In 1854, the mathematician George Boole published a book arguing that logical reasoning could be reduced to algebra — that statements are either true or false, and every way of combining them boils down to three operations: AND, OR, and NOT. It read, at the time, like pure abstraction. A century later it became the working blueprint for every digital device on the planet, because a transistor turns out to be a remarkably good physical implementation of a true-or-false switch.
From a math notation to a physical switch
A transistor is, at its simplest, a gate controlled by voltage — on or off, current flowing or not, which maps directly onto Boole's true or false. Wire a handful of transistors together in the right pattern and you get a logic gate: an AND gate outputs true only if both its inputs are true; an OR gate outputs true if either input is; a NOT gate simply flips its single input. From those, engineers derive others — NAND, NOR, XOR — but one of them, NAND, turns out to be special: every other gate, and by extension every computable boolean function that exists, can be built out of NAND gates alone. That's why chip manufacturing can standardise around fabricating enormous, repeating grids of essentially one component.
How a handful of gates becomes "add these numbers" or "is this face a match"
Combine gates in the right arrangement and you get a circuit that adds two binary digits and correctly carries the overflow — a full adder. Chain enough full adders together and you can add numbers of any size. Stack that logic alongside memory circuits and control circuits, scaled up to the billions of transistors on a modern chip, and the same primitive — true, false, AND, OR, NOT — is what's underneath arithmetic, comparisons, and, with enough layers of abstraction on top, something that looks like recognising a face or predicting the next word in a sentence. However sophisticated the behaviour on the surface looks, it's still cascades of true-false switches underneath, all the way down.
What we're still unsure about
This boolean model is what every conventional computer runs on, but it's worth being precise about where it stops. Quantum computing works from a genuinely different primitive — the qubit, which holds a superposition of states rather than a strict, settled true or false — and it isn't simply "more powerful boolean logic" running faster. It's a different computational model altogether, one that's genuinely useful for a narrow set of problems where that superposition can be exploited, not a faster general-purpose version of the phone in your pocket. Treating quantum computers as an upgrade to classical logic, rather than a different tool for a different job, is a common but real misunderstanding.
This sits inside Digital Logic & Boolean Circuits, one of eight topics in Electrical Engineering, one of four domains in Engineering, one of seventeen subjects the app can quiz you on.