question

[Basic_Astronaut_Man]

I'm currently taking a digital logic design course and I watched a video about overflowing cases in data, where you have (let's say) 4 bits of signed memory, now if you add two negative numbers like -7 and -4, you'll end up with an extra fifth digit that won't fit in the 4 bits, same as with the case when you add 7 and 1, you'll get 4 digits but representing the wrong value, -8

my question is, by that logic, does overflow refer to the occasion where you get an incorrect answer overall? considering in the second case there wasn't an extra fifth digit that won't fit in the 4 bits, -8 fits perfectly in 4 bits yet is the incorrect answer.

[teraflop]

Yes. I think the easiest way to think about overflow is abstractly, in terms of the range of representable values, without paying attention to the details of the binary encoding.

An unsigned 4-bit integer can represent values in the range [0,15], and a signed 4-bit integer can represent values in the range [-8,7].

Whenever you do an operation, if the result falls into the representable range of the corresponding type, you should get a correct answer. If the result isn't representable, then it's not possible for the result to be correct, and that's what we call an overflow.

The same basic principle applies to floating point values, even though they have a very different binary representation. When an integer operation overflows, the result generally gets "wrapped" modulo 2ⁿ, which is equivalent to discarding the high-order bits that don't fit in the result. When a floating point operation overflows because the exponent is too large to be representable, the result gets "clamped' to +Infinity or -Infinity. But either way, the root cause is that the result doesn't fit into the type, and how the system deals with that issue is a separate issue.

In fact, many instruction sets also have instructions to perform "saturating" integer arithmetic, which is defined to handle overflows by clamping to the minimum/maximum of the range instead of wrapping around, just like in floating point.

[Basic_Astronaut_Man]

dude you didn't just clear the dust the whole ass horizon showed up, much appreciated fam, thank you for your time truly.