Would I be correct in saying that we do not use AC current in electronics because in the circuits, the presence of current would be a "1" and no current would be a "0". Thus with DC on = "1", off = "0". With AC, the current becomes zero 60 times a second (for 60 Hz) and thus would not be useful in electronics.
Well , one circuit that makes use of the 60 Hz AC current is your light dimmer. Look up triac or scr ( silicon controlled rectifier ) .
And all circuits are not composed of bits of ones and zeroes, as you mention.
That is usually reserved for circuits that are modeled to work with boolean algebra such as that in your computer - digital circuitry.
Google transistor and see how a transistor can be used to amplify a signal entered into the base of the transistor - bipolar, NPN, PNP, FET, Mosfet for example.. The signal can be thought of as being a type of AC. But then again we need a DC voltage - a DC voltage is at the bipolar collector and emitter for that type of signal amplification.
Early transistorized computer circuitry used bipolar transistors arranged so that they could be led to saturation, producing the on/off , 1/0, high/low, that everyone knows about. A saturated transistor can be in only one of 2 states - conducting current or not conducting current. There was and still are different logic families - RTL, TTl, CMOS are just a few are dated.
One cannot consider evisioning transistor digital circuitry being based on AC.