Computer Science
Foundations

What is this about?

A computer only understands true (1) and false (0). All the complexity of software is logic built on top of that. If you understand boolean logic, you understand the foundation of everything.

The 3 operations you need to know

Why binary?

Computers use electricity: there is current (1) or there is not (0). That is a bit. With 8 bits you have a byte. With bytes you can represent letters, numbers, images, video — anything.

Storage units

What is an algorithm?

A sequence of steps to solve a problem. It does not have to be code. A cooking recipe is an algorithm. IKEA instructions too.

The 3 building blocks of any program

With these three structures you can build any software in the world:

turnOnComputer()
openBrowser()
searchOnGoogle("how to program")

if (grade >= 5) {
    show("Passed ✓")
} else if (grade >= 4) {
    show("You need the oral exam")
} else {
    show("Failed — back to studying")
}

// Count from 1 to 10
for i from 1 to 10 {
    show(i)
}

// While not home, keep walking
while (NOT atHome) {
    walk()
}

🧠 CPU — The Processor

The "brain". Executes instructions. Takes data, processes it, and produces results. Speed is measured in GHz (billions of operations per second). Almost all modern processors have multiple cores.

💾 RAM — Working Memory

Temporary memory. When you open Chrome, the data goes to RAM. Fast but volatile — when you turn off the computer everything is erased. More RAM = more things open without slowing down.

Which language to learn first?

The honest answer: any of them works for learning concepts. But if I had to pick one today: Python. Clean, readable, used everywhere: web, data, artificial intelligence, automation.

How does the Internet work?

The Internet is a huge network of computers that communicate using protocols — common rules for speaking the same language. Without protocols, computers could not understand each other.

Essential concepts

Computer science is vast. You do not need to learn everything now — you need to know what exists so you can find it when you need it.

Suggested roadmap

Everything you just learned, in one machine

Binary (§02), algorithms (§03), hardware (§04), networks (§06) — a language model uses all of it. Understanding the steps below is not optional if you want to work seriously with AI. It is the difference between a user and an engineer.

Step 1 — Tokenization: text becomes numbers

A model cannot read text. It only processes numbers. The first thing it does is split the input into small fragments called tokens and assign each one a numeric ID. Tokens are not words — they are fragments, sometimes smaller, sometimes larger.

"artificial intelligence"
→ ["artif", "icial", " intel", "ligence"]
→ [  8043,   1748,   intel_id,   ligence_id ]

// One word can be 1 token (English) or 3 tokens (Spanish/rare words)
// The context window limit is in tokens, not words
// "128k tokens" ≠ 128k words — it is fewer

Step 2 — Embeddings: numbers get meaning

Token IDs are arbitrary — like primary keys in a database. The ID for "cat" has no mathematical relationship with the ID for "dog". The model needs the opposite: numbers that are close when concepts are close. So each token ID gets converted into a vector of hundreds of dimensions.

"cat"  → ID 4953  → [0.23, -0.81,  1.52, 0.04, -0.33, ...]
"dog"  → ID 39041 → [0.21, -0.79,  1.48, 0.06, -0.31, ...]
"bank" → ID 8821  → [0.91,  0.44, -0.20, 0.77,  0.12, ...]

// cat and dog: nearly identical vectors — they appear in similar contexts
// bank: completely different — different meaning cluster

// Math that actually works on embeddings:
king - man + woman ≈ queen   // not a metaphor, real vector arithmetic

These vectors are contextual: "bank" in "I went to the bank" gets a different vector than "bank" in "sitting on the river bank". The meaning is not fixed — it depends on context.

Step 3 — Attention: every token sees every other token

The breakthrough paper (2017) was literally titled “Attention is All You Need.” For each token, attention calculates: how much should this token pay attention to each other token in the context? The result is a weight matrix.

Sentence: "The cat drank the milk because it was hungry"

Processing "it":
  The      → 0.02
  cat      → 0.71  ← high weight (refers to cat)
  drank    → 0.08
  the      → 0.01
  milk     → 0.06
  because  → 0.04
  it       → 0.05
  was      → 0.02
  hungry   → 0.01

// The model learned "it" refers to "cat" — no rules, just statistics

All tokens are processed in parallel — that is why Transformers can be trained on GPUs with massive datasets. Cost is O(n²): doubling the context quadruples the computation.

Step 4 — Generation: probabilities, not truth

After attention, the model converts the final vector into scores for every token in its vocabulary (~100,000 options). These raw scores are called logits. Softmax converts them to probabilities that sum to 1. Then one token is picked.

// Question: "The capital of France is..."
logits (raw scores):
  "Paris"    →  8.92
  "Lyon"     →  4.11
  "Europe"   →  3.87
  "the"      →  1.23
  "cat"      → -2.41

after softmax (probabilities):
  "Paris"    →  73%   ← chosen
  "Lyon"     →  12%
  "Europe"   →   9%
  ...
// This repeats token by token until the response is complete

The key insight: the model has no internal truth-checker. No component says “this is correct” or “this is false.” It only asks: given everything seen, what token is most probable next? If the most probable token is wrong — it picks it anyway, with full confidence. That is where hallucinations come from.