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The Boolean logic gates AND, OR and NOT comprise transistors, which are on/off switches wired together. Gates have one or two inputs but only one output, and they are wired in patterns that make ...
You guessed it, diodes can also be used to build logic gates, but not all of them ... all other gates can be implemented. The three input, diode-only AND gate is shown in the picture above.
By combining NOT and OR gates, you can easily make a NAND gate, an AND gate, a NOR gate, and any other logic you can dream up. Mechanical computing is decidedly old school, but not at these scales.