Step 1: Recall how numbers are stored.
A computer keeps each number in a fixed number of bits. That fixed size sets a highest value it can hold.
Step 2: Take a simple example.
Suppose a register uses $8$ bits. The largest unsigned value it can store is $11111111$ in binary, which is $255$.
Step 3: Try to go past the limit.
If we compute $255 + 1$, the true answer is $256$.
Step 4: See why this is a problem.
The value $256$ needs more than $8$ bits, so it cannot fit in the storage we have.
Step 5: Name this situation.
When the result of a calculation is bigger than the storage can hold, we call it overflow.
Step 6: Match to the options.
So overflow happens when the result exceeds storage, which is option (A). The other options describe full memory or stopping, which are different things.
\[ \boxed{\text{Result exceeds storage}} \]