19. Combinational Logic: Half Adder Design
We now move into designing functional digital circuits. Combinational logic means the output depends solely on the current inputs (it has no memory).
Arithmetic Circuits: Adders
Adders are the fundamental components for all arithmetic operations within a CPU.
The Half Adder (HA)
The Half Adder performs the binary addition of two single bits, A and B.
Inputs: A, B (two single bits) Outputs:
- Sum (S): The result of the addition.
- Carry Out ($C_{out}$): The carry generated to the next stage.
Truth Table
| A | B | S | $C_{out}$ |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
Logic Implementation
By examining the truth table:
- Sum (S): Matches the XOR operation. $S = A \oplus B$
- Carry Out ($C_{out}$): Matches the AND operation. $C_{out} = A \cdot B$
A Half Adder is implemented using one XOR gate and one AND gate.