Page 70 - Computer science 868 Class 12
P. 70

Representing AND gate using NOR gate only:
              AND operation is achieved by passing complemented input through the NOR gate as shown in the logic circuit diagram.

                           A                    A'                             Output in NOR gate 1 is A'
                                      1
                           A                                           A.B     Output in NOR gate 2 is B'
                                                                 3 3           Output in NOR gate 3 is (A'+B')'
                                                                               = (A')'.('B')'   [De Morgan’s Law]
                          B                     B'
                                      2                                        = A.B    [Involution Law]
                          B


              2.2.3 XOR Gate
              The XOR gate is a digital logic gate that produces 1 (high) as output for an odd number of 1 (high) as input. It is
              pronounced as exclusive OR gate. An encircled plus sign (⊕) is used to show the XOR operation.
              The symbol and truth table of the XOR gate is given below:

                                   A           B          A⊕B
                                                                          A                   A⊕B
                                    0          0           0
                                    0          1           1              B
                                    1          0           1
                                    1          1           0          The  Boolean  expression  of  a  two
                                                                      variable XOR gate is A'.B+A.B'
                              Truth table of 2 variables XOR gate

              The logic circuit diagram of the two variable XOR gate is as follows:

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



                                               A'              A'.B
                                               B

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

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




                6868  Touchpad Computer Science-XII
   65   66   67   68   69   70   71   72   73   74   75