Electronic – 74154 4 to 16 decoder logic diagram

We don't normally talk about a NAND gate having "state". It just responds to its inputs.

Since a NAND gate usually can respond to its inputs within a few nanoseconds, while power supply voltages typically take at least a few milliseconds to come up to valid levels during turn-on, the "state" of the NAND gates output immediately after start-up is rarely relevant.

In general during start-up there will be some time when the voltage rises to the point where the circuit is basically functional, but is not guaranteed to be functional. A NAND gate will start to respond to its inputs during this time and should be completely in sync with its inputs by the time the power supply voltage reaches the minimum voltage for guaranteed operation.

lets say a NAND gate for instance, and I send a 1 through input A, and a 1 through input B.....lets say (for some reason) the A gets there faster

This can happen, and it is called a "glitch". A typical case is when A is switching from 1 to 0 and B is switching from 0 to 1. The output to the prior inputs is 0, and the output to the final inputs is 0, but it's possible to see a 1 asserted for a brief time during the transition if the change in A arrives first.

This is why designing syncronous logic is in many ways simpler than designing combinatorial logic. In syncronous logic we can arrange the timing so that the next flip-flop downstream never has a clock edge arrive during the time when the upstream logic might glitch, so the glitch never propagates through to be seen at the final outputs of the system.

I'm trying to build the NOR/NAND gate with the use of inductively coupled coils. This is my personal interest and research :) I'm trying to prove (or disprove) that it's possible to build asynchronous logic circuits in this way.

Why didn't you ask that in the first place? It would have saved a lot of time.

Yes, it is possible to build logic with transformers. Have you ever heard of "rope memory"? It's a form of read-only memory built entirely from wires and ferrite toroids. It was used, for example, to store the instructions in the Apollo guidance computers.

The point is, a ROM (any ROM, no matter what the technology) is essentially a huge matrix of AND and OR gates, so it meets your basic functional requirement. However, it depends on exactly what you mean by "asynchronous" in this context. Transformers do not couple energy from DC signals, and so magnetic logic of this type is always driven by pulses, not DC currents.