๐ข Adders
Adders circuits are foundational in any complex logic circuit
โ๏ธ Half Adder
Carry
A
+ B
------------
SumLogic Equations $\text{Sum} = A \oplus B$
$\text{Carry} = A \cdot B$
โน๏ธ
Notes
- No carry-in input
- Cannot be chained directly for multi-bit addition
- Gate count: 1 XOR, 1 AND
| A | B | Sum (AโB) | Carry (AยทB) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
More on Subtractors
๐ง Full Adder
Carry-out Carry-in
A
+ B
-------------------
SumLogic Equations $\text{Sum} = A \oplus B \oplus C_{in}$
$C_{out} = A \cdot B + (A \oplus B) \cdot C_{in}$
โน๏ธ
Notes
- Can be chained for multi-bit addition
- Minimal logic avoids redundancy using XOR
- Exhaustive logic is more intuitive but less gate-efficient
- Gate count (minimal): 2 XOR, 2 AND, 1 OR
| A | B | Cin | Sum | Cout |
|---|---|---|---|---|
| 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 |
More on Full Adders
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