Page 73 - Computer science 868 Class 12
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2.3 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 Adders and (ii) Full Adders.


                 2.3.1 Half Adder
                 The half adder is a combinational circuit that is designed to perform the
                 addition of two bits and produce the two binary outputs as sum (S) and
                 carry (C) bits.
                 Let us revise the rules to binary addition done in class XI to get the truth
                 table of half adder. A and B denote two inputs, then sum and carry are:


                                                        Input               Output
                                                     A         B        Sum       Carry
                                                     0         0         0          0
                                                     0         1         1          0
                                                     1         0         1          0
                                                     1         1         0          1
                 We can thus derive the Boolean expression of the sum and carry term as:

                 Sum term = A'.B+A.B' which is the Boolean expression of two variable XOR gate.
                 Carry term = A.B which can be represented using AND gate.

                 The logic circuit diagram of the half adder is shown below:

                                                     A                     Sum = A⊕B
                                                     B



                                                                          Carry = A.B



                 2.3.2 Full Adder
                 The full adder is a combinational circuit that is designed to perform
                 the addition of three bits and produce the two binary outputs as sum
                 (S) and carry (C) bits.
                 The three bits are two standard input bits and the third one is the
                 carry from the previous column called the carry bit in input as carry-in
                 (C ) and the carry bit in output is called carry-out (C ).
                  in
                                                               out
                 The truth table of a full adder is the same as a binary addition of 3 bits.

                                                        Input                    Output
                                                A         B         C in     Sum        C out
                                                0         0         0         0          0
                                                0         0         1         1          0
                                                0         1         0         1          0



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