Circuits / Arithmetic
Full Adder
Adds three 1-bit inputs (A, B, and Carry-In Cin) using two cascaded XOR stages and carry-lookahead AND/OR gates.
A Full Adder adds three single-bit binary inputs: A, B, and Cin.
Sum is 1 when an odd number of inputs are 1 (A ⊕ B ⊕ Cin).
Carry-Out is 1 when two or more inputs are 1.
Standard synthesis: Sum = A ⊕ B ⊕ Cin, Cout = (A·B) + (Cin·(A⊕B)).
Tip: If Carry-Out is stuck at 0, check that the final gate is OR, not AND.
01Z floatingE conflict (dashed)
| 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 |