Code — Chapter 2: Codes and Combinations

Exploring Braille, mathematical combinations (2ⁿ), and how two-state systems scale to represent complex information.

Part of the series on Code: The Hidden Language of Computer Hardware and Software.

Expanding the Concept of a Code

Chapter 2 shifts from “We can represent information with signals” to:

“How much information can we represent using combinations of a small number of states?”

A code doesn’t necessarily mean something secret. Language itself is a code. The letter A is just a shape; there’s nothing physically inherent in that shape that means a particular sound. Humans agreed on its meaning.

Similarly:

Red traffic light $\rightarrow$ stop
Green traffic light $\rightarrow$ go

The physical thing and its meaning are separate. A code establishes the mapping between them.

Braille

The major example in this chapter is Braille. Braille represents characters using raised dots arranged in a cell.

A traditional Braille cell contains six possible dot positions:

● ●
● ●
● ●

For each position, there are two possibilities: raised or not raised.

Each dot position doesn’t need six different states — it needs only two.

Combinations & Binary Scaling

If there were only 1 dot position:

0 = not raised
1 = raised
Total: $2^1 = 2$ possibilities

With 2 dots:

00, 01, 10, 11
Total: $2^2 = 4$ possibilities

With 3 dots:

000, 001, 010, 011, 100, 101, 110, 111
Total: $2^3 = 8$ possibilities

The General Pattern

$\text{Possibilities} = 2^n$

1 position $\rightarrow 2^1 = 2$
2 positions $\rightarrow 2^2 = 4$
3 positions $\rightarrow 2^3 = 8$
4 positions $\rightarrow 2^4 = 16$
5 positions $\rightarrow 2^5 = 32$
6 positions $\rightarrow 2^6 = 64$

Six two-state positions produce 64 distinct combinations. Something constructed purely from raised / not raised can represent dozens of different symbols. This is one of the central mathematical foundations of digital computers.

Connecting Chapters 1 & 2

CHAPTER 1
Information → Encoded using simple signals → dot / dash

CHAPTER 2
Two possible states → Combine n positions → 2ⁿ combinations → Rich multi-symbol meaning

This points directly toward digital computing:

Context	Two-State System
Morse	dot / dash
Braille	raised / not raised
Digital Systems	0 / 1
Electrical Circuits	off / on

The physical representation changes; the underlying principle remains identical.

Core Takeaways Before Chapter 3

What is a code? A convention for representing one kind of information using another set of symbols or states.
Encoding vs. Decoding: Encoding converts information into representation; decoding recovers the original information.
Representation is separate from meaning: Physical signals carry no inherent meaning until we assign rules.
Two states scale exponentially: Combining $n$ independent two-state choices yields $2^n$ combinations.
The physical medium isn’t fundamental: Light, sound, marks on paper, raised dots, or electrical voltages can all carry encoded information.

One-Sentence Summaries

Chapter 1: Information can be communicated by translating it into an agreed system of simple signals.
Chapter 2: Combining multiple simple two-state choices creates enough distinct patterns to encode increasingly complex information.