Full Adder
Inputs
| Pin | Type | Description |
|---|---|---|
| A | bit | First addend |
| B | bit | Second addend |
| CarryIn | bit | Carry-in from previous bit |
Outputs
| Pin | Type | Description |
|---|---|---|
| Sum | bit | A XOR B XOR CarryIn |
| CarryOut | bit | (A ∧ B) ∨ (A ∧ Ci) ∨ (B ∧ Ci) |
How It Works
A Full Adder adds three bits: two operands (A, B) plus a carry-in from the previous bit position. It produces a sum and a carry-out.
Logic:
- Sum = A XOR B XOR CarryIn
- CarryOut = (A AND B) OR (A AND CarryIn) OR (B AND CarryIn)
Full Adders are daisy-chained to build ripple-carry adders: each CarryOut connects to the next stage's CarryIn. The least significant stage uses a Half Adder (no carry-in).
Truth Table
| A | B | Ci | Sum | Co |
|---|---|---|---|---|
| 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 |
Usage
Level 7. Used in the ripple-carry chain of the 8-bit adder: the Half Adder handles the LSB, then seven Full Adders cascade the carry through bits 1–7. Also appears as a foundational building block in the ALU's adder logic.