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.
5858 Touchpad Computer Science-XII

