Page 674 - Computer science 868 Class 12
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PART II – 50 MARKS
                    Answer six questions in this part, choosing two questions from Section A, two from Section B and two from Section C.


                                                            SECTION – A
                                                        Answer any two questions.


              Question 3.
                    (i)  A Football Association coach analyses the criteria for a win/draw of his team depending on the following conditions.
                       •  If the Centre and Forward players perform well but Defenders do not perform well.
                                                                 OR
                       •  If Goalkeeper and Defenders perform well but the Centre players do not perform well.

                                                                 OR
                       •  If all perform well.
                          The inputs are:
                                             INPUTS
                                                C      Centre players perform well

                                                D      Defenders perform well
                                                F      Forward players perform well

                                                G      Goalkeeper perform well
                       (In all the above cases, 1 indicates yes and 0 indicates no.)
                       Output: X - Denotes the win/draw criteria [1 indicates win/draw and 0 indicates defeat in all cases]
                       Draw  the  truth  table  for  the  inputs  and  outputs  given  above  and  write  the SOP expression for X(C, D, F, G).
                                                                                                                    [5]
                   (ii)  Reduce the above expression X (C, D, F, G) by using 4-variable Karnaugh map, showing the various groups (i.e. octal, quads and
                      pairs).
                       Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as
                      inputs.                                                                                       [5]
              Question 4.
                    (i)  (a)   Reduce the Boolean function F(A,B,C,D) = π (0, 1, 2, 3, 4, 6, 9, 11, 13) by using 4-variable Karnaugh map, showing the
                          various groups (i.e. octal, quads and pairs).                                             [4]
                       (b)   Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available
                          as inputs.                                                                                [1]
                   (ii)  (a)   From the logic circuit diagram given below, name the outputs (1), (2) and (3) and finally derive the Boolean expression (F)
                          and simplify it. Identify the propositional connective which is equivalent to the simplified Boolean expression.   [4]
                           X
                                                            (1)
                           Y
                                                                               (3)
                                                                                          f(X,Y,Z)
                                                           (2)
                           Z



                       (b)  If A=1 and B=0 then find the value of (A' + 1) • B                                      [1]
              Question 5.
                    (i)  Draw the logic circuit to  encode the  following  Hexadecimal number
                       (1, 3, 5, 6, 9, A, C, E) to its binary equivalents. Also state the binary equivalents of the given numbers.   [5]


                672672  Touchpad Computer Science-XII
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