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NIMCET 2023 Computer PYQ — Consider the following minterm expression for F:F(P, Q , R, S) = … | Mathem Solvex | Mathem Solvex

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NIMCET 2023 — Computer PYQ

NIMCET | Computer | 2023

Consider the following minterm expression for F:F(P, Q , R, S) = $\sum (0, 2, 5, 7, 8, 10, 13, 15)$ . The minterms 2, 7, 8 and 13 are don’t care terms. The minimum sum of products form for F is

Choose the correct answer:

A.
$\overline{Q} S + Q \overline{S}$
B.
$\overline{Q} \overline{S} + QS$

Correct Answer:

$\overline{Q} R S + \overline{Q} R \overline{S} + Q \overline{R} S + QR S$

Explanation

While putting the terms to $K$ -map following things happen,
- 3rd and 4th columns are swapped

- 3rd and 4th rows,
- term 2 is going to (0,3) column instead of (0,2)
- 8 is going to (3,0) instead of (2,0)

Solving, the above K-map. we get $\overset{ˉ}{Q} S + QS$

Explanation

While putting the terms to $K$ -map following things happen,
- 3rd and 4th columns are swapped

- 3rd and 4th rows,
- term 2 is going to (0,3) column instead of (0,2)
- 8 is going to (3,0) instead of (2,0)

Solving, the above K-map. we get $\overset{ˉ}{Q} S + QS$

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C.
$\overline{Q} R S + \overline{Q} R \overline{S} + Q \overline{R} S + QR S$
(Correct Answer)

D.
$\overline{P} \overline{Q} \overline{S} + \overline{P} QS + P QS + P \overline{Q} \overline{S}$