Page 38 - Computer science 868 Class 12
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Draw the truth table for the inputs and outputs given above and write the POS expression for X(O, F, H, U). [ISC 2019]
              Solution:

              In the first statement, O=1 and H=0

              Second statement is having F=1 and U=1
              Third statement has H=1 and F=1

              Let us draw the truth table and put 1 (true) in the final column X having the above combinations.

                                  O           F          H           U           X       Cardinal Number
                                  0           0          0           0           0             0
                                  0           0          0           1           0             1

                                  0           0          1           0           0             2
                                  0           0          1           1           0             3

                                  0           1          0           0           0             4
                                  0           1          0           1           1             5
                                  0           1          1           0           1             6

                                  0           1          1           1           1             7
                                  1           0          0           0           1             8
                                  1           0          0           1           1             9

                                  1           0          1           0           0             10
                                  1           0          1           1           0             11
                                  1           1          0           0           1             12

                                  1           1          0           1           1             13
                                  1           1          1           0           1             14

                                  1           1          1           1           1             15

              For deriving POS expression, we multiply those maxterms which have 0 in their output column.

              Thus, the final POS expression in the canonical form is:
                            (O+F+H+U).(O+F+H+U').(O+F+H'+U).(O+F+H'+U').(O+F'+H+U).(O'+F+H'+U).(O'+F+H'+U')

              The expression in cardinal from is: π(0, 1, 2, 3, 4, 10, 11)
              Example 2: A training institute intends to give scholarships to its students as per the criteria given below:

              a.  The student has an excellent academic record but is financially weak.
                                                                 OR
              b.  The student does not have an excellent academic record and belongs to a backward class.

                                                                 OR
              c.  The student does not have an excellent academic record and is physically impaired.








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