Full Adder
Adds three 1-bit inputs (A, B, Cin) producing a Sum and Carry output. Built from two XOR + two AND + one OR gate.
Full Adder Circuit
SUM = 0
CARRY = 0
Result: 00
Truth Table
| A | B | Cin | Sum | Carry |
|---|---|---|---|---|
| 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 |
How It Works
SUM = A ⊕ B ⊕ Cin
Two cascaded XOR gates produce the sum bit — same formula as Half Adder but extended with Carry-in.
CARRY = (A·B) + (Cin·(A⊕B))
Carry is produced by two AND gates feeding an OR — carry occurs when ≥2 inputs are 1.