"Pre-toggled" NAND... becoming an OR gate by SL

Movie Description:

Upon seeing http://df.magmawiki.com/index.php/DF2010:Pre-Toggled_Mechanical_Logic I did not believe that it would work (it violated the principles of signal sending), so I decided to build one of the gates with pre-toggled input gears to find out. I built a pre-toggled NAND gate, and tested it.

In this movie, you can see the completed gate, which consists of four gears, with the 'output' gear on the top-left, two input gears on the upper-right and lower-left, and the power-input gear on the lower-right. The power input gear connects to axles leading to windmills on the right.

In the beginning, dwarves disassemble two levers which were connected to the inputs, which had been flipped to ON to pre-toggle the gears. After they are done, the dwarves flip the actual input levers until both are ON, and then flip them some more so run through all the input states, with each input ON, both inputs OFF, and both inputs ON. The result? This is an OR gate, not a NAND gate.

(As you can see, when both levers are ON, the output is also ON, where a NAND gate should be OFF)

Upon closer inspection, however, both the gears became disconnected when the pre-toggling levers were turned ON, and reconnected when the input levers turned ON. So that means they ARE toggling regardless of whether they get an ON or OFF signal, and that in fact the author happens to have designed an OR gate and called it a NAND gate, and vice versa, resulting in me originally thinking that his gates' pre-toggling did not work (as his OR gate design did not use pre-toggling).

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