On-Off State
The on-off state is the binary condition of a device such as a transistor: either conducting (on) or blocking (off), with nothing useful in between. A digital circuit assigns these two physical conditions to the two symbols of binary arithmetic, usually 1 for on or high and 0 for off or low, and the whole of computing rests on that mapping. The pair is an engineering convention laid over analogue physics, and the interesting questions concern how reliably a real, imperfect device can be held to it.
An on state is a low-resistance condition and an off state a high-resistance one, in two different physical senses. A bipolar transistor is off in cutoff, when its base-emitter junction is not forward-biased enough to inject carriers, and on in saturation, when the base is driven hard and the collector-emitter voltage collapses to a few tenths of a volt. A MOS transistor is off when its gate voltage is below the threshold voltage, so no conducting channel forms, and on when the gate is well above it. Shockley's junction transistor and the earlier point-contact device both worked as switches in this way, and the claim that a solid piece of crystal could take either state under external control is what made them replacements for relays and vacuum tubes. The wider the gap between on and off resistance, the more clearly the device distinguishes the two states.
Digital logic works because voltages are read in ranges, not as exact values. A real gate does not output exactly 0 or 5 volts, so the designers specify bands. In classic 5-volt TTL logic, an output below 0.4 volts counts as low and above 2.4 volts counts as high, while an input is guaranteed to be read as low below 0.8 volts and as high above 2.0 volts. The gaps between those numbers are the noise margins, 0.4 volts in each direction, meaning that noise on the wire up to that amount is ignored and then wiped out when the next gate regenerates a clean level. This is the reason digital signals can be copied, stored and transmitted through billions of gates without accumulating error, unlike analogue signals, in which every disturbance adds. Voltages in the middle, between the bands, are undefined; a gate may read either value or oscillate.
The off state is never perfectly off, and the on state is never perfectly on. A closed transistor has a small resistance and so drops some voltage and wastes heat, and an open transistor still passes a leakage current, from reverse-biased junctions in bipolar devices and from subthreshold conduction, gate tunnelling and junction leakage in MOS devices. In a chip with billions of transistors, even picoamps per device sum to a large standby current, and as dimensions fell below about a hundred nanometres, leakage became a main source of power loss, a major reason that supply voltages were lowered and that techniques such as power gating, multiple threshold voltages and new gate structures were introduced. Raising the threshold voltage reduces leakage but slows switching, a trade-off every processor designer has to balance.
The binary abstraction is a layer, and it leaks when pushed. Above the transistor, designers write logic equations and software, and need not think about carriers or threshold voltages, which is why a program is portable across processors. The abstraction holds only while the signal stays inside its margins: lower supply voltages shrink the margins, so a circuit becomes more sensitive to noise, power dips, cosmic-ray strikes and manufacturing variation, and timing failures appear when a signal changes too close to the clock edge. A frequent misunderstanding is that digital circuits are somehow free of analogue behaviour. They are analogue circuits operated so that only two outcomes matter, and when that fails, as with metastability in flip-flops sampling an asynchronous input, the analogue physics shows through. Today, memory cells, logic gates in AI accelerators and flash storage all follow this model, and multi-level cells in flash storage extend it by distinguishing four or more states in the same voltage window.
Read the on-off state as the digital abstraction made physical: a device pushed to one of two extremes, with generous margins and regeneration, so that a messy analogue world can behave as a clean pair of symbols.