Page 664 - Computer science 868 Class 12
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1        1        0        0        1       M 12
                          1        1        0        1        0       M 13
                          1        1        1        0        1       M 14
                          1        1        1        1        1       M 15
                       POS expression of X(P, F, H, A)=π(0,1,2,4,5,9,13)
                   (b)   What is Half Adder?  Draw the truth table of a Half adder and write the boolean expression of its SUM and CARRY terms  [3]
                  Ans.  The half adder is a combinational circuit that is designed  to perform the addition of two bits and produces the two binary
                      outputs as sum (S) and the carry(C) bits.
                       The truth table of Half Adder is
                             Input             Output
                          A        B       Sum      Carry
                          0        0        0        0
                          0        1        1        0
                          1        0        1        0
                          1        1        0        1
                       The Boolean expression of SUM term = A'.B+A.B'
                       CARRY term: A.B
                   (c)   Simplify the following expression using Boolean laws:                                      [2]
                       F = P.Q' + (P' + Q') . (P + P.R').Q
                  Ans.  P.Q' + (P’ + Q') . (P + P.R').Q
                       = P.Q' + (P'.Q + Q'.Q).P                [Distributive and absorption law]
                       = P.Q' + (P'.Q + 0).P                   [Complement law]
                       = P.Q' + (P'.Q).P                       [Properties of 0]
                       = P.Q' + P'.P.Q                         [Distributive law]
                       = P.Q'                                  [Distributive law and properties of 0]
              Question 5.
                   (a)  What is Multiplexer? Draw the logic circuit diagram for a 4×1 Multiplexer circuit and explain briefly it’s working   [5]
                                                                                                          n
                  Ans.  Multiplexer is a combinational circuit which selects a single output from a set of inputs. A multiplexer has 2  input lines and
                      one output line, where n is the number of selection lines.
                       The logic circuit diagram is
                               S 1       S 0







                       A' 0



                       A' 1



                       A 2



                       A 3


                       From the truth table the Boolean expression for output Y can be written as
                          Y = S '.S '.A  + S'S .A  + S .S'.A  + S .S .A 3
                                                2
                                              0
                                                     0
                                                   1
                                            1
                               0
                             1
                                 0
                                        1
                                     1 0
                662662  Touchpad Computer Science-XII
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