Page 71 - Computer science 868 Class 12
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Applications of the XOR gate:
                 •  Used in half and full adders.                   •  Used in pseudo-random number generation.

                 2.2.4 XNOR Gate
                 The XNOR gate is the digital logic gate that produces 0 (low) as output for an odd number of 1 (high) as input. It
                 is pronounced as exclusive NOR gate. It is the complement of the XOR gate. An encircled dot sign ⊙ is used to
                 represent the XNOR operation.

                 The symbol and truth table of the XNOR gate is given below:

                                      A          B          A⊙B
                                      0          0           1             A                     A⊙B
                                      0          1           0             B
                                      1          0           0
                                      1          1           1          The Boolean expression of the two
                                 Truth table of 2 variable XNOR gate    variable XNOR gate is A'.B' + A.B.
                 The logic circuit diagram of the two variables XNOR gate is as follows:

                                                  A
                                                                  A.B
                                                  B
                                                                                 A'.B' + A.B

                                                 A'              A'.B'
                                                 B'

                 The truth table of the three variable XNOR gate, Boolean expression and logic circuit diagram is as follows:

                       A          B         C        A⊙B⊙C       A'             A'.B'.C'
                                                                 B'
                       0          0         0           1        C'
                       0          0         1           0                                            A'.B'.C' + A'.B.C + A.B.C'
                       0          1         0           0        A'            A'.B.C
                                                                 B
                       0          1         1           1        C
                       1          0         0           0
                                                                 A               A.B'.C
                       1          0         1           1        B'
                       1          1         0           1        C
                       1          1         1           0        A                A.B.C'
                                                                 B
                    Boolean expression of the three variable XNOR   C'
                    gate is A'.B'.C'+A'.B.C+A.B'.C+A.B.C'.

                 Example 1: Draw the logic circuit diagram of the following Boolean expression A'.C + A.B'.
                 Ans. The gates will be (A' AND C) OR (A AND B').

                                                 A'              A'.C
                                                 C
                                                                                 A'.C + A.B'

                                                 A               A.B'
                                                 B'




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