Question about NOR gates and overflow

[seang]

How do I develop a minimal NOR circuit that detects overflow by examining the sign bits of two addends (A and B) and their sum (S)?

Doesn't this depend on how long the addends A and B are? Is there anyway I can generalize the result to n bit addends?

or perhaps I can just designate one input as 'the carry in', compare the MSB of the two addends and go from there?

 

[doodle]

I believe the problem requires you to consider only the MSB of A and B, and the sum S of these bits. What are the overflow conditions given these 3 inputs? Work it out from there.

 

[ravenprp]

How do I develop a minimal NOR circuit that detects overflow by examining the sign bits of two addends (A and B) and their sum (S)?

Doesn't this depend on how long the addends A and B are? Is there anyway I can generalize the result to n bit addends?

or perhaps I can just designate one input as 'the carry in', compare the MSB of the two addends and go from there?

When adding, you MUST add two strings that are both of N bits. So, if you're adding strings of N bits, the sum of the carry out when adding the msb MUST NOT EQUAL 1.

If it equals 1, you have overflow.

For ex:

If you have two 8 bit strings...

1
10001
+11100
-------
01101

That 1 in the bold is a carry-out, hence overflow.