Bits all the way down

Classroom resources

Load these into Waypoints Prepare: choose Load URL and paste the copied address, or download the file and import it. In Prepare, the worksheet's Teacher edition shows the answers; the student copy hides them.

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Students will be able to

• 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.

Timing

Predict and Try 6 min · Worked example 10 min · Vary 9 min · Practise and Make 10 min

Before class

The integration node (the kit calls it the cross-standard point between K03 and K04): students assemble data → number → binary for two kinds of data.

Simplification: text here is one byte a character (ASCII). Unicode characters beyond 255 take two to four bytes (Text as numbers).

Running the lesson

1. Predict: students who chose 65 or A haven't joined the two halves yet; the Try does it.
2. Worked example: ask what the 24 bits of a black pixel look like.
3. Vary: ask why lower case is always the 32 card added.
4. Make: have students write their initials as bytes on paper.

The hard part (on purpose)

Students think a character is one bit. Ask how many different things one bit can be (two), then how many characters there are.

When students get stuck

Answers to the checks

1. the letter A: The letter **A** has the code 65. How is it stored in the computer's memory?
   01000001. The computer stores only bits: 65 = 64 + 1, so on 8 bits (one byte) the 64 and 1 places are 1.
2. Try: one byte for A: Set the eight cards to 65, the code for A. What pattern of bits is it?
   
   65 = 64 + 1, so A is 01000001: one byte.
3. Text and a pixel: One pixel is three numbers (red, green, blue), each one byte. How many **bits** is one pixel?
   24
   3 bytes × 8 bits = 24 bits.
4. Find the mistake: Sam works out how many bits the word cat takes. Click the line where it first goes wrong.
   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.
5. What does a byte mean?: The byte **01000001** is in memory. What does it mean?
   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.
6. H to I: The cards show 72, the code for H. Make 73, the code for I.
   
   One more: only the 1 card changed. 01001001.
7. Lower case: Now make 104, the code for lower case h. Which card did you have to add?
   
   104 = 72 + 32: lower case adds the 32 card. 01101000.
8. Full colour: Make 255, a colour amount at full.
   
   255 is every card up: 11111111, the biggest byte.
9. Silence: Make 128, a sound sample at the middle (silence).
   
   128 is just the left card: 10000000.
10. A space: Make 32, the code for a space.
    
    A space is 00100000: still a whole byte, though nothing shows.
11. Bits in a word: How many bits does the word **hello** take, at one byte a character?
    40
    5 bytes × 8 = 40 bits.
12. Bytes in a picture: A 2 × 2 picture, three bytes a pixel. How many bytes?
    12
    4 pixels × 3 = 12 bytes (96 bits).
13. Sound samples: Music often uses 65 536 levels a sample. How many bytes is each sample?
    2 (16 bits)
    2¹⁶ = 65 536, so 16 bits: 2 bytes.
14. Byte to character: As text, which character is the byte **01000010**?
    B (66)
    64 + 2 = 66, which is B.
15. a lower case letter: The number is hidden. Set the cards to the byte for lower case a.
    
    a is 65 + 32 = 97 = 64 + 32 + 1, so 01100001.

Solutions

One possible solution for each task. Other correct programs are fine.

Vary: one letter at a time › H to I

Open task: any program that does what the step asks.

Vary: one letter at a time › Lower case

Open task: any program that does what the step asks.

Vary: one letter at a time › Full colour

Open task: any program that does what the step asks.

Vary: one letter at a time › Silence

Open task: any program that does what the step asks.

Vary: one letter at a time › A space

Open task: any program that does what the step asks.

a lower case letter

Open task: any program that does what the step asks.

Stretch and support

Stretch: A phone photo is about 4000 × 3000 pixels. Roughly how many bytes before compression? (36 million.) Why do we need compression?

Support: Keep the 128 64 32 16 8 4 2 1 card values written above the board.

Exit ticket

Write the letter C as a byte. How many bits is the word Hi?

C = 67 = 64 + 2 + 1 = 01000011. Hi = 2 bytes = 16 bits.

What each step is for

• the letter A: Committing to how A sits in memory tests the new move: the character becomes its code, and the code becomes a fixed number of bits.
• Try: one byte for A: Setting the code 65 on eight cards settles the prediction: A becomes 01000001.
• Worked example: trace the chain: Tracing a character and a pixel through data → number → binary models the new move. Sam counts one bit per character, the misconception planted after the method.
• Vary: one letter at a time: Each task changes one character or one value: H to I (one more), H to h (one card, the 32), a colour amount at full, a sound sample at the middle, then a space.
• bytes and bits: Counting bytes and bits for text, images and sound, and reading a byte back to a character.
• a lower case letter: Building the byte for lower case a from the code rule reverses the chain: from a character to its code to its bits, with the number hidden.

Where it leads

This closes the Data representation course.

Next (Years 9–10): Making data smaller (compression). Code links: Secret messages shifts these codes; colour values in turtle are these bytes.