Full adder: build and simulate it online
Two half adders and an OR: Sum = A ⊕ B ⊕ Cin, Cout = A·B + Cin·(A ⊕ B).
Build the full adder in the free online simulator — it checks your circuit automatically.
What you need
- 3 logic switches labelled A, B, Cin
- 2 probes labelled Sum, Cout
- 2 XOR gates
- 2 AND gates
- 1 OR gate
Step by step
- Place three inputs and two outputs. From the Logic section of the library, drop digital inputs (0/1 boxes) or logic switches for the inputs, and digital outputs or probes for the outputs; give each its label in the inspector (the checker finds them by label). Switches A, B, Cin; Probes Sum and Cout
- Place the five gates. Stage 1 is a half adder on A and B; stage 2 adds Cin; the OR merges the two carries. Two XOR gates; Two AND gates; One OR gate
- Wire stage 1. A and B go into XOR 1 and AND 1. A, B → XOR 1 and AND 1
- Wire stage 2. XOR 1 and Cin go into XOR 2 (the sum) and AND 2; both ANDs feed the OR (the carry). XOR 1, Cin → XOR 2 → Sum; XOR 1, Cin → AND 2; AND 1, AND 2 → OR → Cout
- Prove all eight rows. Check runs every combination of A, B and Cin. Sum is 1 for an odd number of 1s; Cout for two or more
Truth table
| 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 |
Frequently asked questions
How do you build a full adder?
Two half adders and an OR: Sum = A ⊕ B ⊕ Cin, Cout = A·B + Cin·(A ⊕ B). In short: place three inputs and two outputs, then place the five gates, then wire stage 1, then wire stage 2, then prove all eight rows.
What is the truth table of a full adder?
It has 3 inputs (A, B, Cin) and 2 outputs (Sum, Cout), so 8 rows. The full table is on this page; the Embedded Lab checks all of them against your circuit.
What parts do you need for a full adder?
2 XOR gates; 2 AND gates; 1 OR gate — plus logic switches for the inputs and probes for the outputs.
Can I simulate a full adder online for free?
Yes. Open it in the BitForBytes Embedded Lab, a free browser-based circuit and logic simulator: drag in the gates, wire them, and press "Check my circuit" — every input combination is simulated and marked for you. No download or sign-up needed.
Part of DSD 8 · Full adder in the free BitForBytes digital system design course.