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Example 3: Draw the logic circuit diagram of the Boolean expression ((A'+B+C).(B+C'))'.
                 Ans. The gate sequence will be (A' OR B OR C) NAND (B OR C') or  NOT((A’ OR B OR C) AND (B OR C’) ).

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




                                         C'                    (B+C')


                 Example 4: Derive the Boolean expression for the following logic circuit.


                                                     A
                                                     B


                                                     C

                 Ans.
                      A                A'.B+A.B'
                      B
                                                        (C.(A'.B+A.B'))'
                      C

                 Hence, the derived expression is (C.(A'.B + A.B'))'.

                 Example 5: Derive the Boolean expression for the following logic circuit.


                                                  A
                                                  B




                                                  C

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

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



                      C                 (B+C)'


                 Hence, the derived expression is (A'.B' + A.B).(B+C)'

                     3.8 HALF ADDER AND FULL ADDER
                 In digital systems,  combinational  circuits  are  designed to perform  various  data processing tasks like  addition,
                 subtraction, multiplication, complement, shift, increment, decrement, etc. One such combinational circuit is the adder,
                 which performs the addition of binary numbers. Adders are of two types: (i) Half Adder and (ii) Full Adder.


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                                                           Propositional Logic, Hardware Implementation, Arithmetic Operations  85
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