) · (A + B + C) · (A + B + C) · (A + B + C)
Solution
The given sum of products (SOP) expression is:
In minterm notation, this corresponds to:
The product of sums (POS) form consists of the maxterms whose indices are not present in the SOP form. For a 3-variable function, the indices are . The missing indices are .Thus, .Converting these indices to maxterm expressions:
In minterm notation, this corresponds to:
The product of sums (POS) form consists of the maxterms whose indices are not present in the SOP form. For a 3-variable function, the indices are . The missing indices are .Thus, .Converting these indices to maxterm expressions:
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