--- title: "Bits all the way down" subtitle: "Data representation · Binary numbers · Lesson 8" --- # Bits all the way down **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** You now know how text, pictures and sound become numbers, and how numbers become bits. What does the letter A actually look like inside the computer? :::teacher-note **In one sentence:** Students trace characters, colours and sound samples from data to numbers to bytes on eight binary cards, closing the loop between data representation and binary (AC9TDI8K04 node 4). **Students should be able to say:** I can turn a character into its code and then into binary. I can work out how many bits a word or a picture takes. I can explain that all data becomes bits. **Width:** the unmarked parts are the floor every student does (predict, run, investigate and make). Typical adds the modify practice; wider adds the real-world contexts. They add contexts, not difficulty. Students work in the online tutorial alongside this sheet. ::: ## Predict :::keep-together **The letter **A** has the code 65. How is it stored in the computer's memory?** ☐ 65 ☐ A ☐ 01000001 ☐ 1 My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** 01000001. The computer stores only bits: 65 = 64 + 1, so on 8 bits (one byte) the 64 and 1 places are 1. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Worked example: trace the chain :::keep-together ### Text and a pixel 1. $\text{A} \to 65$ — Text: the character's code. 2. $65 = 64 + 1 \to 01000001$ — Binary on 8 bits: one byte. 3. $\text{yellow} \to 255, 255, 0$ — A pixel: three colour amounts. 4. $11111111\ 11111111\ 00000000$ — Each amount is one byte: 24 bits for the pixel. 5. $\text{data} \to \text{numbers} \to \text{bits}$ — Every kind of data follows the same chain. Now count the bits in a pixel. **One pixel is three numbers (red, green, blue), each one byte. How many **bits** is one pixel?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 24 3 bytes × 8 bits = 24 bits. ::: :::keep-together ### Find the mistake **Sam works out how many bits the word cat takes. Click the line where it first goes wrong.** ``` 1 How many bits does the word cat take? 2 c, a and t are three characters. 3 Each character is one bit. 4 So cat takes 3 bits. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 3 Line 3: one bit can only be 0 or 1, not one of all the letters. Each character's code needs a byte: 8 bits. So cat is 3 × 8 = 24 bits. ::: :::keep-together ### What does a byte mean? **The byte **01000001** is in memory. What does it mean?** ☐ Always the number 65 ☐ Nothing until it is decoded ☐ Always the letter A ☐ It depends on how a program reads it: A as text, 65 as a number, a dark shade as a colour amount ::: :::teacher-note **Answer:** It depends on how a program reads it: A as text, 65 as a number, a dark shade as a colour amount Bits are just bits. The encoding (text, number, colour, sound) decides what they mean, as in Everything is numbers. ::: :::typical ## Vary: one letter at a time **H to I.** **Lower case.** **Full colour.** **Silence.** **A space.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Bytes and bits :::keep-together ### Bits in a word **How many bits does the word **hello** take, at one byte a character?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 40 5 bytes × 8 = 40 bits. ::: :::keep-together ### Bytes in a picture **A 2 × 2 picture, three bytes a pixel. How many bytes?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 12 4 pixels × 3 = 12 bytes (96 bits). ::: :::keep-together ### Sound samples **Music often uses 65 536 levels a sample. How many bytes is each sample?** ☐ 2 (16 bits) ☐ 65 536 ☐ 1 (8 bits) ☐ 4 ::: :::teacher-note **Answer:** 2 (16 bits) 2¹⁶ = 65 536, so 16 bits: 2 bytes. ::: :::keep-together ### Byte to character **As text, which character is the byte **01000010**?** ☐ 2 ☐ B (66) ☐ A (65) ☐ b (98) ::: :::teacher-note **Answer:** B (66) 64 + 2 = 66, which is B. ::: ## Make: a lower case letter Then write your initials as bytes. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **Write the letter C as a byte. How many bits is the word Hi?** {{lines-3}} ::: :::teacher-note **Answer:** C = 67 = 64 + 2 + 1 = 01000011. Hi = 2 bytes = 16 bits. :::