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For left-handed people, the difference between left and right is less salie nt that for most right-handed people, and they do tend to confuse right and left more frequently (still not all that often). I'm left-handed and my wi fe gets irritated when I confuse right and left. I don't confuse 0 and 1 in logic designs - or at least not often enough for anybody to have commented on it.
As I understand it, left handed people represent roughly half the populatio n who aren't born with the right-handed brain-pruning gene (which is nearly half the population). Psychological researchers who are looking at where t hings go on in the brain tend to exclude left-handers because the distribut ion of where things actually happen tends to be idiosyncratic in left-hande rs (and some right-handers). It's not random, but the non-right-handed prop ortion of the population chooses out of broader palette of possibilities.
The right-handed brain pruning gene does seem to put language processing in to a particular configuration that works well, but the current edition of t he human genome seems to generate brains that can do language processing we ll enough no matter how you parcel out the processing. This might not have been true earlier.