Logic Gates - What's the Most Complex Form of Representation?

The gates themselves take as input some number of input wires and then they'll spit out one output wire. This allows you to basically map any type of computational logic down into a set of additions and multiplications. You can use this to compose and represent all sorts of typical computer language primitives like your for loops and your while loops, if statements and your else statements. There's actually been some papers in the past that map the entire assembly language instructions down to these types of circuits.