Everything so far — the gates, the adder, the subtractor, the multiplier, the divider — was built from a handful of transistors you could count on your fingers. A real computer does the exact same thing. It just does it with billions of switches instead of a handful, ticking on and off billions of times a second instead of once per click.
Before transistors existed, computers were built from relays — electromagnetic switches that click a metal arm open or closed, the same job your finger was doing back in Chapter 1. The Harvard Mark I, completed in 1944, was wired from roughly 3,500 relays into the same kind of adders you built in Chapter 5. Each click took a fraction of a second, so the whole machine could add two numbers in about 0.3 seconds — slow enough to hear it think, tick by tick.
A handful of the ~3,500 relay-switches in the Mark I. Slow, loud, and big enough to see with your own eyes — but wired together with the exact same logic as the gates from Chapter 3.
The transistor from Chapter 1 does the relay's job with no moving parts, which means it can be made almost unimaginably small and flipped on and off almost unimaginably fast. A modern CPU — the kind in an ordinary laptop or phone — packs somewhere around fifteen to twenty billion transistors onto a chip smaller than a postage stamp, each one flipping billions of times per second.
180 tiny squares standing in for roughly 20,000,000,000 transistors — each one is a switch identical in principle to the relay above, just small enough that millions of them fit under a fingernail.
That's over five million times as many switches — on a chip you can hold between two fingers, running billions of times faster.
In the 1960s, Grace Hopper — a Navy admiral and one of computing's most influential pioneers — started handing people an 11.8-inch piece of wire: the exact distance light travels in one nanosecond, a billionth of a second. That's the actual speed limit an electrical signal is stuck with inside a computer. Her point: a computer isn't slow because someone was lazy, it's fighting the literal speed of light.
Run that math on a modern CPU clocked around 3 GHz, and each clock tick lasts about a third of a nanosecond — in that sliver of time, even light only makes it about 4 inches down a wire before the next tick arrives. Slower, older chips give light more room: a ~650 MHz processor, typical of the late 1990s, ticks about once every 1.5 nanoseconds — enough time for light to travel roughly 18 inches, a foot and a half, before the next calculation even starts.
Your CPU finishes a calculation, waits for the next tick, and starts again in less time than light needs to cross a dinner plate — billions of times a second, every second it's turned on.
Nothing new happened between the Mark I and your phone — the idea never changed, only the scale. Wire a few transistors together and you get the AND/OR/NOT/XOR gates from Chapter 3. Wire enough gates together and you get the adder, subtractor, multiplier, and divider from Chapters 5 through 8. A real CPU is millions of those same little circuits — called an ALU (arithmetic logic unit) — plus billions more transistors acting as short-term memory, and a control unit that, billions of times per second, decides which operation to run next and feeds it the switches it needs.
That's the whole trick, top to bottom. A transistor the size of a virus, flipped on and off. Wired into a gate. Wired into an adder. Repeated billions of times, ticking billions of times a second. Everything your phone, laptop, or any computer has ever done is that same idea, scaled up.