Page 89 - Computer science 868 Class 12
P. 89

Ans.  A'           (A+B')'-A"+B"-A+B

                       B'
                                      (A'+C)'
                                      -A"+C'          ((A+B).(A+C).(A'+C'))'
                       A'              -A+C'                                    (A+B).(A+C).(A'+C')'

                       C


                       A'             (A'+C)'
                                       (AC)'
                       C'
                                      -A'+C'
                    9.  Write the boolean expression of  (1), (2), (3) and (4) for the following logic circuit diagram and finally minimise the given
                       expression.
                                     A                         (1)
                                     B                                       (2)
                                     C
                                                                                                 (4)




                                     A                                       (3)


                                      B
                   Ans.  1.  (A.B.C)'  2. (A.B.C)'+C   3. (A+B)'  4. ((A.B.C)'+C).(A+B)'
                          Simplify the final result
                          ((A.B.C)'+C).(A+B)'
                          = (A'+B'+C'+C).A'.B'                         [ (X.Y)'=X'+Y'  (X+Y)'=X'.Y']
                          = (A'+B'+ 1).A'.B'                           [ X+X'=1]
                           = 1.A'.B'                                   [ X+1=1]
                           = A'.B'                                     [X.1=X]
                   10.  Write the boolean expression of (1), (2), (3) and (4) for the following logic circuit diagram and finally minimise the given
                       expression.
                                             A                       (1)
                                             B
                                             C

                                             A'                      (2)                  (4)
                                             B
                                             C

                                             A                       (3)
                                             B
                                             C'

                   Ans.  1.  (A.B.C)'    2. (A'.B.C)'    3. (A.B.C')'   4. (A.B.C)'+(A'.B.C)'+(A.B.C')'
                          Simplification
                          (A.B.C)'+(A'.B.C)'+(A.B.C')'
                           = A'+B'+C'+A"+B'+C'+A'+B'+C"                [DeMorgan’s Law]
                           = A'+B'+C'+A+B'+C'+A'+B'+C                  [Involution law]
                           = (A+A')+(C+C')+B'+C'                       [Associative law & Idempotent law]
                           = 1+B'+C'                                   [Complement law]
                           = 1                                                             [Properties of 0 and 1]


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                                                                                                   Computer Hardware    87
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