Arithmetic Overflow vs. Arithmetic Carry

Question

One of my lecture slides gives an example of arithmetic overflow and carry in a topic for conditional branching flags on an ARM chip, quoted below:

• V (overflow) - 

Answer 1

• Overflow flags get set when the register cannot properly represent the result as a signed value (you overflowed into the sign bit).
• Carry flags are set when the register cannot properly represent the result as an unsigned value (no sign bit required).

Answer 2

You get an overflow, if the sign bit is corrupted. So you know that you have to adjust your result.

You get a carry if the result does not fit in this value. (need more bits than you have).

In the old days you had to write your own addition and multiplication subroutines for multi byte values.