Page 62 - Computer science 868 Class 12
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Quad 2: ( m +m +m +m ) = B'D'
                                         10
                                      8
                                  2
                               0
                     Quad 3: (m +m +m +m ) = AC'
                                  9
                               8
                                         13
                                     12
                     Hence, F (A, B, C, D) = C'D' + B'D' + AC'
                 40.  Given the Boolean function: F (A, B, C, D) = π(3,4,5,6,7,10,11,14,15).
                     Reduce the above expression by using 4-variable Karnaugh map, showing the various groups (i.e. octal, quads and pairs). [ISC 2018]
                 Ans.  F (A, B, C, D) = π(3,4,5,6,7,10,11,14,15)
                           C+D    C+D'  C'+D'  C'+D
                     A+B  0      1      3     2
                              1      1     0      1
                     A+B'   4   0  5   0  7   0  6   0
                     A'+B'  12   13     15    14
                              1      1     0      0
                     A'+B  8   1  9   1  11   0  10   1
                     = There are three quads:
                     Quad 1: (M +M +M +M ) = A+B'
                                       7
                                    6
                             4
                                5
                     Quad 2: (M +M +M +M ) = C'+D'
                                7
                                    11
                                       15
                             3
                     Quad 3: (M +M +M +M ) = A'+C'
                                 11
                                         15
                             10
                                     14
                     Hence, F (A, B, C, D) = (A + B').(C' + D').(A' + C')
                 41.  (a)  A training institute intends to give scholarships to its students as per the criteria given below:    [ISC 2018]
                        The student has excellent academic record but is financially weak.
                                                                 OR
                        The student does not have an excellent academic record and belongs to a backward class.
                                                                 OR
                        The student does not have an excellent academic record and is physically impaired.
                        The inputs are:
                          INPUT
                            A     Has excellent academic record
                            F     Financially sound
                            C     Belongs to a backward class
                            I     Is physically impaired
                        (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 SOP expression for X(A, F, C, I).
                Ans.    A        F        C        I        X

                        0        0        0        0        0
                        0        0        0        1        1
                        0        0        1        0        1
                        0        0        1        1        1
                        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        1
                        1        0        1        1        1
                        1        1        0        0        0
                        1        1        0        1        0
                        1        1        1        0        0
                        1        1        1        1        0



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