0011 1111
11
1101 0010 210_{10}
0110 1101 109_{10}
0011 1111 63_{10}
The carry bit of 1 indicates overflow.
The correct application of the "Binary Addition Algorithm" sometimes gives incorrect results (because of overflow). With paperandpencil arithmetic, overflow is not a problem because you can use as many columns as needed.
Correct Unsigned Binary Addition 

When the "Binary Addition Algorithm" is used with unsigned binary integer representation: The result is CORRECT only if the CARRY OUT of the high order column is ZERO.

But digital computers use fixed bitlengths for integers, so overflow is possible. For instance some processors represent integers in 8, 16, or 32 bits. When 8bit operands are added, overflow is certainly possible. Our MIPS processor uses 32bit integers, but even with them, overflow is possible.
Compute the following sum using 8 bits:
0000 0001 1111 1111