# Class 1: From binary and hardware to wireless data and software

## Class record

- **Class date:** September 15, 2026.
- **Notes recorded:** September 15, 2026.
- **Sources:** Bradley's descriptions of the base-ten and binary activities, the base-ten whiteboard photo IMG_5295.HEIC, and the binary whiteboard photo IMG_5296.HEIC.
- **Note for next year:** Begin with familiar base-ten place values and exponents, then introduce binary counting in the same class using powers of two. Follow with the photographed conversion example, 0110₂ = 6₁₀. Then connect binary to semiconductors, silicon, and electronic switches, explain why Silicon Valley has its name, then introduce bits, bytes, and kilo through tera using exponents.

## Main idea

A digit's position determines its value. In base ten, the places from right to left are ones, tens, hundreds, and thousands. These are powers of ten, beginning with exponent zero in the ones place.

Binary follows the same positional rule, using powers of two. In both systems, multiply each digit by its place value and add the contributions.

## Example from the whiteboard

The number is **3,247₁₀**. The subscript 10 identifies its base.

| Place | Thousands | Hundreds | Tens | Ones |
| --- | --- | --- | --- | --- |
| Power of ten | 10³ | 10² | 10¹ | 10⁰ |
| Place value | 1,000 | 100 | 10 | 1 |
| Digit | 3 | 2 | 4 | 7 |
| Digit × place value | 3 × 10³ | 2 × 10² | 4 × 10¹ | 7 × 10⁰ |
| Contribution | 3,000 | 200 | 40 | 7 |

**3,247₁₀ = (3 × 10³) + (2 × 10²) + (4 × 10¹) + (7 × 10⁰)**

**= 3,000 + 200 + 40 + 7**

**= 3,247**

The photo explicitly develops the ones term: **7 × 10⁰ = 7 × 1 = 7**.

## Suggested teaching sequence for next year

The sequence and prompts below are planning suggestions based on the recorded example.

1. Write **3,247** and ask students to name each place: thousands, hundreds, tens, ones.
2. Identify each digit's contribution: 3,000, 200, 40, and 7.
3. Add the powers of ten above the columns: 10³, 10², 10¹, 10⁰.
4. Explain that the exponent counts positions from the right, starting at zero. Each move left multiplies the place value by ten.
5. Write each digit multiplied by its place value, then add the terms to reconstruct the original number.
6. Introduce the base subscript. Base ten uses the ten digits 0 through 9; after 9, counting carries into the next place.

## Suggested checks for understanding

- Why is the 4 worth 40? **It occupies the tens place: 4 × 10¹.**
- Why does the ones column use 10⁰? **10⁰ = 1, so it counts single units.**
- What does the subscript 10 mean? **The number is written in base ten.**
- Expand **3,047** using powers of ten. **3 × 10³ + 0 × 10² + 4 × 10¹ + 7 × 10⁰.** Use this to discuss zero as a placeholder.

## Binary counting: continuation of Class 1

**Recorded activity:** Begin counting in binary with **0000 for zero**, **0001 for one**, and **0010 for two**, then continue the pattern. Connect the places to exponents.

The explanations, completed counting table, and practice prompts below build out this activity for reuse next year.

### Place values are powers of two

Binary is base two and uses only the digits **0 and 1**. Each binary digit is called a **bit**. Four bits give four places:

| Place | Eights | Fours | Twos | Ones |
| --- | --- | --- | --- | --- |
| Position, counted from the right | 3 | 2 | 1 | 0 |
| Power of two | 2³ | 2² | 2¹ | 2⁰ |
| Place value | 8 | 4 | 2 | 1 |

Start at the right with **2⁰ = 1**. Moving left, each place is twice the previous value: **1, 2, 4, 8, 16, ...**. The exponent tells us which position we are in, starting at zero. For example, **2³ = 2 × 2 × 2 = 8**.

A **1** includes that place value in the total. A **0** contributes nothing from that place. Leading zeros keep the four columns aligned without changing the value: **0010₂ = 10₂ = 2₁₀**. The subscripts identify the bases.

### Count from zero to fifteen

| Decimal (base ten) | Binary (base two) | Sum of included place values |
| --- | --- | --- |
| 0 | 0000 | 0 |
| 1 | 0001 | 1 |
| 2 | 0010 | 2 |
| 3 | 0011 | 2 + 1 |
| 4 | 0100 | 4 |
| 5 | 0101 | 4 + 1 |
| 6 | 0110 | 4 + 2 |
| 7 | 0111 | 4 + 2 + 1 |
| 8 | 1000 | 8 |
| 9 | 1001 | 8 + 1 |
| 10 | 1010 | 8 + 2 |
| 11 | 1011 | 8 + 2 + 1 |
| 12 | 1100 | 8 + 4 |
| 13 | 1101 | 8 + 4 + 1 |
| 14 | 1110 | 8 + 4 + 2 |
| 15 | 1111 | 8 + 4 + 2 + 1 |

### How carrying works

In base ten, adding one to 9 gives 10: the ones place returns to zero and we carry into the tens place. In binary, adding one to 1 gives **10₂**: the ones place returns to zero and we carry into the twos place.

To count upward, work from the right. Change a 0 to 1 and stop. If a place already contains 1, change it to 0 and carry one place left, repeating as needed.

- **0000 → 0001:** Add one in the ones place.
- **0001 → 0010:** Two ones become one two.
- **0010 → 0011:** Add one in the ones place again.
- **0011 → 0100:** Carry through the ones and twos places. Two twos become one four.
- **0111 → 1000:** Carry into the eights place.

After **1111₂ (15₁₀)** comes **10000₂ (16₁₀)**, which needs a fifth place, **2⁴ = 16**. Four bits represent **2⁴ = 16 different nonnegative values**, from **0 through 15**.

### Converting from base two to base ten

**Recorded whiteboard example (IMG_5296.HEIC): 0110₂ = 6₁₀.** The photo also shows the opening count from 0000₂ through 0011₂, paired with decimal 0 through 3.

**Question:** Given a number written in binary, how do we find its value in base ten?

Use the same expansion method as the base-ten example. The quantity stays the same; we change how it is written.

1. **Label the positions from right to left**, starting with exponent zero: 2⁰, 2¹, 2², 2³, and so on.
2. **Evaluate the powers of two.** For four digits, the place values read **8, 4, 2, 1** from left to right.
3. **Multiply each binary digit by its place value.** A 1 contributes that value; a 0 contributes zero.
4. **Add the contributions.** Write the result with subscript 10 to identify base ten.

| Binary digit, left to right | 0 | 1 | 1 | 0 |
| --- | --- | --- | --- | --- |
| Power of two | 2³ | 2² | 2¹ | 2⁰ |
| Place value | 8 | 4 | 2 | 1 |
| Digit × place value | 0 × 8 | 1 × 4 | 1 × 2 | 0 × 1 |
| Contribution | 0 | 4 | 2 | 0 |

**0110₂ = (0 × 2³) + (1 × 2²) + (1 × 2¹) + (0 × 2⁰)**

**= 0 + 4 + 2 + 0 = 6₁₀**

Read this as zero eights, one four, one two, and zero ones. The two 1s have different values because they occupy different positions.

**Shortcut once the method is understood:** Add only the place values whose digits are 1. For **0110₂**, those are **4 + 2 = 6**.

**Exponent reminder:** 2⁰ is 1, so the final term is **0 × 1 = 0**. It contributes zero because the digit is zero. The leading zero can be removed without changing the number: **0110₂ = 110₂ = 6₁₀**. Keep the remaining digits aligned with the ones place on the right.

### Additional suggested conversion example

This example extends the photographed class material:

**1011₂ = (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰)**

**= 8 + 0 + 2 + 1 = 11₁₀**

Read this as one eight, zero fours, one two, and one one. The exponent gives the place value; the digit tells us how many of that place value to include.

### Suggested teaching sequence and checks

1. Replace the base-ten column headings with **2³, 2², 2¹, 2⁰**, then evaluate them as **8, 4, 2, 1**.
2. Count together from **0000**. Pause at **0001**, **0011**, and **0111** to ask what changes when one is added.
3. Reproduce the photographed **0110₂ = 6₁₀** example, then expand **1011₂** as another example. Compare the method with **3,247₁₀**.
4. Ask students to represent **6₁₀** and **9₁₀** with four bits. **Answers: 0110₂ and 1001₂.**
5. Ask why **0100₂** is four. **Its 1 is in the 2² place, so its value is 4.**
6. Ask what follows **1111₂** and why another place is needed. **10000₂; sixteen requires the 2⁴ place.**
7. Ask students to convert **0101₂**, **1010₂**, and **1100₂** to base ten, showing the powers of two. **Answers: 5₁₀, 10₁₀, and 12₁₀.**
8. Ask why **0011₂** and **1100₂** have different values even though each contains two 1s. **Their 1s occupy different places: 2 + 1 = 3, while 8 + 4 = 12.**

Watch for students treating **10₂** as decimal ten, starting the ones-place exponent at one, or confusing **2³** with **2 × 3**. These are anticipated teaching points, not recorded student errors.

## Semiconductors: connecting binary to computer hardware

**Recorded lesson progression:** Introduce semiconductors, silicon (**Si**, atomic number **14**), and **transistors**, the semiconductor devices used as electronic switches. Connect on/off, open/closed, and 0/1. Explain why the region is called Silicon Valley. The explanations and suggested activity below develop these teaching points.

### 1. What is a semiconductor?

A conductor, such as copper, allows electric current to flow easily. An insulator, such as plastic, strongly resists current. A **semiconductor** is a material whose ability to conduct electricity can be controlled. This makes it useful for building electronic devices. Adding carefully chosen amounts of other elements, called **doping**, changes its electrical properties. [Background: IBM](https://www.ibm.com/think/topics/semiconductors).

### 2. Silicon: Si, atomic number 14

- **Si** is the chemical symbol for silicon, a semiconductor widely used in computer chips.
- **14** is its atomic number: each silicon atom has **14 protons**. A neutral silicon atom also has **14 electrons**.
- Silicon has **four outer-shell electrons**, which help it form bonds with neighbouring atoms in a crystal.

Use a periodic table to locate silicon and distinguish its symbol, atomic number, and outer-shell electron count. [Reference: Royal Society of Chemistry](https://periodic-table.rsc.org/element/14/silicon).

### 3. Transistors: electronic switches

A **transistor** is a device made using semiconductor material. In digital circuits, it can act as a tiny electrically controlled switch. In the common transistor type used in computer chips, a voltage applied to a control terminal called the **gate** controls how readily current flows through a channel. This gives us an on/off model without moving mechanical contacts. [Reference: Intel, The Transistor, Explained](https://www.intel.com/content/www/us/en/newsroom/tech101/the-transistor-explained.html).

### 4. Open and closed: a simple circuit analogy

Draw a battery, a switch, and a lamp in one loop. For this demonstration, agree to label lamp off as **0** and lamp on as **1**.

| Switch in the lamp circuit | Electrical path | Lamp | Assigned bit |
| --- | --- | --- | --- |
| Open | Broken path, so current cannot complete the loop | Off | 0 |
| Closed | Complete path, so current can flow | On | 1 |

**Teaching point:** Closing an electrical switch completes the path and turns the lamp on. Opening the switch breaks the path and turns it off.

**Teacher precision note:** This table is a classroom model. Digital circuits typically represent 0 and 1 with low and high voltage ranges. A particular transistor being on does not always mean the circuit's output is 1; that depends on its connections. Keep the central idea as **two distinguishable electrical states can represent the two binary digits**.

### 5. Connect the switches to the number six

**Suggested activity:** Draw four lamps or use four on/off cards. Label their positions **8, 4, 2, 1**. Set them to **off, on, on, off**.

| Place value | 8 | 4 | 2 | 1 |
| --- | --- | --- | --- | --- |
| Lamp state | Off | On | On | Off |
| Bit | 0 | 1 | 1 | 0 |

The pattern represents **0110₂ = 4 + 2 = 6₁₀**. Each position has only two states, but combinations of positions let us represent many numbers. This connects the physical model directly to the earlier whiteboard example.

### 6. Why is it called Silicon Valley?

The name refers to the concentration of companies making silicon semiconductor devices and computer chips in California's Santa Clara Valley and surrounding area. **Silicon** names the material central to that industry; **Valley** refers to the region. Companies such as Shockley Semiconductor and Fairchild Semiconductor helped establish the local industry. [Reference: Computer History Museum](https://computerhistory.org/fairchildren/).

### Suggested checks for understanding

- What does the 14 in silicon's periodic-table entry mean? **Its atomic number, or number of protons.**
- What is the difference between silicon and a transistor? **Silicon is a material; a transistor is a device that can be made using it.**
- Is the switch open or closed when the lamp is on? **Closed, completing the circuit.**
- Why does binary suit digital electronics? **Two distinguishable electrical states can encode 0 and 1.**
- What decimal number does on, off, on, off represent in the 8, 4, 2, 1 positions? **1010₂ = 8 + 2 = 10₁₀.**
- Why the name Silicon Valley? **The region became a centre of silicon semiconductor and chip manufacturing.**

## Bits, bytes, and powers of ten: continuation of Class 1

**Recorded lesson progression:** Continue in this same September 15 class with what a bit is, what a byte is, and kilo, mega, giga, and tera expressed using exponents.

### Main idea

A **bit** is one binary digit, either **0 or 1**. A **byte** is a group of **8 bits**. Prefixes such as kilo and mega tell us how many units we have, using powers of ten.

The examples, teaching sequence, and checks below develop the recorded topics for reuse next year.

### 1. From a bit to a byte

Connect a bit to the two-state model from Class 1: off/on can represent 0/1.

| Term | Meaning | Example |
| --- | --- | --- |
| Bit | One binary digit | `1` |
| Byte | Eight bits grouped together | `00000110` |

**1 byte = 8 bits.** Uppercase **B** means byte; lowercase **b** commonly means bit. Writing out “bits” and “bytes” initially helps avoid confusion. [Reference: NIST binary prefixes](https://physics.nist.gov/cuu/Units/binary.html).

As an unsigned binary number, **00000110₂ = 6₁₀**, linking back to the earlier binary example. Leading zeros bring the example to eight bits without changing its value.

Each bit has two possible values, so eight bits have:

**2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2⁸ = 256 possible patterns.**

If those patterns represent unsigned whole numbers, the range is **0 through 255**. Distinguish the **8 bits in a byte** from the **256 patterns those bits can form**.

### 2. Kilo, mega, giga, and tera as exponents

These decimal prefixes describe multiples of a unit. The same prefixes can apply to bits or bytes. [Reference: NIST SI prefixes](https://www.nist.gov/pml/special-publication-330/sp-330-section-3).

| Prefix | Symbol | Power of ten | Multiplier | Example in bytes |
| --- | --- | --- | --- | --- |
| kilo | k | 10³ | 1,000 | 1 kB = 1,000 bytes |
| mega | M | 10⁶ | 1,000,000 | 1 MB = 1,000,000 bytes |
| giga | G | 10⁹ | 1,000,000,000 | 1 GB = 1,000,000,000 bytes |
| tera | T | 10¹² | 1,000,000,000,000 | 1 TB = 1,000,000,000,000 bytes |

**Pattern:** Each step from kilo to mega to giga to tera multiplies the quantity by **1,000**, adding **3** to the exponent.

**10³ × 10³ = 10⁶**, so one million is one thousand thousands.

**1 TB = 1,000 GB = 1,000,000 MB = 1,000,000,000 kB.**

### 3. Suggested worked examples

- **3 kB to bytes:** 3 × 10³ = **3,000 bytes**.
- **2 MB to bytes:** 2 × 10⁶ = **2,000,000 bytes**.
- **5 GB to MB:** 5 × 10⁹ ÷ 10⁶ = 5 × 10³ = **5,000 MB**.
- **2 bytes to bits:** 2 × 8 = **16 bits**.
- **1 MB to bits:** 10⁶ bytes × 8 bits per byte = **8,000,000 bits**, or **8 megabits**.

Changing a prefix uses powers of ten. Changing between bytes and bits uses a factor of eight.

### 4. Teacher note: decimal and binary prefixes

This distinction supports accurate teaching; it was not explicitly recorded as a class topic.

**Kilo means 10³ = 1,000.** The nearby power of two, **2¹⁰ = 1,024**, has a separate prefix, **kibi**. Older or informal computing usage sometimes calls 1,024 bytes a kilobyte, so explain the convention when it appears.

| Decimal unit | Bytes | Binary unit | Bytes |
| --- | --- | --- | --- |
| Kilobyte (kB) | 10³ | Kibibyte (KiB) | 2¹⁰ |
| Megabyte (MB) | 10⁶ | Mebibyte (MiB) | 2²⁰ |
| Gigabyte (GB) | 10⁹ | Gibibyte (GiB) | 2³⁰ |
| Terabyte (TB) | 10¹² | Tebibyte (TiB) | 2⁴⁰ |

Decimal steps multiply by **1,000**; binary steps multiply by **1,024**. [Reference: NIST binary prefixes](https://physics.nist.gov/cuu/Units/binary.html).

### Suggested teaching sequence for next year

1. Recall the 0/1 switch model and name one binary digit a **bit**.
2. Draw eight boxes, put one bit in each, and label the group **one byte**.
3. Use **2⁸** to count the possible patterns; connect this to the earlier four-bit count of **2⁴ = 16**.
4. Build the kilo-to-tera table together, emphasizing exponents **3, 6, 9, 12**.
5. Practise prefix conversions and bit/byte conversions separately, then combine them.
6. Introduce the binary-prefix distinction if students encounter 1,024 in computing examples.

### Suggested checks for understanding

- How many bits are in 4 bytes? **32.**
- How many patterns can one byte represent? **256, because 2⁸ = 256.**
- Write giga as a power of ten. **10⁹.**
- How many MB are in 3 GB? **3,000 MB.**
- Is 1 megabit the same quantity as 1 megabyte? **No. One megabyte is eight megabits.**
- Why do the prefix exponents increase by three? **Each step multiplies by 1,000 = 10³.**

## Wave theory and transmitting data over Wi-Fi: continuation of Class 1

**Recorded lesson progression:** Introduce hertz, begin with **60 Hz**, then connect gigahertz to the earlier prefix work. Explore encoding and transmitting data over Wi-Fi. The starting classroom analogy is **peak = 1, trough = 0**. The explanations below develop this analogy and clarify its limits.

### 1. A sine wave and its parts

Draw a smooth repeating sine wave with **time** on the horizontal axis and **signal value** on the vertical axis.

- **Peak:** Highest point of the wave.
- **Trough:** Lowest point of the wave.
- **Amplitude:** Maximum displacement from the middle line.
- **Cycle:** One complete repetition, such as from one peak to the next peak. A peak to the following trough is half a cycle.
- **Frequency:** Number of complete cycles per second.

### 2. Hertz: how often the wave repeats

**1 hertz (Hz) = 1 cycle per second.** Therefore **60 Hz = 60 complete cycles each second**. [Reference: NIST](https://www.nist.gov/pml/time-and-frequency-division/popular-links/time-frequency-z/time-and-frequency-z-h).

The **period** is the time for one cycle:

**Period = 1 ÷ frequency.**

At **60 Hz**, one cycle takes **1/60 second ≈ 0.0167 seconds = 16.7 milliseconds**.

On two graphs with the same time scale, a higher-frequency wave fits more complete cycles into the same interval. Frequency measures repetition rate, not the speed at which the wave travels.

### 3. From hertz to gigahertz

Reuse the prefixes from the data-units section. Here they multiply **cycles per second**, rather than bytes.

| Unit | In hertz | Meaning |
| --- | --- | --- |
| 1 Hz | 1 Hz | 1 cycle per second |
| 1 kHz | 10³ Hz | 1,000 cycles per second |
| 1 MHz | 10⁶ Hz | 1,000,000 cycles per second |
| 1 GHz | 10⁹ Hz | 1,000,000,000 cycles per second |

**2.4 GHz = 2.4 × 10⁹ Hz = 2,400,000,000 cycles per second.**

Wi-Fi uses radio waves in frequency bands such as **2.4 GHz, 5 GHz, and 6 GHz**, depending on the equipment. These names identify frequency ranges used for communication. [Reference: Cisco](https://www-cloud-cdn.cisco.com/site/ca/en/learn/topics/networking/what-is-wi-fi-7.html).

### 4. From a wave to encoded bits

**Introductory analogy:** Label a peak “1” and a trough “0” to introduce the idea of assigning binary meaning to distinguishable signal states.

**Clarification to teach alongside the analogy:** A sine wave does not inherently contain binary digits. An unchanged sine wave keeps repeating the same peaks and troughs; those alone do not encode an arbitrary message. A standard sine wave with amplitude 1 and centre 0 has a peak of +1 and a trough of −1. Calling the trough “0” assigns a bit label, not its numerical height.

To send chosen data, the transmitter **modulates** the wave: it changes a property according to an agreed encoding. The receiver detects those changes and recovers the bits. Properties that can be varied include amplitude, frequency, or **phase**, the position within a wave's cycle. Wi-Fi uses schemes involving phase and amplitude, including QAM. [Reference: Cisco radio configuration guide](https://www.cisco.com/c/en/us/td/docs/routers/access/1900/software/configuration/guide/Software_Configuration/radio_config.html).

**Suggested simple example:** In each agreed time slot, choose one of two wave phases to represent 0 or 1. These are two possible versions of the wave, not its naturally alternating peak and trough. The receiver needs a timing and phase reference to distinguish them.

### 5. How can we transmit more data per second?

Separate three ideas:

| Quantity | What it measures |
| --- | --- |
| Carrier frequency, in Hz or GHz | How rapidly the underlying radio wave oscillates |
| Channel bandwidth, in Hz or MHz | The width of the frequency range available to carry the signal |
| Data rate, in bits/s or Mbit/s | How many bits are transmitted each second |

**A 2.4 GHz signal does not automatically transmit 2.4 billion bits per second.** Wi-Fi data rates depend on channel width, the encoding scheme, and other transmission settings. Wider channels can support more data; more distinguishable signal states can encode more bits per symbol when signal quality permits. A **symbol** is one selected signal state during a defined interval. [Reference: Cisco Wi-Fi throughput guide](https://www.cisco.com/c/en/us/support/docs/wireless-mobility/wireless-lan-wlan/212892-802-11ac-wireless-throughput-testing-and.html).

**Suggested arithmetic model, ignoring error correction and overhead:**

- Two possible symbols encode **1 bit per symbol**, since 2¹ = 2.
- Four possible symbols encode **2 bits per symbol**, since 2² = 4: 00, 01, 10, 11.
- At 1,000 symbols per second, these give **1,000 bits/s** and **2,000 bits/s**, respectively.

This connects transmission back to exponents: more reliably distinguishable choices allow more bits per symbol. Real useful data rates are lower than the raw rate because transmissions also include error protection and control information.

### Suggested teaching sequence and checks

1. Draw one cycle, label peak and trough, then explain **60 cycles in one second**.
2. Convert **1 GHz** and **2.4 GHz** into cycles per second using powers of ten.
3. Introduce peak/1 and trough/0 as labels, then show why a repeating wave needs controlled changes to carry a chosen message.
4. Compare two possible signal states with four, linking them to **2¹** and **2²**.
5. Ask: Does 60 Hz mean 60 bits per second? **No; it specifies cycles per second. The encoding determines the relationship to bits.**
6. Ask: Does higher carrier frequency alone guarantee a faster connection? **No; channel bandwidth, encoding, and signal conditions also matter.**
7. Ask: How many bits can eight distinguishable symbols represent per symbol? **3, because 2³ = 8.**

## From received bits to a movie: software and apps

**Recorded lesson progression:** A computer can receive billions of bits. A **3 GB movie contains 24 billion bits**. How does the computer know what to do with them? Introduce **software and apps** as the instructions that interpret and use the data.

### 1. How many bits are in a 3 GB movie?

Using decimal gigabytes, as in the earlier prefix table:

**3 GB = 3 × 10⁹ bytes = 3,000,000,000 bytes.**

**3,000,000,000 bytes × 8 bits per byte = 24,000,000,000 bits.**

So an exactly **3 GB** file contains **24 billion bits**. This counts the file's contents; transmission also involves additional control information.

### 2. What tells the computer how to use those bits?

The bits do not explain their own meaning. **Software** provides instructions for processing them. An **app**, short for application, is software designed for a task, such as playing a movie, displaying a photograph, or editing a document.

A movie file follows an agreed **file format**, a set of rules describing how its data is organized. A compatible media player uses those rules to find and interpret the video, audio, and information needed for playback.

**Student-facing explanation:** “The hardware receives and stores the bits. The app provides the instructions for turning that organized data into the pictures and sound we experience.”

### 3. Suggested walkthrough: play the movie

1. **Receive and store:** The computer receives the data and makes the movie file available to the app.
2. **Read the format:** The media player reads the file's structure to locate its video and audio.
3. **Decode:** Software interprets the encoded data. A **decoder** reconstructs playable pictures and sound from their encoded representation, often with help from specialized hardware.
4. **Present:** The app coordinates playback through the operating system and hardware, sending pictures to the display and sound to the speakers at the right times.

This walkthrough develops the recorded idea; these details were not separately reported as class activities.

### 4. Data and instructions are both represented by bits

| Part | Role in the movie example |
| --- | --- |
| Hardware | Receives, stores, and processes bits; drives the display and speakers |
| Movie data | Contains the encoded video, audio, and supporting information |
| Software/app | Supplies instructions for interpreting and playing the data |

Software is also stored as bits. The processor executes program instructions that operate on the movie's data. **The role and interpretation of the bits depend on the program and the format.**

### Suggested checks for understanding

- Why multiply 3 billion by eight? **There are eight bits in each byte.**
- Does knowing a file's size tell us how to play it? **No. We also need to understand its format and encoding.**
- What makes a media player useful? **It provides the instructions needed to interpret supported movie formats and coordinate playback.**
- Does renaming a movie file to end in `.jpg` turn it into a photograph? **No. Changing the name does not convert the data inside.**

**Class 1 connection:** Binary represents information; hardware stores and processes it; waves can carry it; software interprets and uses it.

## How combinations of bytes acquire meaning

**Recorded discussion:** We create rules under which particular combinations of bytes mean different things. Bradley asked whether these rules are examples of different computer languages. The clarification below supports teaching this distinction next year.

### Main distinction: encodings, formats, and programming languages

The idea is related to computer languages, but assigning meanings to data bytes is usually called **encoding** or defining a **data format**. Programming languages are used to write instructions for what a computer should do with data.

| Concept | Purpose | Example |
| --- | --- | --- |
| Encoding | Defines how information is represented by bit or byte patterns | ASCII represents the letter A with the value 65 |
| File format | Defines how a file's data is organized and identified | A movie format organizes video, audio, and playback information |
| Programming language | Lets people express instructions and algorithms | Python or Java can be used to write software that reads and processes data |
| Machine language | Defines the instruction patterns a particular processor can execute | A processor's instruction set specifies how to encode operations such as addition |

### One byte, different interpretations

Write **01000001** on the board. It is one byte, or eight bits.

**01000001₂ = 64 + 1 = 65₁₀.**

- Interpreted as an **unsigned integer**, it is the number **65**.
- Interpreted as **ASCII text**, it represents the letter **A**.
- Interpreted as one **8-bit colour-channel value**, it represents an intensity of **65** on a scale from 0 to 255.

The bits are identical. The agreed interpretation determines their meaning. A byte does not carry a universal label saying “I am text” or “I am a colour.” Software uses context, such as a file's structure, format information, or the data type it expects.

**Teacher note:** ASCII is a seven-bit character code, commonly stored in an eight-bit byte with a leading zero. The example above also represents A in UTF-8. Some other characters require several bytes in UTF-8, so avoid teaching that every character is exactly one byte.

### Where programming languages fit

A programmer writes instructions in a language such as Python or Java. A compiler or interpreter helps turn those instructions into actions performed by the computer. The program can apply an encoding's rules to interpret data, such as displaying A when it reads the corresponding text value.

Different programming languages can work with the **same encoding or file format**. Two media players written in different languages can both play the same movie if they support its format and encoding.

Machine language is the related case where encoded patterns represent processor instructions. Those meanings depend on the processor's instruction set; there is no single universal meaning for every byte across all computers.

### Suggested explanation to students

“Bits are the symbols we store. An encoding or format gives us rules for interpreting them. A program gives the computer instructions for using those rules. The same pattern can represent a number, a letter, or part of a picture, depending on how we interpret it.”

### Suggested checks for understanding

- What is **01000001** as an unsigned number? **65.**
- What does that value represent in ASCII? **A.**
- Did the bits change between those interpretations? **No; the interpretation changed.**
- Must two apps use the same programming language to read the same file? **No; they must support its format and encoding.**

## Working memory, storage, ROM, and processors

**Recorded discussion:** Introduce short-term and long-term memory, RAM and ROM, and how the CPU and GPU use memory while working. The initial description was that they work in RAM and then store in ROM. The clarification below corrects that distinction for next year's teaching.

### 1. RAM versus long-term storage

The most useful everyday comparison is **RAM versus storage**:

| Component | Purpose | Keeps its contents without power? |
| --- | --- | --- |
| RAM, Random Access Memory | Working space for programs and data currently in use | Normally no; ordinary system RAM is volatile |
| SSD or hard drive | Long-term storage for apps, documents, movies, and other files | Yes |
| ROM, Read-Only Memory | Nonvolatile memory traditionally used to hold fixed instructions, such as firmware | Yes |

**Correction:** When we save ordinary work, it usually goes to an **SSD or hard drive**, rather than ROM. Storage is designed for repeatedly saving and changing files. ROM is not a general name for everything that retains data after shutdown.

**Firmware** is low-level software that helps initialize or control hardware. Modern firmware is often kept in rewritable flash memory rather than permanently fixed ROM. Although SSDs also use flash memory, their role is everyday file storage.

### 2. A classroom analogy

Think of **RAM as a desk** and **storage as a filing cabinet**:

- Take a document from the cabinet and put a working copy on the desk.
- Work on that copy while the original saved version remains in the cabinet.
- Save your changes to update the version in the cabinet.
- Clearing the desk does not erase the saved document in the cabinet.

RAM provides the workspace; the processor performs the work. More RAM lets the computer keep more working data available at once, but does not automatically make each calculation faster.

### 3. CPU and GPU: who does the work?

- **CPU, Central Processing Unit:** Executes program instructions, performs general-purpose calculations, and coordinates tasks. It uses RAM for active programs and data, along with smaller, faster internal storage called caches and registers.
- **GPU, Graphics Processing Unit:** Performs many calculations in parallel, especially graphics work and other suitable tasks. It also needs working memory for the data it processes.
- A separate graphics card commonly has its own **video memory (VRAM)**. Integrated graphics commonly share system RAM. Some computers use unified memory accessible to both CPU and GPU.

**Teacher note:** Avoid implying that every GPU uses only the computer's main RAM. The arrangement depends on the hardware.

### 4. Follow the movie through the computer

1. **Stored file:** The 3 GB movie is saved on an SSD or hard drive.
2. **Open:** The operating system and media player load needed instructions and movie data into working memory. The entire movie need not fit in RAM at once; it can be read in portions.
3. **Process:** The CPU runs the player and coordinates playback. Depending on the system, specialized video hardware or the GPU helps decode or display the images, using its available working memory.
4. **Display:** The computer sends the resulting pictures and sound to the screen and speakers. Playing a movie does not normally require saving a new copy.
5. **Save when needed:** If the user edits and exports the movie, software arranges for the resulting file to be written to long-term storage.

### Suggested explanation to students

“Storage keeps our files. RAM holds the information we are working with right now. The CPU and GPU process that information. When we save our work, software writes it back to storage. ROM or firmware memory has a different role: keeping instructions that help the hardware start or operate.”

### Suggested checks for understanding

- Where does a saved movie remain when the computer is off? **On nonvolatile storage, such as an SSD or hard drive.**
- Where does the computer keep much of the data it is actively using? **In RAM; graphics work may also use dedicated video memory.**
- Why might unsaved changes be lost if power fails? **Their latest state may exist only in volatile working memory. Autosave can preserve a copy in storage.**
- Does the CPU normally save your document in ROM? **No; software normally saves documents to writable storage.**
- Must a 3 GB movie be loaded into RAM all at once? **No; a player can process it in portions.**

## Connection to the next class

Revisit the shared rule: **digit × base raised to the position**, then sum the terms. Connect binary digits to electrical states, groups of bits to bytes, and prefixes to powers of ten. Review how changing waves can carry encoded data, distinguishing GHz from bits per second. Use the 3 GB movie example to connect received data to the software that interprets it. The next class's content has not yet been recorded.

## Reflection for next year

- What students understood readily: To be recorded.
- Questions or misconceptions that arose: To be recorded.
- Timing and adjustments: To be recorded.

## Source photos

- [Base-ten whiteboard example: 3,247](../sources/base-ten.jpg).
- [Binary counting and conversion example: 0110₂ = 6₁₀](../sources/binary.jpg).