L02 §1 · Why Quantum? ~18 min

What Classical Computers
Actually Do

Before you can understand why quantum computers are different, you need to understand precisely what classical computers are. Not vaguely — precisely. The answer is surprisingly simple, and surprisingly profound: it is switches. All the way down.

✦ One Idea A classical computer is billions of switches — transistors that are either on (1) or off (0). Every image, video, song, email, and AI model is a pattern of those two states. The entire digital world is built from this single, tiny distinction: on or off.

bits transistors binary numbers logic gates classical computing §1 · Why Quantum?

Section 01

① Hook

What Is a Computer, Really?

💭

Think before you read

What is the smallest, most fundamental thing a computer does?

A modern laptop can run a 3D game, play music, send emails, and run an AI model simultaneously. What is the single most fundamental operation it is performing in all of these cases?

The question "what does a computer do?" has many valid answers depending on what level you look at it. At the level of software, it follows instructions. At the level of hardware, it moves electrons. But at the most fundamental level — the level that actually determines what a computer can and cannot do — the answer is this: it manipulates bits.

And a bit is the simplest possible thing: a distinction between two states. On or off. True or false. 1 or 0. Everything else is built from this.

Section 02

② Intuition

Everything Is Lego

Imagine you are handed a single Lego brick. It is small, simple, and by itself unremarkable. But give someone enough Lego bricks — millions of them — and the instructions for how to assemble them, and they can build a model of the Eiffel Tower. Or a working mechanical clock. Or a full-scale X-wing fighter.

The Lego brick is not interesting in itself. What is interesting is that complexity emerges from simple pieces combined according to simple rules.

🧩

The Lego analogy, made precise

The Lego brick is the bit. The rules for connecting bricks are logic gates — AND, OR, NOT — simple operations on bits. The blueprint is the program. And the complex result — a 3D game, a song, a document — is what you get when you run millions of those simple operations in sequence, billions of times per second. The complexity of the output is not in any individual piece. It emerges from their combination.

This is the insight that makes computers possible: you do not need a different kind of hardware for every different kind of task. You need exactly one kind of hardware — something that can represent 0 or 1, and switch between them on command — combined in the right patterns, enough times, fast enough.

The history of computing is essentially the history of making that one operation — flip a switch — faster, cheaper, and smaller.

Section 03

③ Framework

Bits, Switches, and Transistors

A transistor is an electronic switch. It has three terminals: one that lets current flow in, one that lets current flow out, and one that controls whether the switch is open or closed. When the control terminal receives a small voltage, the switch closes and current flows — the bit is 1. When the control terminal receives no voltage, the switch opens and no current flows — the bit is 0.

That is the complete description of the physical mechanism underlying all digital computing. Everything else — CPUs, memory, graphics cards, neural networks — is transistors arranged in patterns.

The scale is what makes it astonishing

One transistor

8-bit byte

One letter ('A')

8 bits

One photo (12 MP)

~288 million bits

Modern CPU

~100 billion transistors

🔬

How small is a modern transistor?

A 2024 laptop CPU has transistors with feature sizes around 3–5 nanometres. A nanometre is one-billionth of a metre. A strand of human hair is about 70,000 nanometres wide. There are roughly 20,000 modern transistors across the width of a single hair. This miniaturisation is why Moore's Law held for 60 years — and it is also approaching fundamental physical limits, which is part of why alternative computing paradigms like quantum are being explored.

Logic gates: operations on bits

A transistor on its own is just a switch. Combining transistors in specific wiring patterns creates logic gates — devices that take one or two bits as input and produce one bit as output. The three fundamental gates:

NOT gate: takes 1 input, flips it. NOT(0) = 1. NOT(1) = 0. Built from a single transistor wired as an inverter.

AND gate: takes 2 inputs, outputs 1 only if both inputs are 1. AND(1,1) = 1. AND(1,0) = 0. Everything else = 0. Four transistors.

OR gate: takes 2 inputs, outputs 1 if at least one input is 1. OR(0,0) = 0. OR(1,0) = 1. OR(0,1) = 1. OR(1,1) = 1. Four transistors.

Universality

These three gates — NOT, AND, OR — are universal. Any computation that can be performed by any computer can be performed using only combinations of these three gates applied to bits. This was proved by Claude Shannon in 1937, connecting Boolean algebra (the mathematics of true/false logic) to electrical circuits. Every piece of software you have ever used runs, at the bottom, on these three operations.

Section 04

④ Theory

Building Numbers from Bits

You know the decimal (base-10) number system from everyday life. It has ten digits: 0 through 9. Each position in a number represents a power of 10: the rightmost digit is the ones place ($10^0 = 1$), the next is tens ($10^1 = 10$), then hundreds ($10^2 = 100$), and so on.

Computers use binary (base-2), which has only two digits: 0 and 1. Each position represents a power of 2. With 4 bits, you can represent any whole number from 0 to 15. Here is how:

How 4 bits build any number 0–15

$$\underbrace{b_3}_{2^3=8} \;\underbrace{b_2}_{2^2=4} \;\underbrace{b_1}_{2^1=2} \;\underbrace{b_0}_{2^0=1}$$ $$\text{value} = b_3 \times 8 + b_2 \times 4 + b_1 \times 2 + b_0 \times 1$$

Example: bits 1011 = $1\times8 + 0\times4 + 1\times2 + 1\times1 = 8+0+2+1 = 11$

The interactive section below lets you feel this directly. Toggle each bit switch and watch the decimal number update in real time. Try to build every number from 0 to 15.

🔢

Why binary and not decimal?

Decimal requires ten distinct voltage levels to represent ten digits. This is fragile — voltages drift, noise corrupts them. Binary requires only two levels: "voltage present" (1) and "voltage absent" (0). These two states are robust against noise — a signal has to drift very far before a 0 is misread as a 1. This reliability is why all digital electronics use binary, even though it means longer numbers (1011 instead of 11).

Section 05

⑤ Interactive

Bit Toggler — Build Every Number 0–15

Toggle each switch to turn it on (1) or off (0). The decimal, binary, and hex values update live. Try to reach every number from 0 to 15 — the number line at the bottom tracks your progress.

⚡ Bit Toggler

Toggle bits · build numbers 0–15 · reach them all

INTERACTIVE

Decimal

base 10

Binary

0000

base 2

Hexadecimal

0x0

base 16

Click any row to toggle that bit

Numbers reached (0–15)

Lesson Summary

What a Classical Computer Actually Is

🔀
A bit is the simplest unit of information: on or off, 1 or 0
Every piece of digital information — text, image, sound, video, code — is ultimately encoded as a sequence of bits. There is no smaller unit of classical information than this single binary distinction.
⚡
A transistor is a physical switch that represents one bit
Modern CPUs contain around 100 billion transistors in an area the size of a thumbnail. Each can switch states billions of times per second. The power of a computer is not in the sophistication of its individual parts — it is in the scale and speed of their combined operation.
🔧
Logic gates (NOT, AND, OR) are universal — any computation reduces to them
Shannon's 1937 proof: every logical and mathematical operation can be expressed as a combination of NOT, AND, and OR gates on bits. The entire software stack — operating systems, databases, AI models — rests on this foundation.
🔢
Binary encodes numbers: each bit doubles the representable range
4 bits represent 0–15 (16 values = $2^4$). 8 bits represent 0–255 (256 values = $2^8$). 64 bits represent over 18 quintillion values. Binary is used (not decimal) because two voltage levels are far more robust against noise than ten.
🏗️
Complexity emerges from simple rules applied at scale
A single transistor is not interesting. 100 billion transistors, wired according to the right patterns, running at 3 GHz, represent the most complex artefact humans have ever built. The Lego principle: everything complex is assembled from something simple.

Quick Check

How clearly do you understand what a classical computer is doing at the hardware level?

You now know what a classical computer is.
It is very good at what it does.
So why do we need something different?

→ Why We Need Something Different — L03

Sources & Further Reading

Shannon, C. E. (1937). "A Symbolic Analysis of Relay and Switching Circuits." — Proved that Boolean algebra maps directly to electrical circuits; the theoretical foundation of all digital computing. Shannon was 21 years old.
Nielsen, M. A. & Chuang, I. L. — Quantum Computation and Quantum Information, Cambridge, 2000. §1.2 "Quantum bits" — opens with classical bits as the baseline, which is exactly this lesson's role in the curriculum.
Feynman, R. P. — Feynman Lectures on Computation, Addison-Wesley, 1996. Chapter 1 — Feynman's treatment of the bit and classical logic, written for a general audience with characteristic clarity.
Intel — "Transistor Count History." A public record showing transistor counts in CPUs from 1971 (2,300 transistors in the Intel 4004) to 2024 (~100 billion in Apple M3 Ultra). Every doubling is Moore's Law in action.

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Welcome

L01 — Why this feels like magic

Why We Need Something Different

L03 — Classical limits and the quantum gap

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