Half and Full Adders A half adder is a basic combinational circuit that performs the logical operation of adding two binary numbers. It consists of two l...
A half adder is a basic combinational circuit that performs the logical operation of adding two binary numbers. It consists of two logic gates: a sum gate (also called an OR gate) and a carry gate.
The sum gate takes two binary numbers as input and outputs a single binary number. The output is true if at least one of the two input numbers is true, and false otherwise.
The carry gate takes two binary numbers as input and outputs a single binary number. If the two input numbers are different, the carry gate outputs a high-level logic 1; otherwise, it outputs a low-level logic 0.
A full adder is a half adder with an additional feature that allows it to add two n-bit numbers. It consists of two half adders, one for the high-order bits and another for the low-order bits.
The high-order adder takes two n-bit numbers as input and outputs a single n-bit number.
The low-order adder takes two n-bit numbers as input and outputs a single n-bit number.
The full adder combines the outputs of the two half adders into a single n-bit number.
Example:
Let's consider a full adder with n=2. The following truth table shows how the full adder works:
| Input A | Input B | Carry | Output |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 3 |
Therefore, the full adder outputs the value 3 for the input combination (0, 1)