Page 52 - Computer science 868 Class 12
P. 52

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:


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