this strikes me as a chesterton's fence situation - "what kind of weird nonsense is this 2's complement where it's asymmetric (yuck) and you can't negate -0x800

this strikes me as a chesterton's fence situation - "what kind of weird nonsense is this 2's complement where it's asymmetric (yuck) and you can't negate -0x8000" i seriously doubt the folks who think this is a good idea know enough about the math and computer architecture to understand why in fact it's a terrible idea. - programming languages are abstractions. but (old joel) leaky ones sometimes. we don't like this, but you have to live with it. - in this case, the choice might be between reality-leaks such as "integers have limits", "the limits are asymmetric, leading to this negation pseudo-paradox" and a much worse leak such as "why does this spiffy safe integer type run 100,000 times slower than the weird C int" - actually math itself is a series of ever complicated abstractions. first counting numbers. then ZERO. then NEGATIVE numbers. ACK! now wait until you get to Fields and Rings and Galois Fields, which are very close to the concept of 2's complement integers. i believe that if ignoring the botched C standard that makes signed integer wraparound UB, "normal" 2's complement integers (and unsigned) form a finite ring. - so what? well even these fancy, and frankly, impenetrable math abstractions are just abstractions. they leak too and aren't "perfect" if you take into account the real universe which doesn't always match the perfect math. doesn't mean it isn't very useful. - these concepts can be used to reason about the behavior physical things, like the behavior of an array of flip-flops representing a 64 bit number and especially how you can create circuits and simplify them to do things that implement addition, multiplication, etc. - the problem with a sorta-1's-complement-without-two-zeros idea is it has none of these connections to grounded theoretical basis. so how do you simplify an adder? can you perform algebraic simplifications to it? what is the model for this thing? - symmetry is in the eye of the beholder. draw a 4-bit signed 2's complement drawing using "clock diagram". it works. now do it with 1's complement or this suggestion which is even worse with an odd, sometimes prime, number of nodes. - implementation: 2's complement is a very clever hardware technique that lets you interpret N bits as N digits of a binary number. each digit has weight 2^n: 1, 2, 4, 8, etc. except the last digit which has weight -2^n. this simple trick lets the signed and unsigned integers use the same addition, subtraction, and with minor processing, multiplication and division logic unchanged. it's very unlikely that you can implement the suggested scheme at even 1/10th the performance or cost. - and, yes, i think C really got it wrong calling "overflow" or wraparound UB. if it was defined to wrap, at least it would be theoretically analyzable. you'd still have overflow flaws, but that's provably impossible to avoid with finite sized integers of any design.