Page 53 - Computer science 868 Class 12
P. 53

A       A'      A + A'  (A + A')
                           0        1        1        0
                           1        0        1        0
                    4. Given the Boolean function F(A, B, C, D) = S(2, 3, 6, 7, 8, 10, 12, 14, 15).
                       Reduce the above expression by using 4-variable Karnaugh map, showing the various groups (i.e., octal, quads and pairs).
                                                                                                                 [ISC 2023]
                   Ans.  F(A, B, C, D) = S(2, 3, 6, 7, 8, 10, 12, 14, 15)
                              C'.D'  C'.D  C.D  C.D'
                       A'.B'               1     1

                       A'.B                1     1
                       A.B     1           1     1
                       A.B'    1                 1

                      Quad 1: (2, 3, 6, 7) = A'.C
                       Quad 2: (6, 7, 14, 15) = B.C
                       Quad 3: (8, 10, 12, 14) = A.D'
                       F(A, B, C, D) = A'C + BC + AD'
                    5.  Given the Boolean function F(A, B, C, D) = p(0, 1, 2, 4, 5, 8, 10, 11, 14, 15).
                       Reduce the above expression by using 4-variable Karnaugh map, showing the various groups (i.e., octal, quads and pairs).
                                                                                                                 [ISC 2023]
                   Ans.  F(A, B, C, D) = p(0, 1, 2, 4, 5, 8, 10, 11, 14, 15)
                              C+D   C+D'  C'+D'  C'+D
                       A+B'    0     0           0
                       A+B'    0     0

                       A'+B'               0     0
                       A'+B    0           0     0

                       Quad 1: (0, 1, 4, 5) = A + C
                       Quad 2: (10, 11, 14, 15) = A’ + C’
                       Quad 3: (0, 2, 8, 10) = B + D
                       F(A, B, C, D) = (A + C) . (A’ + C’) . (B + D)
                    6. Verify the following expression by using the truth table:                                 [ISC 2023]
                      (A ⊕ B)' = (A ⊕ B)
                    Ans.
                           A        B     No of I's  A 9 B  (A 9 B')  A ⊕ B
                           0        0        0        1        0        0
                           0        1        1        0        1        1
                           1        0        1        0        1        1
                           1        1        2        1        0        0
                       Hence proved
                    7. Convert the following cardinal expression to its canonical form:                          [ISC 2023]
                        F(P, Q, R) = p(0, 1, 3, 4)
                   Ans.  F(P, Q, R) = (P + Q + R).(P + Q + R’).(P + Q’ + R’).(P’ + Q + R)

                    8. The Boolean equation which holds true for the Involution Law is:                          [ISC 2022]
                       (a)  A' + 1 = 1                                     (b)  ((A + B)' )' = A + B
                       (c)  (A + B)' = A'. B'                              (d)  A.(B + C) = (A + B).C
                   Ans.  (b)


                                                                                                                        51
                                                                                                      Boolean Algebra   51
   48   49   50   51   52   53   54   55   56   57   58