Adding binary numbers...
Enter two or more binary numbers to see the sum and carry steps.
How Binary Addition Works
A Binary Addition Calculator adds base-2 numbers using the same carrying idea as decimal addition. The difference is that binary has only two digits, so any column total of 2 or more creates a carry into the next column.
The four basic rules are `0 + 0 = 0`, `0 + 1 = 1`, `1 + 0 = 1`, and `1 + 1 = 10`. That last result means write 0 in the current column and carry 1 to the next power of two.
Worked Example: 1010 + 11
To add `1010` and `11`, align the values on the right. The ones column gives `0 + 1 = 1`. The twos column gives `1 + 1 = 10`, so write 0 and carry 1. The fours column adds that carry to `0 + 0`, producing 1. The eights column remains 1, so the result is `1101`.
1010 + 0011 = 1101
Binary `1101` equals decimal 13, because the set bits contribute 8, 4, and 1.
Carry Chains in Binary
A carry chain happens when a carry moves through several columns. For example, `1111 + 1` becomes `10000`. Every one-bit column receives a carry, writes 0, and passes a new carry to the left until the final carry creates a new leading bit.
Adding Binary Fractions
Binary fractions are aligned around the radix point. In `101.1 + 10.01`, the fractional places become `101.10 + 010.01`. The result is `111.11`, which equals decimal 7.75. The calculator pads shorter fractional parts only for alignment; it does not change the value.
Binary Addition FAQ
How do you add binary numbers?
Align the numbers by place value, add each column from right to left, write the result bit, and carry any value of 2 or more to the next column.
What is 1010 + 11 in binary?
`1010 + 11` equals `1101` in binary, which is decimal 13.
Can this calculator add more than two binary numbers?
Yes. It accepts up to 20 addends separated by new lines, commas, semicolons, or plus signs.
Does it support binary decimals?
Yes. Binary fractions such as `101.1 + 10.01` are aligned by fractional place and calculated exactly.
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