A half adder can add two bits. It has two inputs, generally labeled A and B, and two outputs, the sum S and carry C.
S is the two-bit XOR of A and B, and C is the AND of A and B. Essentially the output of a half adder is the sum of two one-bit numbers, with C being the most significant of these two outputs.
A full adder is capable of adding three bits: two bits and one carry bit. It has three inputs - A, B, and carry C,
such that multiple full adders can be used to add larger numbers. To
remove ambiguity between the input and output carry lines, the carry in
is labelled Ci or Cin while the carry out is labelled Co or Cou
Full adder
Full adder circuit diagram
Inputs: {A, B, CarryIn} → Outputs: {Sum, CarryOut}
Schematic symbol for a 1-bit full adder
A full adder is a logical circuit that performs an addition
operation on three one-bit binary numbers. The full adder produces a
sum of the two inputs and carry value. It can be combined with other
full adders or work on its own.
| Input |
Output |
| A |
B |
Ci |
Co |
S |
| 0 |
0 |
0 |
0 |
0 |
| 0 |
0 |
1 |
0 |
1 |
| 0 |
1 |
0 |
0 |
1 |
| 0 |
1 |
1 |
1 |
0 |
| 1 |
0 |
0 |
0 |
1 |
| 1 |
0 |
1 |
1 |
0 |
| 1 |
1 |
0 |
1 |
0 |
| 1 |
1 |
1 |
1 |
1 |
Note that the final OR gate before the carry-out output may be
replaced by an XOR gate without altering the resulting logic. This is
because the only difference between OR and XOR gates occurs when both
inputs are 1; for the adder shown here, this is never possible. Using
only two types of gates is convenient if one desires to implement the
adder directly using common IC chips.
A full adder can be constructed from two half adders by connecting A and B to the input of one half adder, connecting the sum from that to an input to the second adder, connecting Ci to the other input and OR the two carry outputs. Equivalently, S could be made the three-bit XOR of A, B, and Ci, and Co could be made the three-bit majority function of A, B, and Ci.
Half adder
Half adder circuit diagram
Schematic Symbol of Half Adder
___________
A ------| |
| Half |----- 
| Adder |
| |----- 
B ------|___________|
A half adder is a logical circuit that performs an addition
operation on two one-bit binary numbers. The half adder outputs a sum
of the two inputs and a carry value.
The drawback of this circuit is that in case of a multibit addition, it cannot include a carry.
Following is the logic table for a half adder:
| A |
B |
C |
S |
| 0 |
0 |
0 |
0 |
| 0 |
1 |
0 |
1 |
| 1 |
0 |
0 |
1 |
| 1 |
1 |
1 |
0 |