MskProdComputing

Year 9 · Y9.2 Data Representation · Lesson 2

Stretch tasks Binary addition and units

Task 1

Quiz Challenge

A quiz game against four computer players, then short and long written answers.

  1. Quiz Blitz12 questions against the clock
  2. Quick Fire4 short answers
  3. Big Think2 long answers

About 20 minutes

Task 2

This or That

Pixel the cat asks 8 questions. Each has two answers: pick the right one.

  • Two answers to every question
  • A fish treat for every right answer
  • Streaks win Pixel shades, then a party hat

About 4 minutes

Task 3

Memory Match

Flip the cards two at a time to match each unit card to its size card.

  • 12 cards: each unit has a size
  • One peek at every card
  • Combo points for pairs found in a row

6 pairs, about 4 minutes

The games need JavaScript. Every question is below, with the answers at the end.

Read the lesson: Binary addition and units

Binary addition and units: the questions

Quiz Challenge, round 1: Quiz Blitz

  1. Add 00110110 and 00011011. Give the 8-bit answer.

  2. In binary addition, what is 1 + 1 + 1?

    • 1 carry 0
    • 11 carry 1
    • 1 carry 1
    • 0 carry 1

  3. 11001000 + 01000000 overflows in 8 bits. Why?

    • The answer is 264, which needs 9 bits
    • The numbers are both even
    • There are too many 1s in the numbers
    • Binary cannot add numbers over 100

  4. An overflow error means the stored answer will be wrong.

    • True
    • False

  5. Order these from smallest to largest.

    Number these 1 to 5.

    • Byte
    • Kilobyte
    • Megabyte
    • Bit
    • Nibble

  6. How many bits are in 3 bytes?

  7. A 2 GB file is how many MB?

    • 20
    • 20,000
    • 2,000
    • 200

  8. How many bytes are in 4 kilobytes?

  9. Which TWO additions overflow in 8 bits?

    Tick 2.

    • 128 + 128
    • 100 + 100
    • 127 + 128
    • 250 + 5
    • 200 + 100

  10. What is 01111111 + 00000001?

    • 00000000
    • 10000000
    • 01111110
    • 11111111

  11. A nibble is half a byte.

    • True
    • False

  12. A song is 4 MB. Roughly how many fit on an empty 16 GB phone?

    • 64
    • 4,000
    • 400
    • 40,000

Quiz Challenge, round 2: Quick Fire

  1. Add 01011010 and 00101101. Give the answer in 8-bit binary, with your working. [2 marks]

  2. What is an overflow error, and why does it make the stored answer wrong? [2 marks]

  3. Explain why 255 is the largest number that 8 bits can store. [2 marks]

  4. A photo is 3 MB. How many could you store on a 1.5 GB memory card? Show your working. [2 marks]

Quiz Challenge, round 3: Big Think

  1. Add 10110110 and 01101101 using 8 bits. Explain what happens, and why the stored answer is wrong. [4 marks]

  2. A phone has 64 GB of storage. Photos are 5 MB each and songs are 4 MB each. Work out how many of each would fit, and explain why the real number would be lower. [6 marks]

This or That: tick the right answer

  1. What is 1 + 1 in binary?

    • 0 carry 1
    • 2

  2. Which is bigger, a nibble or a byte?

    • A nibble
    • A byte

  3. An 8-bit addition comes to more than 255. What happens?

    • An overflow error
    • A ninth bit is added

  4. How many megabytes make a gigabyte?

    • 1000
    • 100

  5. What is 00000011 + 00000001?

    • 00000100
    • 00000012

  6. How many bits are in a byte?

    • 4
    • 8

  7. A file is 3,000 KB. How big is that in MB?

    • 3,000,000 MB
    • 3 MB

  8. Which unit is the largest?

    • Gigabyte
    • Terabyte

Memory Match: match each unit to its size

UnitSize
A Bit1 1000 kilobytes
B Nibble2 A single 1 or 0
C Byte3 4 bits
D Kilobyte4 1000 megabytes
E Megabyte5 8 bits
F Gigabyte6 1000 bytes
Answers

Round 1: Quiz Blitz

  1. 01010001 54 + 27 = 81, which is 01010001. Check by converting both ways.
  2. 1 carry 1 1 + 1 + 1 is 3, which is 11 in binary: write 1 and carry 1.
  3. The answer is 264, which needs 9 bits 200 + 64 = 264, but 8 bits only go up to 255.
  4. True The carry out of the leftmost column has nowhere to go, so it is lost.
  5. Bit → Nibble → Byte → Kilobyte → Megabyte 1 bit, 4 bits, 8 bits, then 1000 bytes, then 1000 kilobytes.
  6. 24 8 bits in a byte, so 3 x 8 = 24.
  7. 2,000 1 GB is 1000 MB, so 2 GB is 2,000 MB.
  8. 4000 1 KB is 1000 bytes, so 4 KB is 4,000 bytes.
  9. 200 + 100; 128 + 128 Anything over 255 overflows: 300 and 256 do. 127 + 128 and 250 + 5 are exactly 255, which just fits.
  10. 10000000 127 + 1 = 128. Every carry ripples to the left, leaving 10000000.
  11. True A nibble is 4 bits and a byte is 8 bits.
  12. 4,000 16 GB is 16,000 MB, and 16,000 / 4 = 4,000 songs.

Round 2: Quick Fire

    • Uses carries correctly, working from right to left
    • 10000111
    Model answer

    Working from right to left and carrying 1 whenever a column adds to 2 or 3 gives 10000111. Check: 90 + 45 = 135, which is 10000111.

    • The result needs more bits than are available
    • The extra carry bit is lost, so the stored value is wrong
    Model answer

    An overflow error happens when the result of a calculation needs more bits than are available. The final carry has nowhere to go, so it is lost, and the value stored is wrong.

    • All eight bits are 1: 11111111
    • 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255; there are 256 values starting from 0
    Model answer

    The largest number is when all eight bits are 1, 11111111, which is 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. There are 256 different values, but they start at 0.

    • 1.5 GB = 1,500 MB
    • 1,500 / 3 = 500 photos
    Model answer

    1.5 GB = 1,500 MB, and 1,500 / 3 = 500 photos.

Round 3: Big Think

    • Carries move from right to left, column by column
    • The true answer, 291, needs 9 bits
    • The final carry is lost: an overflow error
    • The stored answer is 00100011, which is 35
    Model answer

    Adding from right to left, carries ripple across the columns. The true answer is 182 + 109 = 291, which is 100100011 and needs 9 bits. With only 8 bits available, the final carry out of the leftmost column is lost: this is an overflow error. The stored answer is 00100011, which is 35, completely wrong.

    • 64 GB = 64,000 MB
    • 64,000 / 5 = 12,800 photos
    • 64,000 / 4 = 16,000 songs
    • 1 GB is 1000 MB
    • The operating system and apps already use some of the space
    • Real file sizes vary, for example with quality or compression
    Model answer

    1 GB is 1000 MB, so 64 GB is 64,000 MB. That would hold 64,000 / 5 = 12,800 photos, or 64,000 / 4 = 16,000 songs. The real number would be lower, because the operating system and apps already use some of the storage, and real files vary in size: a high quality photo or a song with less compression is bigger.

This or That

  1. 0 carry 1 Binary has no digit 2. 1 + 1 makes 10, so write 0 and carry 1.
  2. A byte A nibble is 4 bits and a byte is 8 bits.
  3. An overflow error There are only 8 bits, so the carry out of the leftmost column is lost and the answer stored is wrong.
  4. 1000 Each unit is 1000 of the one below it, so 1000 MB make 1 GB.
  5. 00000100 3 + 1 = 4. In binary, 1 + 1 gives 0 carry 1 twice, leaving 100.
  6. 8 A byte is 8 bits. Four bits is a nibble.
  7. 3 MB Going up a unit means dividing by 1000, so 3,000 KB is 3 MB.
  8. Terabyte A terabyte is 1000 gigabytes.

Memory Match

  • A 2 Bit: A single 1 or 0
  • B 3 Nibble: 4 bits
  • C 5 Byte: 8 bits
  • D 6 Kilobyte: 1000 bytes
  • E 1 Megabyte: 1000 kilobytes
  • F 4 Gigabyte: 1000 megabytes