What logic gates are required for Turing completeness?

Question

My son has been playing Little Big Planet 2 lately, and I noticed that the game editor allows AND gates, OR gates and NOT gates... Is it Turing complete? If so, can anyone recom

Answer 1

You need NOT and one of AND or OR to be able to do all binary logic. This is DeMorgan's Law, basically.

However, this is not sufficient for Turing completeness. For that you also need random (or reducably equivalent) access (theoretically) infinite memory.

Odds are, you'll be able to build a flip flop (a D flip flop is built using NANDs, so it's straightforward) using the available logic gates. From those, you can build a register, and with enough of those you'll be equipped to build some simple programs.