Unit 1 · Digital Information · Lesson 1.13 · Review

Rebuild the Map

Twelve lessons, twenty-two words, one idea. Today you put it back together from memory.

Big Idea 2 — DataReview — the test is 1.14

Before this lesson — read on Runestone

A short recap of the book's version of this material. Read it after you try the map below, not before — retrieving beats re-reading, and you want to find your gaps while there is still time to fix them.

1

Where We Are

People→ Bits→ Programs→ Internet→ Security→ Big Data→ Impact

End of Bits. This little map has sat at the top of every lesson for three weeks. Today you build the one underneath it — the map of what actually happens inside that second box — and you build it without looking.

2

The Hook

Close everything. No notes. No previous lessons open. Just you and one question: how does the world turn into bits, and what goes wrong on the way?

If you can answer that out loud in about ninety seconds, you are ready for the test. If you can't, you have just found out something genuinely useful while there is still time to do something about it — which is the entire reason this lesson exists the day before and not the day after.

3

The Idea

Here is the whole unit as one sentence, and everything else is detail hanging off it:

The world is continuous. Computers are finite. So we sample the world, encode the samples as agreed-upon numbers, store those numbers in a fixed number of bits, and compress them when they don't fit — and every one of those steps loses something or has a limit.

Read that again and notice that it names the whole unit in order. Sampling is 1.6. Encoding is 1.1, 1.2, 1.4 and 1.5. Fixed bits is 1.3. Compression is 1.8 and 1.9. And 1.7 is the reason you can say the sentence at all — abstraction is what lets you talk about "a photo" instead of thirty-six million numbers.

The five traps

These are the pairs students actually mix up. Every one has shown up on real exams, and every one is worth thirty seconds of your attention right now:

Don't confuseThe one-line difference
bit vs byteA bit is one 0 or 1. A byte is 8 of them.
2n vs 2n−12n is how many patterns. 2n−1 is the largest value, because 0 uses one up.
overflow vs round-offOverflow = the number was too big. Round-off = it was too precise.
analog vs digitalAnalog is continuous, every value in between. Digital is discrete, a finite set.
lossless vs lossyLossless gives the original back exactly. Lossy does not, ever.
How to actually revise this. Re-reading feels productive and mostly isn't. What works is retrieval: close the page, say the answer out loud or write it down, then check. Both widgets below are built that way on purpose — they make you produce the answer before they show you one. If a drill feels uncomfortable, that is the feeling of it working.
4

Try It

Rebuild the map

Four stages are missing. Click a term, then click the slot it belongs in. Click a filled slot to take it back.

All 22 terms

A definition, four terms. Miss one and it comes back later in the round — you're done when every term has been answered correctly once.

The ninety-second test

Find a partner. One of you talks for ninety seconds, no notes, answering the hook question: how does the world turn into bits, and what goes wrong on the way? The other listens with this page open and ticks off which of the seven map stages got mentioned.

Then swap. Whatever your partner didn't say is exactly what they should study tonight — and you will find that saying it out loud is much harder than recognising it in a list. That gap is the thing the test measures.

5

Vocabulary

Nothing new — everything old. All 22 terms are in the drill above, pulled from the lessons that taught them. If you want to study away from a screen, here they are grouped by lesson:

Representing numbers 1.1 – 1.3
bit · byte · binary number system · place value · base-10 (decimal) · base-2 (binary) · fixed-width representation · integer overflow · round-off error
Representing everything else 1.4 – 1.6
character encoding · ASCII · Unicode · pixel · RGB · hexadecimal · analog data · digital data · sampling
Managing it 1.7 – 1.9
abstraction · data compression · lossless compression · lossy compression
6

Check

Six questions, deliberately picked from the traps above. These are the ones that cost marks.

0 of 6 answered
7

Impact Check

Nine stories, one shape

Every lesson this unit ended with a real consequence. Line them up: perfect copies reshaping music and privacy (1.1). A spacecraft lost to a disagreement about units (1.2). A rocket and a missile battery lost to numbers that didn't fit (1.3). Names that a 1963 standard had no room for (1.4). Photographs that stopped settling arguments (1.5). Phone audio tuned for a "typical" voice (1.6). Decisions nobody can see inside of (1.7). An impossible product sold to real investors (1.8). And the blurry lecture that lands on the student with the worst internet (1.9).

They are not nine unrelated cautionary tales. They share a shape, and it is worth naming because it will repeat in every unit left this year: a technical decision, made for defensible reasons under real constraints, distributes its costs and benefits unevenly — and outlives the constraints that justified it.

Notice what that framing does not say. It doesn't say the decisions were wrong; most were reasonable when made. It doesn't say someone is to blame; usually nobody is. What it says is that "it worked as designed" and "it caused harm" are not opposites, and that noticing who ends up carrying the cost is a separate skill from understanding the technology. The AP written responses ask for both. So does being any good at this.

8

Connections

Came from everywhere — this lesson has no new content by design. If something here felt unfamiliar, that is the lesson to reopen tonight.
Next is 1.14 — the unit test. The traps table above is not a hint; it is a list of what actually gets missed.
Opens Unit 2 — you stop asking "how is this stored" and start asking "how do I tell the machine what to do." Every representation you learned stays underneath.
Returns in Unit 10 — boot camp reassembles this map alongside the other nine. Building it once properly now is the cheapest version of that work.
← 1.11–1.12 Mini-Project 1