One of the perks of being a logic-gate neophyte is that I get to ask the naïve questions. So, why is the textbook example of the half-subtractor (upper schematic) so easily surpassed by rerouting one of its outputs to express the other?

I noticed in the output table that the D column was a meager AND Y away from the B. How did the one with the third gate get the popular vote? Answer however you like, but remember that you're dealing with a mathematical purist who may just disagree with real-world behaviors. Razz
The are functionally equivalent.. and I see no reason to favour the 3-gate version unless xbar is available as well (in that case it would be 1 delay faster)
But then of course it wouldn't really be a 3-gate thingy anymore..
In the top version, D=X xor Y, and B=Y and !X. In the bottom version, D=X xor Y still, and now B=Y and (X xor Y). Karnaugh maps tell us that those are functionally identical; I'm not sure why the first one would be preferable.
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