Page 52 - Computer science 868 Class 12
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8. a. Given the Boolean function F(A, B, C, D) = Σ(2, 3, 4, 5, 6, 7, 8, 10, 11).
Reduce the above expression by using a 4-variable Karnaugh map, showing the various groups (i.e., octals, quads and pairs).
b. Given the Boolean function F(P, Q, R, S) = π(0, 1, 2, 4, 5, 6, 8, 10).
Reduce the above expression by using a 4-variable Karnaugh map, showing the various groups (i.e., octals, quads and pairs).
[ISC 2017]
9. a. Given the Boolean function F(A, B, C, D) = Σ(1, 3, 5, 7, 8, 9, 10, 11, 14, 15).
Reduce the above expression by using a 4-variable Karnaugh map, showing the various groups (i.e., octals, quads and pairs).
b. Given the Boolean function F(P, Q, R, S) = π(4, 6, 7, 10, 11, 12, 14, 15).
Reduce the above expression by using a 4-variable Karnaugh map, showing the various groups (i.e., octals, quads and pairs).
[ISC 2016]
#Problem Solving & Logical Reasoning
#Coding & Computational Thinking
Previous Years' Questions
1. (i) According to De Morgan’s law (a + b + c')' will be equal to: [ISC 2023]
(a) a' + b' + c' (b) a' + b' + c
(c) a' . b' . c' (d) a' . b' . c
Ans. (d) a' . b' . c
Explanation: a'.b'.c (Using De Morgan’s Law of (A+B)' = A' . B')
(ii) The dual of (X' + 1) . (Y' + 0) = Y' is: [ISC 2023]
(a) X . 0 + Y . 1 = Y (b) X' . 1 + Y' . 0 = Y'
(c) X' . 0 + Y' . 1 = Y' (d) (X' + 0) + (Y' + 1) = Y'
Ans. (c) X' . 0 + Y' . 1 = Y'
Explanation: X'.0 + Y'.1 = Y' Principle of duality states that each Boolean expression has its dual expression which can be obtained
by replacing:
• AND (.) with OR (+) or OR (+) with AND (.)
• 0 with 1 or 1 with 0
• Complements remain unchanged
(iii) The reduced expression of the Boolean function F(P, Q) = P' + PQ is: [ISC 2023]
(a) P' + Q (b) P
(c) P' (d) P + Q
Ans. (a) P’ + Q
Explanation: P' + PQ
= (P' + P)(P' + Q)
= 1.(P' + Q)
= P' + Q
(iv) If (∼p => ~q) then its contrapositive will be: [ISC 2023]
(a) p => q (b) q => p
(c) ∼q => p (d) ∼p => q
Ans. (b) q => p
Explanation: q => p (The contrapositive of a conditional is obtained by interchanging the complemented antecedent with
the complemented consequent of that conditional. It is equivalent to the converse of the inverse of that conditional. For any
conditional a → b, its contrapositive will be b' → a'.
2. Write the minterm of F(A, B, C, D) when A = 1, B = 0, C = 0 and D = 1. [ISC 2023]
Ans. minterm of F(A, B, C, D) when A = 1, B = 0, C = 0 and D = 1 is A.B'.C'.D.
3. Verify if (A + A')' is a Tautology, Contradiction, or a Contingency. [ISC 2023]
Ans. (A + A')'
= A'.A"
= A'.A
= 0
Hence, it is a contradiction. Following is the truth table of the above expression:
5050 Touchpad Computer Science-XII

