What is a bit made of, and why have computers become so powerful?
In a modern chip, bits are stored and switched by transistors: tiny electronic switches made of silicon. A voltage on one terminal, the gate, lets current flow between the other two (a 1) or stops it (a 0). Each logic gate of the previous lesson is built from a handful of transistors.
In 1965 Gordon Moore, who later co-founded Intel, noticed that the number of transistors that fit on a chip was doubling at a steady pace. The pace settled at about every two years, and the industry kept it up for decades. This is Moore's law: not a law of nature, but an observation that became a target.
The Intel 4004 of 1971 had 2,300 transistors. Roughly how many does a large chip of 2023 have? Apple's M2 Ultra (2023) has about 134 billion transistors: some 58 million times more than the 4004.
Fitting more transistors in the same space means making each one smaller. Smaller transistors switch faster, use less energy and cost less per switch, so computers became both more powerful and cheaper at the same time.
But shrinking cannot go on forever. Somewhere along the way, a transistor becomes so small that it is only a few dozen atoms across, and atoms do not follow the rules we are used to. That is the next lesson.
Doubling every two years means N(t) = N0 × 2^(t − t0) / 2.
From 1971 to 2023 there are 52 years, so 26 doublings: 2,300 × 2^26 ≈ 154 billion. The real 2023 chip has about 134 billion: the rule of thumb held for half a century.
Computers got powerful by making transistors smaller and smaller; that shrinking is reaching the size of atoms.