When you add two n-bit numbers, the top column can produce a carry with nowhere to go. That bit is the carry-out. In an adder circuit it's the final carry Cₙ (C4 in a 4-bit adder), the Cout of the top full adder.
The word is also used for a single stage: each full adder has a carry in and a carry-out, and the carry-out of bit i feeds the carry-in of bit i + 1.
What the final carry-out tells you depends on the operation and the format:
- Unsigned addition: carry-out 1 means the true sum needed n + 1 bits. That's unsigned overflow.
- Unsigned subtraction done as A + (inverted B) + 1: carry-out 1 means no borrow (A ≥ B), and 0 means a borrow (A < B).
- Two's complement: the carry-out alone means nothing. −1 + −1 carries out and is perfectly correct. Signed overflow compares the carry into the MSB with the carry out of it.
Processors store the carry-out in the carry flag C after each addition, so software can test it or feed it into the next addition when adding numbers wider than the adder.
1
16
0
8
0
4
1
2
1
1