Page 60 - Computer science 868 Class 12
P. 60

The inputs are:
                           INPUTS
                             O          Works overtime for more than 4 hours
                             F          Festival sales are on
                             H          Working on an off day/holiday
                             U          Updates showroom arrangements
                     (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(O, F, H, U).
                Ans.        O                F                H                U              OUTPUT
                      Work Ovetime for   Festival sales    Working on an off  Updates showroom
                      more than 4 hours    are on         day/holiday      arrangements
                            0                0                 0                0                0
                            0                0                 0                1                0
                            0                0                 1                0                0
                            0                0                 1                1                0
                            0                1                 0                0                0
                            0                1                 0                1                1
                            0                1                 1                0                1
                            0                1                 1                1                1
                            1                0                 0                0                1
                            1                0                 0                1                1
                            1                0                 1                0                0
                            1                0                 1                1                0
                            1                1                 0                0                1
                            1                1                 0                1                1
                            1                1                 1                0                1
                            1                1                 1                1                1

                     X(O, F, H, U) = π(0,1,2,3,4,10,11)
                 35.  Simplify the following expression, using Boolean laws:                                   [ISC 2019]
                     (X + Z).(X.Y + Y.Z') + X.Z + Y
                Ans.  (X + Z).(X.Y + Y.Z') + X.Z + Y
                     = (X + Z).(Y.Z') + X.Z + Y                     (because a.b = 0)
                     = X.Y.Z' + Z.Z' + X.Z + Y                      (because a.a' = 0) and (a.c = 0)
                     = 0.Z' + 0 + 0 + Y
                     = Y
                 36.  Verify the following proposition with the help of a truth table:                         [ISC 2018]
                     (P ∧ Q) ∨ (P ∧ ∼Q) = P
                Ans.
                        P        Q       P ∧ Q   P ∧ ∼Q   (P ∧ Q) ∨ ( P ∧ ∼Q)
                        0        0        0        0            0
                        0        1        0        0            0
                        1        0        0        1            1
                        1        1        1        0            1

                      The last resultant column has the same combinations of 0 and 1 as that of P (first column). Hence proved.




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