Page 57 - Computer science 868 Class 12
P. 57
Ans. F(P,Q,R) = P'Q'R + P'QR + PQ'R' + PQR'
= 001 011 100 110
F(P,Q,R) = Σ( 1,3,4,6 )
29. A company intends to develop a device to show the high-status power load for a household inverter depending on the criteria
given below: [ISC 2020]
• If Air conditioner and Geyser are on
OR
• If Air conditioner is off, but Geyser and Refrigerator are on
OR
• If Geyser is off, but Air conditioner and Water purifier are on
OR
• When all are on
The inputs are:
INPUT
A Air conditioner is on
G Geyser is on
R Refrigerator is on
W Water purifier is on
In all the above cases 1 indicates yes and 0 indicates no.) Output: X [1 indicates high power, 0 indicates low power for all cases]
Draw the truth table for the inputs and outputs given above and write the SOP expression for X(A,G,R,W).
Ans.
A G R W X(OUTPUT)
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 0
1 0 0 1 1
1 0 1 0 0
1 0 1 1 1
1 1 0 0 1
1 1 0 1 1
1 1 1 0 1
1 1 1 1 1
SOP Expression: X(A,G, R, W) = Σ(6, 7, 9, 11, 12, 13, 14, 15)
OR
X = A'GRW' + A'GRW + AG'R'W + AG'RW + AGR'W' + AGR'W + AGRW' + AGRW
30. Simplify the following expression using Boolean laws: [ISC 2020]
F = [ (X' + Y) • (Y' + Z) ]' + (X' + Z)
Ans. [(X'+Y)•(Y'+Z)]' + (X'+Z)
= (X'+Y)' + (Y'+Z)' + (X'+Z)
= XY' + YZ' + X' + Z
= X' + XY' + Z + YZ'
= (X'+X)•(X'+Y')+(Y+Z)•(Z+Z')
= X'+Y'+Z +Y
= 1 as (Y + Y' =1)
55
Boolean Algebra 55

