Systematically altering functions
You can represent a function by its truth table.  Then, any two functions with the same truth table will be the same function, in the sense that they map the same inputs to the same outputs, so this gives you a way to recognize those.

The truth table has 4 entries, each of which are 2 bits, so the truth table is 8 bits long.  Thus, each function can be associated with an 8-bit binary string, or equivalently, an integer between 0 and 255.  You can "increment" the function by incrementing the corresponding integer and converting it back to a truth table.