Full Adder Calculator
Calculate the sum and carry-out of a full adder using inputs A, B, and carry-in (Cin). Explore all eight truth-table combinations, inspect the Boolean logic, or add two multi-bit binary numbers using a ripple-carry full adder.
Single-bit full adder
Choose 0 or 1 for each input. The outputs update when you click Calculate, without reloading the page.
Full adder outputs
The least significant bit of the total.
The carry passed to the next bit position.
Logic evaluation
Full adder truth table
A full adder has three binary inputs, giving eight possible input combinations. The highlighted row follows your current input selection.
| A | B | Cin | Sum (S) | Carry-out (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 |
Multi-bit ripple-carry adder
Add two binary integers using a chain of full-adder stages. Each stage's carry-out becomes the carry-in of the next stage to its left. Optionally provide an initial carry-in of 1.
Multi-bit addition result
Bit-by-bit carry propagation
| Bit position | A | B | Carry-in | Sum | Carry-out |
|---|
Bit position 0 is the least significant (rightmost) bit. The carry propagates toward the most significant bit.
What is a full adder?
A full adder is a combinational digital circuit that adds three single-bit values: input A, input B, and a carry-in bit. Its two outputs are the sum bit S and carry-out bit Cout. The arithmetic total of the three inputs ranges from 0 to 3, so two output bits are sufficient to represent the result.
S = A XOR B XOR Cin Cout = (A AND B) OR (A AND Cin) OR (B AND Cin)An equivalent factored expression for the carry is:
Cout = (A AND B) OR (Cin AND (A XOR B))How the sum output works
The sum is 1 when an odd number of the three inputs are 1. This is
exactly the behavior of three-input XOR. The sum output is therefore
A XOR B XOR Cin.
How the carry output works
The carry-out is 1 whenever at least two of the three inputs are 1.
For example, 1 + 1 + 0 equals binary 10: the sum bit is
0 and the carry-out is 1. Likewise, 1 + 1 + 1 equals binary
11, producing both a sum bit and a carry.
Full adder versus half adder
| Feature | Half adder | Full adder |
|---|---|---|
| Inputs | A and B | A, B and Cin |
| Outputs | Sum and carry | Sum and carry-out |
| Sum expression | A XOR B |
A XOR B XOR Cin |
| Carry expression | A AND B |
AB + ACin + BCin |
| Handles incoming carry? | No | Yes |
| Multi-bit addition | Cannot independently process a carry-in | Can be chained into a ripple-carry adder |
How a ripple-carry adder works
A ripple-carry adder connects multiple full adders to add binary numbers with more than one bit. Each stage calculates one sum bit and sends its carry-out to the next more significant stage.
A3 A2 A1 A0
B3 B2 B1 B0
| | | |
Initial Cin → FA0 → FA1 → FA2 → FA3
| | | |
S0 S1 S2 S3
Carry propagates →
The diagram is conceptual: the rightmost stage handles the least significant bit. Its carry-out becomes the next stage's carry-in. If the final stage produces a carry-out, that bit is placed to the left of the sum bits.
Full adder calculator FAQs
What does a full adder calculate?
It adds A, B and the incoming carry. The sum output contains the least significant bit of that total, while carry-out contains the next bit.
Why are there two outputs?
Three single-bit inputs can total 0, 1, 2 or 3. These four possibilities require two binary output bits, represented by Cout followed by Sum.
When does a full adder produce a carry?
It produces a carry-out of 1 whenever at least two of its inputs are 1. Thus 1 + 1 + 0 produces sum 0 and carry 1, while 1 + 1 + 1 produces sum 1 and carry 1.
Can full adders perform multi-bit binary addition?
Yes. Connecting the carry-out of one stage to the carry-in of the next stage allows a chain of full adders to add multi-bit binary integers.
Is this calculator suitable for learning digital logic?
Yes. You can compare outputs against all eight truth-table combinations, inspect the Boolean expressions, and follow carry propagation through a multi-bit addition.