Page 96 - Computer science 868 Class 12
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Decoder is a combinational circuit that converts any binary number to its equivalent Octal, Decimal or Hexadecimal form. It has
                                           n
                    ‘n’ input lines and maximum 2  output lines.
                 14.  Draw the circuit of a two input XOR gate with the help of NOR gates.                     [ISC 2020]
                Ans.  XOR gate using only NOR gates: Expression for XOR in POS : F = (A’+B’) • (A+B)
                 15.  Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as
                    inputs.                                                                                    [ISC 2020]
                Ans.  Logic gate diagram:
                    B'


                    D
                    A'


                    D'
                     B
                    C'
                    D'

                 16.  Draw the truth table and derive an SOP expression for sum and carry for a full adder. Also, draw the logic circuit for the carry
                    of a full adder.                                                                           [ISC 2020]
                Ans.  Truth Table for a Full adder:
                        A        B        C        S        C 0
                        0        0        0        0        0
                        0        0        1        1        0                A                 AB
                        0        1        0        1        0
                        0        1        1        0        1                B
                        1        0        0        1        0                B
                        1        0        1        0        1                                   BC              CARRY
                        1        1        0        0        1                C
                        1        1        1        1        1
                    SOP Expression:                                          C                 CA
                    Sum = A'B'C + A'BC' + AB'C' + ABC
                    Σ(1,2,4,7)                                               A
                    Carry = A'BC + AB'C + ABC' +ABC
                    Σ(3,5,6,7)
                    Circuit for carry: C0 = AB + BC + AC

                 17.  Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as
                    inputs.                                                                                    [ISC 2018]
                Ans.  C'

                    D'
                    B'                                    F

                    D'

                     A

                    C'









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