Binary Addition Calculator
Add binary numbers and see the result, with the carries worked out.
Adding in base two
Adding binary numbers follows the same logic as decimal, but in base two, where one plus one is zero carry one. This adds binary values and shows the result, which is useful for learning how binary arithmetic works, checking a calculation by hand, or understanding what happens at the level a processor actually operates.
Enter the binary numbers and see their sum.
Carries and overflow
The instructive part is the carries. Just as in decimal you carry when a column exceeds nine, in binary you carry when a column reaches two, and because you only have two digits, carries cascade often. Seeing them worked out makes binary addition click. The other lesson is overflow: if the sum needs more bits than are available, it overflows, which in a fixed-width computer register wraps around — the same mechanism behind two's-complement wraparound and a whole class of real bugs. For learning computer arithmetic, watching binary addition step through its carries is the clearest way in.
Questions & answers
How does carrying work in binary?
You carry when a column reaches two, since binary only has the digits 0 and 1 — so carries cascade more often than in decimal.
What is binary overflow?
When a sum needs more bits than are available it overflows, wrapping around in a fixed-width register — a common source of bugs.
Is anything uploaded?
No. The calculation happens in your browser.