Boolean functions

There are 16 possible functions with 2 bits of input and 1 bit of output.

Of these, only 6 are gates:

AND, OR, XOR, NAND, NOR, XNOR

All possible Boolean functions can be written using at most 3 gates:

Set {AND, OR, NOT} is computationally complete.

Also {NAND}, {NOR}, and some others.

Example: use NAND to implement OR

x | y

= ~~(x | y)

= ~(~x & ~y)

= ~x NAND ~y

Looks like we also need NOT