I am not speaking of cups and doughnuts though, or even (as i stressed out already) about a binary base system developed by us, and a quaternary base system developed by us. The difference here is that the computer will be working with dna, not some system simulating dna. Do you think both are the same? I heavily doubt they are the same at all, given that dna works by itself not just because someone planted a quaternary system in it, but because it is itself the quaternary system it uses. The computer is not its own developer or user. We are not the computer. This is why i claimed this may not work well.
DNA is not an ideal quaternary system, you can have deviations from that ideal behavior. A DNA strand could break for example, rendering the information useless. But if you want to use it to do computations in a quaternary system, you should better try and make it behave as close to the ideal system as possible.
The system, whether binary, quaternary, quantum binary, quantum quaternary or whatever is always a model we try to emulate with the underlying system, no matter whether that is a semiconductor, DNA, atom, photon or anything else. The physical system matters only so far as there might be deviations from the ideal model that have not been addressed properly by the constructors of the system
Are these 'gates' that take in 4 inputs as powerful as binary gates though, in the sense that you can build any function you can think of with them?
Cause that's another good thing about binary gates - you can build anything using just 1 type of gate - a NAND gate. That helps reduce costs because you essentially have everything built out of 1 type of building block.
It's easy to prove, that you can build any function you want with a 4 input gate: Use a gate that ignores the two extra inputs and thus emulates a binary gate. Actually using 4 input gates that way would not be very efficient, but as you add true 4 input gates, the functionality can only grow, not decrease.
And while you can build any function from NAND gates, actually doing so when designing a chip would be quite wasteful. If you need a NOR gate at one point, you could either use 4 NAND gates (requiring 16 transistors in CMOS logic) or just implement the NOR gate directly (only 4 transistors). The amount of transistors on a chip is limited and every additional transistor in a function will increase the power consumption of that function. So for advanced chips you do not have the luxury of building everything with NAND gates.