Can you show a diagram of the gates please. I don’t understand what you’ve writte
The gate picture for the proposed solution is quite messy, as it involves several layers of gates. You can do it yourself of course from the equations---I tried and it was a complete spaghetti, and the equations actually explain the idea behind the solution a little better.
Having said that, I came up with a different, simpler design:
Aout = not Ain
Bout = not(Bin and Cin) and Bin
Cout = not(Bin and Cin) and Cin
which is fairly easy to draw, as it involves only five total gates.
It works because not(Bin and Cin) is notBin or notCin by de Morgan laws, and when you OR it with e.g. Bin you can cancel out Bin OR notBin, so notCin is what's left.
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