--- marp: true theme: default html: true --- # Everything is numbers Data representation · Data as numbers --- ## Today **We are learning to** a computer stores text, pictures and sound all as numbers. The same numbers mean different things depending on how a program reads them: 72 is the letter H to a text program, a dark grey to a paint program and a sound level to a music program. - I can say how text, pictures and sound are all stored. - I can explain why the same number can mean different things. - I can give an example of a number standing for something that is not a number. --- ## Why it matters > A message, a photo and a song all end up in the same computer memory. What is actually stored there? --- 💬 Discussion ## Predict **A file holds three numbers: 72, 105, 33. A text program opens it and shows **Hi!**. A paint program opens the same file. What does it show?** - The letters Hi! drawn as a picture - Three shades of grey, one for each number - Nothing: a text file cannot be a picture - The numbers 72, 105 and 33 written out --- ✍️ Activity ## Try it {{embed: https://studio.learningwaypoints.com/tutorials/_playground-board/index.html?id=deck%2Fsystems%2Fdata%2Fdata-as-numbers%2Fstep-2&code=widget%3A+decode%0Anumbers%3A+72%2C+105%2C+33%0Aas%3A+text%0A&fresh=1}} [Open this step in the tutorial](https://studio.learningwaypoints.com/tutorials/systems/data/data-as-numbers/?full=step-2#step-2) --- ✅ Check ## What happened? * Three shades of grey. The paint program reads each number as a shade (0 black, 255 white), so 72, 105 and 33 are three darkish greys. The letters only exist when a text program reads the numbers. --- 💬 Discussion ## Read 72 three ways Now read 255 as a shade. $$72$$ 1) $72 \to \text{H}$ — As text: the letter whose code is 72. 2) $72 \to \text{dark grey}$ — As a grey shade: 0 is black and 255 is white, so 72 is darkish. 3) $72 \to \text{below the middle}$ — As sound: 128 is the middle (silence), so 72 is a level below it. 4) $\text{same number, different rule}$ — The encoding, not the number, decides what it means. --- ✅ Check ## Read 72 three ways **A paint program reads numbers as grey shades from 0 (black) to 255 (white). What does it show for 255?** - Mid grey - Black - White - The letter ÿ * Answer: White --- ✅ Check ## Find the mistake **Sam reasons about a file holding 72, 105, 33. Click the line where the reasoning first goes wrong.** ``` 1 A file holds the numbers 72, 105, 33. 2 A text program shows them as "Hi!". 3 So the numbers 72, 105, 33 mean "Hi!". 4 A paint program opens the same file. 5 It shows the letters "Hi!" drawn as a picture. ``` * Answer: line 3 --- ✅ Check ## A number for something else **Which of these is an example of a number standing for something that is not a number?** - 65 kg written on a scale - 65 as the answer to 60 + 5 - 65 written in a maths book - 65 stored for the letter A in a text message * Answer: 65 stored for the letter A in a text message --- ✍️ Activity ## Vary: change one number - **White:** - **Black:** - **The next letters:** - **Silence:** - **Not a letter:** [Open this step](https://studio.learningwaypoints.com/tutorials/systems/data/data-as-numbers/?full=step-4#step-4) --- ✅ Check ## Letter codes **In text, A is stored as 65 and the letters go in order. What number stores C?** * Answer: 67 --- ✅ Check ## Wrong program **A music program opens a text file. What will you most likely hear?** - Noise: it reads the letter codes as sound levels - The program refuses to open it - The text read aloud - Silence * Answer: Noise: it reads the letter codes as sound levels --- ✅ Check ## Shades **A grey shade of 0 is…** - Invisible - Black - Mid grey - White * Answer: Black --- ✅ Check ## File types **Why does a file need to say what kind of data it holds (for example .txt or .png)?** - Because text and pictures are stored as different kinds of electricity - So the program knows which rule to read the numbers with - So the numbers take up less space - It doesn't: every program can tell from the numbers * Answer: So the program knows which rule to read the numbers with --- ✍️ Activity ## Make: write a word Then switch the reading: what does your word look like as grey shades, and as sound? [Open this step](https://studio.learningwaypoints.com/tutorials/systems/data/data-as-numbers/?full=step-6#step-6) --- ✅ Check ## Exit ticket **The number 66 is stored in memory. Give two different things it could mean.** * Any two of: the letter B (as text), a dark grey (as a shade), a sound level below the middle (as audio), or the number 66 itself. Which one depends on the program's encoding.