Page 55 - Computer science 868 Class 12
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Or
                       •   The student is a graduate in Mass Communication with an aggregate percentage of 75 or above but has no record of literary
                        skills.
                                                                    Or
                       •   The student is a graduate in Mass Communication and with a record of literary skills but does not have an aggregate
                        percentage of 75 or above.
                       The inputs are:
                           Inputs
                             G        Graduate in any discipline
                             M        Graduate in Mass Communication
                             P        Aggregate percentage of 75 and above
                             S        Record of Literary Skills
                       (In all the above cases 1 indicates yes and 0 indicates no).
                       Output: X   [1 indicates eligible and 0 indicates not eligible for all cases).
                       Draw the truth table for the inputs and outputs given above and answer the following questions:
                       Truth tables are not drawn in the answer
                       (i)  What will be the SOP expression for X(G,M,P,S)?                                      [ISC 2022]
                          (a)  Σ(5,6,11,13,14,15)                          (b)  Π(5,6,11,13,14,15)
                          (c)  Σ(0,1,2,3,4,7,8,9,10,12)                    (d)  Π(0,1,2,3,4,7,8,9,10,12)
                   Ans. (a)
                       (ii)  What will be the complement of the above SOP expression?
                          (a)  Σ(5,6,11,13,14,15)                          (b)  Π(5,6,11,13,14,15)
                          (c)  Σ(1,2,3,4,8,9,10,12)                        (d)  Π(0,1,2,3,8,9,10,12)
                   Ans. (d)
                    20. Reduce the given Boolean function F(A,B,C,D) = π(3,4,5,6,7,10,12,13,14,15) by using 4-variable Karnaugh map and answer the
                      following questions.
                       (i)  What will be the least number of groups and its types of formed for reduction?       [ISC 2022]
                          (a)  1 octet and 2 pairs                         (b)  2 quads and 2 pairs
                          (c)  1 octet and 3 pairs                         (d)  4 pairs
                   Ans. (a)
                       (ii)  What is the reduced expression of the Boolean function given above?                 [ISC 2022]
                          (a)  (A'+C').(C'+D).(A'+C'+D).(A+C+D')           (b)  B'.(A'+C'+D).(A+C'+D')
                          (c)  B'.(A'+C').(C'+D')                          (d)  (A'+C'+D).(A+C+D').(A+B'+C)  .(B'+C+D')
                   Ans. (b)
                    21. Given the Boolean expression F = P + ((Q+R).(Q'+S')):                                    [ISC 2022]
                       (i)  Identify the complement of the expression:
                          (a)  P'+(Q'R'+QS)                                (b)  P'.(QR+Q'S')
                          (c)  P'.(Q'.R'+Q.S)                              (d)  P'QR + P'QS
                   Ans. (c)
                      (ii)  De Morgan’s law states that the complement of a sum is equal to:                     [ISC 2022]
                          (a)  the complement of their product             (b)  the product of their individual complements
                          (c)  the sum of their individual complements     (d)  the complement of their sum
                   Ans. (b)
                    22.  State the properties of zero in Boolean algebra.                                        [ISC 2020]
                   Ans.  Properties of zero: A + 0 = A and A • 0 = 0
                    23.  Find the complement of the following Boolean expression using De Morgan’s law:          [ISC 2020]
                        F(P, Q, R) = P + (Q' • R)
                   Ans.  F(P, Q, R) = P + (Q' • R)
                        = ( P + (Q' • R))'
                        = P' • (Q' • R )'
                        = P' • ( Q + R')

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                                                                                                      Boolean Algebra   53
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