How does a computer carry a value when adding binary numbers?

Binary place values grow by factors of two: one, two, four, eight and so on. A place holds either zero or one. Adding one and one therefore gives binary 10: zero in the current place and one carried into the next place.

A full adder receives three bits: one from each number and a carry from the previous place. Their total can be zero, one, two or three. The circuit outputs the total’s remainder after division by two as its sum bit, and whether a pair must be carried onward as its carry bit.

For example, 011 plus 001 gives 100. At the ones place, one plus one makes zero with a carry. At the twos place, one plus zero plus the incoming carry again makes zero with a carry. At the fours place, zero plus zero plus that carry makes one.

Logic gates implement these rules using electrical signals. A simple ripple arrangement connects one stage’s carry output to the next stage’s carry input, which introduces delay. Faster circuits work out carries differently. The central idea is still the same: the extra value moves to a place worth twice as much.