Page 95 - Computer science 868 Class 12
P. 95

10.  X              (1)

                       Y              (X+Y)
                                                          F
                       X'              (2)             ((X+Y)+(X'.Z)')'
                                     (X'.Z)'
                       Z
                       With reference to the logic diagram given above, where X,X',Y and Z are inputs and F is the output, answer the following
                      questions:                                                                                 [ISC 2022]
                        (i)  What is the expression at (1)?
                          (a)  X.Y                                         (b)  X'+Y'
                          (c)  X + Y                                       (d)  X+Y'
                   Ans.  (c)
                         (ii)  What is the expression at (2)?                                                    [ISC 2022]
                          (a)  (X+Z)'                                      (b)  (X+Z')
                          (c)  X’+Z                                        (d)  (X'.Z)'
                   Ans.  (d)
                        (iii)  What is the final expression F(X,Y,Z)?                                            [ISC 2022]
                          (a)  (XY + X'Z)'                                 (b)  ((X+Y) + (X'.Z)')'
                          (c)  ((X+Y) .(X'.Z)')'                           (d)  (X'+Z) + (XY)'
                   Ans.  (b)
                    11.  Draw the logic circuit of the XOR gate using the NOR gate only.                         [ISC 2020]
                   Ans.  The POS expression of the XOR gate is (A'+B').(A+B)
                                                A'

                                                B'              (A'.B')'
                                                                                 (A'+B').(A+B)

                                                 A

                                                 B              (A+B)'
                    12.  Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as
                       inputs.                                                                                   [ISC 2020]
                   Ans.  B'


                       C'
                       A

                       B
                    13.  Draw the logic circuit diagram for an octal to binary encoder and explain its working when a particular digit is pressed. Also,
                       state the difference between encoders and decoders.                                       [ISC 2020]
                   Ans.  The logic circuit diagram of an Octal to Binary Encoder is as   0
                       shown here.
                                                                         1
                       Working Principle of Octal to Binary Encoder: Say the switch of   2
                       Octal number 2 is closed. 2 is connected only with OR gate B .   3
                                                                     1
                       So a trigger applied makes B  = 1 while B  and B  will retain their   4
                                            1
                                                          2
                                                     0
                       default value of 0. Thus B  = 0 B  = 1 and B0 = 0 or 0 1 0 which is   5
                                          2
                                              1
                       the binary equivalent of 2 Similarly on pressing switch 5 which   6
                       is connected with B  and B , we get B  = 1 B  = 0 and B  = 1 or     7
                                                         1
                                                                 0
                                      2
                                           0
                                                    2
                       1 0 1 which is the binary equivalent of 5.
                        An  Encoder  is  a  combinational  circuit  that  convert  decimal,
                       octal or hexadecimal numbers to its equivalent binary from. An
                                             n
                       encoder has a maximum of 2  input lines and n output lines.  B 2              B 1            B 0
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                                                                                                   Computer Hardware    93
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