Page 64 - computer science (868) class 11
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2.8.1 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 of binary addition of two bits covered in the first
              chapter of this book to draw the truth table of the half adder. A and B
              denote two bits each, then sum and  will be as given in the following table.

                                                      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 terms as:

              Sum term = A'.B + A.B' which is the Boolean expression of two variables 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


              2.8.2 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.

              Out of the three bits, two are standard input bits and the third one is the
              carry from the previous column called the carry bit in input as carry-in
              (C ). Out of two output bits, the resultant output is the sum bit and the
                in
              output carry bit is called carry-out (C ).
                                               out
              The truth table of a full adder is the same as a binary addition of three bits.


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


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