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Answer (Detailed Solution Below)

Option 1 : B'D' + BD (B'D' + BD)

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Detailed Solution

सही उत्तर B'D' + BD (B'D' + BD) है।

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PrepSnapprepsnap.in • Part -A

Question:

For the Boolean function F(A, B, C, D) = Σm(0, 2, 5, 7, 8, 10, 13, 15), what is the minimized sum-of-products form? / बूलियन फलन F(A, B, C, D) = Σm(0, 2, 5, 7, 8, 10, 13, 15) का न्यूनीकृत SOP रूप क्या है?

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B'D' + BD (B'D' + BD)
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B'D' + B'D (B'D' + B'D)
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B'D + BD' (B'D + BD')
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B'C' + BC (B'C' + BC)

Correct Answer: B'D' + BD (B'D' + BD)

Minterms {0, 2, 8, 10} differ only in A and C, giving B'D', and {5, 7, 13, 15} differ only in A and C, giving BD; hence F = B'D' + BD (XNOR of B and D). The tempting B'D + BD' is the XOR pattern — the exact complement of the correct function. / {0, 2, 8, 10} केवल A और C में भिन्न हैं, अतः B'D'; {5, 7, 13, 15} से BD मिलता है — F = B'D' + BD (B और D का XNOR)। B'D + BD' वाला विकल्प XOR पैटर्न है, अर्थात् सही फलन का पूरक — यही भ्रम है।

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