Lets say the question is 01001 - 1110
Now we have two options. Calculate is using Unsigned System and then do it using signed system.
Unsigned System
01001 is five bits while 1110 is four bytes.
The first step is to sign extend and make sure they both are of equal length.
For unsigned, we sign extend by adding "0s" on left most side.
Hence,
1110 -> 01110
Now the subtraction.
In term of decimal the question looks like this: 9-14. Which is -5
// Taking 2s compliment of 01110
01110 -> 10001 // Inverting Bits
10001 + 1 -> 10010 // Adding one
Now,
01001 // 9
10010 // -14
+ -----
11011 // -5 if we consider it signed system, otherwise 27
"No final carry in step 2 indicates a final borrow, or a greater “2nd number” than the “1st number”, hence an impossible subtraction." In unsigned, -5 can't be represented anyways. Hence Overflow occured.
Signed System
For signed System the procedure is more or less the same. The major difference would be the sign extension.
For signed numbers, to do signed extension, we just repeat whatever the MSB is.
For 1110, MSB is 1
Hence,
1110 -> 11110
Now the subtraction.
In term of decimal the question looks like this: 9-(-2). Which is 11.
// Taking 2s compliment of 01110
11110 -> 00001 // Inverting Bits
00001 + 1 -> 00010 // Adding one
Now,
01001 // 9
00010 // -2
- -----
01011 // 11, as expected
Since the carry bit arriving arriving at the sign column is same from the carry bit leaving this column. We have no overflow.
Best Answer
Based on wiki's entry on Method of complements.
Assuming you have copied down the method of complements correctly and it is indeed four's complement we are talking about, a $n$-digit negative number $-x$ will be represented by the string corresponds to $4^n - x$. For example, the number $-1$ will be represented as a string with $n$ characters of '$3$'.
In general, the legal range for numbers will be $[-\frac{4^n}{2}, \frac{4^n}{2} - 1 ]$. In certain sense, working with numbers in four's complement is like working with ordinary integers under modulus arithmetic with modulus equal to $4^n$.