Page 663 - Computer science 868 Class 12
P. 663

(b)   Given F(P, Q, R, S) = Π(1, 3, 4,5,6, 7, 9, 11, 12, 13, 14, 15)
                         (i)  Reduce the above expression by using 4 variable Karnaugh map, showing the various groups (,i.e., octal, quads and pairs).   [4]
                        Ans.
                                   R+S     R+S'    R'+S'   R'+S
                            P+Q    0 0     0 1     1 3     0 2
                            P+Q'   0 4     0 5     0 7     0 6
                            P'+Q'   0    12   0    13   0    15   0    14
                            P'+Q   0 8     0 9      0    11   1    10

                        Octet 1: M1.M3. M5.M7. M12.M13.M14.M15 = S’
                        Octet 2: M4.M5. M6.M7 .M12.M13.M14.M15 = Q’
                        Reduced POS expression : Q’.S’
                         (ii)   Draw the Logic gate diagram of the reduced expression using gates. AND/OR gates. Assume that the variables and it’s
                           complements are available as inputs.                                                        [1]

                        Ans.  Q'           Q'.S
                            S'


                 Question 4.                                                                                           [5]
                      (a)   The owner of a company pays the bonus to his salesmen as per the criteria are given below:
                           If the salesman sells product worth Rs 500000 per month but  is not  involved in advertising and marketing of the product.
                                                                    OR
                          If the salesman works on an off day/holiday and is involved in advertising and marketing of the product.
                                                                    OR
                          If the salesman works on an off day/holiday and when the festival sales are on.
                          The inputs are:
                                  INPUTS
                                     P            Sells product worth Rs 500000  per month
                                     F            Works when festival sales are on
                                    H             Working on an off day/holiday
                                     A             Involved in advertising and marketing of the product
                          (In all the above cases 1 indicates yes and 0 indicates no)
                          Output: X [1 indicates yes, 0 indicates no for all cases]
                          Draw the truth table for the inputs and outputs given above and write the POS expression for X(P, F, H, A).
                    Ans.

                             P        F        H        A        X     Maxterm
                             0        0        0        0        0       M0
                             0        0        0        1        0       M 1
                             0        0        1        0        0       M 2
                             0        0        1        1        1       M 3
                             0        1        0        0        0       M 4
                             0        1        0        1        0       M 5
                             0        1        1        0        1       M 6
                             0        1        1        1        1       M 7
                             1        0        0        0        1       M 8
                             1        0        0        1        0       M 9
                             1        0        1        0        1      M 10
                             1        0        1        1        1      M 11




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