Foundations — Physical layer — encoding (NRZ, Manchester), bandwidth, Nyquist, Shannon-Hartley

Before you can read the parent note, you need a small toolbox. Below is every symbol and idea the parent leans on, built from nothing, each one earning the next.

0. The very first picture: a bit as a voltage

Look at s01: the same three bits 1 0 1 drawn as a voltage picture. The whole chapter is about choosing how to draw that picture.

1. Time, period, and "how fast" — Hz

2. Bandwidth $B$ — the wire's "wiggle budget"

In s02, the shaded band is the set of frequencies that survive; anything outside is chopped off. A wider band = more room to wiggle fast = more bits/sec possible. This single number $B$ is the star of every capacity formula.

3. Powers of two and the logarithm — counting choices

Encoding often uses more than two voltage levels. To count how many bits that buys, we need one tool.

s03 shows the doubling tree: 1 bit → 2 patterns, 2 bits → 4, 3 bits → 8.

4. Ratios and the decibel — measuring noise

5. Symbol, baud, bit rate — three "speeds"

6. The $2B$ factor — why sampling gives "twice bandwidth"

You don't need the proof yet — just carry the fact: bandwidth $B$ → up to $2B$ symbols/sec. That single fact powers both Nyquist and Shannon in the parent note.

Prerequisite map

Everything on the left feeds the single box on the right: the capacity laws of the parent note, the parent topic.

Equipment checklist

Cover the right side and test yourself — if any line stumps you, re-read its section above.