Binary Addition Calculator | Free Binary Sum & Base-2 Converter

Binary Addition Calculator

Add two or more binary numbers and see the answer as you type. Along with the binary sum, the calculator shows each number in decimal and hex, lays the problem out in columns with every carry marked, and explains each column in plain words. It handles numbers of any length.

How to use it

1. Type a binary number in box A and another in box B. Spaces, underscores, and a 0b prefix are ignored, so 0b1010_1100 works.
2. Press Enter or click + Add a number to add up to ten numbers at once.
3. Read the sum, the decimal and hex check, and the column layout. Open Explain each column for a step-by-step walkthrough.
4. Pick a Bit width to see whether the sum would overflow an 8-, 16-, 32-, or 64-bit register.

Binary addition rules

How to add binary numbers by hand

Line the numbers up on the right, then add one column at a time from right to left, just like decimal addition. When a column adds up to 2 or more, write the last binary digit and carry the rest into the next column to the left.

For example, 101101 (45) + 11011 (27):

1. Column 1: 1 + 1 = 10, so write 0 and carry 1.
2. Column 2: 0 + 1 + carry 1 = 10, so write 0 and carry 1.
3. Column 3: 1 + 0 + carry 1 = 10, so write 0 and carry 1.
4. Column 4: 1 + 1 + carry 1 = 11, so write 1 and carry 1.
5. Column 5: 0 + 1 + carry 1 = 10, so write 0 and carry 1.
6. Column 6: 1 + carry 1 = 10, so write 0 and carry 1.
7. The last carry becomes a new leftmost digit, giving 1001000, which is 72.

Adding more than two numbers

With three or more numbers, a column can add up to 3, 4, or more, and the carry can be larger than 1. For example, 1 + 1 + 1 + 1 = 4, which is 100 in binary, so you write 0 and carry 2 into the next column. The column layout shows those carries above each column.

Overflow and bit width

Computers store numbers in a fixed number of bits. If a sum needs more bits than the register has, the extra high bit is lost and the stored value wraps around. For example, in 8 bits, 11111111 (255) + 1 = 1 0000 0000, which wraps to 00000000 with a carry out of 1. Set the Bit width option to see this for any problem. Leading zeros the register adds are shown in gray, and bits that don't fit are shown in red.

Frequently asked questions

What is 1 + 1 in binary?

1 + 1 = 10 in binary, which is 2 in decimal. In column addition, you write 0 and carry 1 to the next column.

Can I check my answer in decimal?

Yes. Each number and the sum are shown in decimal and hexadecimal, so you can confirm the result with regular arithmetic.

Is there a limit on how long the numbers can be?

No. The sum and the decimal check work for numbers of any length. The column layout appears for sums up to 256 bits, and the written explanation for sums up to 64 bits.

Does it handle negative numbers or subtraction?

No. This calculator adds unsigned binary numbers. With a fixed bit width, adding the two's complement of a number gives you subtraction, and the overflow note shows the wrapped result.

Is my input sent anywhere?

No. Everything is calculated in your browser.