Math
Binary Addition Calculator
Type two binary numbers and the calculator adds them column by column, exactly as you would on paper.
The carry row shows where each carry goes, each column is explained (0+1, 1+1, 1+1+1), and the sum is checked in decimal.
Digits 0 and 1 only. A leading minus sign is allowed; spaces or underscores can group bits (1011 0110).
Digits 0 and 1 only.
Try an example
Result
Binary result
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- Decimal check
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- Hexadecimal
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- Octal
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Student quick launch
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Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the binary addition calculator solves
Binary addition is the foundation of every arithmetic circuit in a computer. There are only four single-column facts to learn, and a carry happens whenever a column totals 2 or 3. This page adds whole binary numbers of any length and shows the carries so you can follow each column.
Binary addition rules
| Column | Result | Write | Carry |
|---|---|---|---|
| 0 + 0 | 0 | 0 | 0 |
| 0 + 1 or 1 + 0 | 1 | 1 | 0 |
| 1 + 1 | 10 | 0 | 1 |
| 1 + 1 + 1 (with carry in) | 11 | 1 | 1 |
How to use it
- Enter the first binary number (0 and 1 only; spaces or a 0b prefix are okay).
- Enter the second binary number. They do not need to be the same length; shorter numbers are padded with zeros on the left.
- Read the grid from right to left: the amber row is the carry into each column and the blue row is the sum.
- Use the decimal check to confirm the result.
How to read the answer
The sum is a binary number that may be one bit longer than the longer input (a final carry). The decimal check converts both inputs and adds them in base 10, so the two answers must agree. The hex and octal equivalents are useful when the sum is used as a memory address or color value.
Common mistakes and edge cases
- 1 + 1 is 10, not 2. Write the 0 and carry the 1.
- A carry into a column that already has 1 + 1 gives 11: write 1 and carry 1 again.
- Remember the final carry; 111 + 1 = 1000, one bit longer than either input.
- In fixed-width hardware that final carry is an overflow and is dropped; this page keeps it.
- If one number is negative, the calculator subtracts magnitudes instead, and the grid shows borrows.
Worked examples
Typical addition
1011 + 110
Binary result
10001
Chained carries
1111 + 1
Binary result
10000
Adding zero
10110 + 0
Binary result
10110
Negative addend
110 + (−1011)
Binary result
-101
Long inputs
32-bit values
Binary result
100000000000000000000000000000000
Invalid digit
1021 + 1
Binary result
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Frequently asked questions
What is 1 + 1 in binary?+
1 + 1 = 10 in binary, which is 2 in decimal. You write 0 in the current column and carry 1 to the next column.
What is 1 + 1 + 1 in binary?+
1 + 1 + 1 = 11 in binary (3 in decimal). Write 1 and carry 1. This happens when a column already has a carry coming in.
Do the two numbers need the same number of bits?+
No. The calculator pads the shorter number with leading zeros so the columns line up, which does not change its value.
Why is the sum longer than the inputs?+
When the leftmost column produces a carry, the sum gains a new leading 1. For example 100 + 100 = 1000.
What happens with a negative number?+
Adding a negative is subtraction of magnitudes. The calculator shows the borrow-based column work and gives the answer with a minus sign.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026