Why would one choose the memory representation of the number based on the advantages of the internal ALU wiring?
Of all those reasons, the only one I can make sense of is the "I can’t transparently widen fields after the fact!", and that one is way too niche to explain anything.
I don’t understand? Why not make the memory representation sympathetic with the operations you’re going to do on it? It’s the raison d’être of computers to compute and to do it fast.
Another example: memory representation of pixels in GPUs which are swizzled to make computations efficient
> I don’t understand? Why not make the memory representation sympathetic with the operations you’re going to do on it?
There's no reason to, as there's no reason not to. It's basically irrelevant.
If carrier passing is so important, why can't you just mirror your transistors and operate on the same wires, but on the opposite order? Well, you can, and it's trivial. (And, by the way, carrier passing isn't important. High performances ALU pass carrier only though blocks, that can appear anywhere. And the wiring of those isn't even planar, so how you arrange them isn't a showstopper.)
Of all those reasons, the only one I can make sense of is the "I can’t transparently widen fields after the fact!", and that one is way too niche to explain anything.