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
   52   53   54   55   56   57   58   59   60   61   62