Binary Addition Calculator
Add two binary numbers and see the sum in binary, along with its decimal value. Enter each number using only 0s and 1s; the calculator adds them following base-2 carry rules and shows the binary sum plus the decimal equivalent so you can check your work.
Formula
Add bit by bit in base 2 (with carry): the binary sum of A and B
- Binary addition works like decimal addition but in base 2, carrying whenever a column reaches 2.
- Column rules: 0+0=0, 0+1=1, 1+0=1, and 1+1=10 (write 0, carry 1); 1+1+1=11 (write 1, carry 1).
- Enter each number using only the digits 0 and 1.
- The result is shown in binary and as a decimal value so you can verify it.
- For example, 1010 (10) + 11 (3) = 1101 (13).
1010 + 11
Inputs
- First binary number: 1010
- Second binary number: 11
1010 is 10 in decimal and 11 is 3. Adding them gives 13, which is 1101 in binary.
Frequently asked questions
How do you add binary numbers?
Add column by column from the right in base 2, carrying a 1 whenever a column sums to 2 or more. The tool does this automatically.
What is 1 + 1 in binary?
1 + 1 = 10 in binary — you write 0 and carry 1, just like 9 + 1 = 10 carries in decimal.
Why is the decimal value shown too?
Seeing both the binary sum and its decimal equivalent makes it easy to confirm the addition is correct.
Can I add more than two numbers?
This tool adds two binary numbers at a time. To add several, add the first two, then add the next number to that result.