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AQA 8525 GCSE Computer Science · 3.3 Fundamentals of Data Representation

Stretch tasks Number Bases and Units of Information

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 value card to its denary card.

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

6 pairs, about 4 minutes

Task 4

Sort It

Sort each statement into the right box, like the tick-box tables in the exam.

  • 11 cards to sort into 3 boxes
  • Drag a card, tap a box or press its number
  • Combo points for cards sorted in a row

11 cards, about 4 minutes

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

Read the lesson: Number Bases and Units of Information

Number Bases and Units of Information: the questions

Quiz Challenge, round 1: Quiz Blitz

  1. Convert binary 10110100 to denary.

  2. Convert denary 180 to hexadecimal.

  3. Convert hex 2F to 8-bit binary.

  4. Why do computers use binary?

    • Binary numbers are shorter
    • Denary cannot store text
    • Their components have two easily distinguishable states
    • Binary is easier for people to read

  5. How many bits are in a nibble?

    • 8
    • 2
    • 16
    • 4

  6. AQA uses 1024 bytes in a kilobyte.

    • True
    • False

  7. One byte is always how many hex digits?

    • 8
    • 2
    • 1
    • 4

  8. How many bytes are in 4 kB, using AQA's units?

  9. Order these units from smallest to largest.

    Number these 1 to 6.

    • Nibble
    • Byte
    • Kilobyte
    • Megabyte
    • Terabyte
    • Bit

  10. What is hex B4 in denary?

    • 1,104
    • 180
    • 114
    • 164

  11. What is the safest route from denary to hex?

    • Denary to binary, then binary to hex
    • Divide by 2, then by 8
    • Add 16 to each digit
    • Read the digits backwards

  12. A value written in hex takes a quarter of the characters of the same value in binary.

    • True
    • False

Quiz Challenge, round 2: Quick Fire

  1. Explain why computers use binary rather than denary. [2 marks]

  2. Convert 180 to hexadecimal, showing your working. [2 marks]

  3. Give two reasons why memory addresses are written in hexadecimal. [2 marks]

  4. A file is 3,500,000 bytes. Convert this to megabytes using AQA's units. [2 marks]

Quiz Challenge, round 3: Big Think

  1. Convert the denary number 180 into binary, then into hexadecimal. Show your working. [4 marks]

  2. A file is 24,000,000 bits. Convert it to megabytes, showing each step and saying why it is done. [4 marks]

This or That: tick the right answer

  1. Which hex digit comes after 9?

    • 10
    • A

  2. Binary place values double going from...

    • Left to right
    • Right to left

  3. Which is bigger?

    • Denary 14
    • Hex F

  4. Where do the hex digits stop?

    • At F, which is 15
    • At G, which is 16

  5. How many bits are in 2 bytes?

    • 16
    • 10

  6. Splitting 10110100 into groups of four, which end do you start from?

    • The right
    • The left

  7. For AQA, 1 MB is how many kB?

    • 1000
    • 1024

  8. Why can binary survive a noisy signal?

    • Only two states need telling apart
    • Binary signals are louder

Memory Match: match each value to its denary

ValueDenary
A Binary 11111 8
B Hex FF2 180
C Hex 103 255
D Binary 10004 16
E Hex B45 32
F Binary 1000006 15

Sort It: tick one box in each row

Binary, denary or hexadecimal?

StatementBinaryDenaryHexadecimal
Base 16
One digit stands for four bits
Base 2
Place values 1, 2, 4, 8
Uses A to F for ten to fifteen
Only the digits 0 and 1
Used because components have two states
Place values 1, 10, 100, 1000
The everyday number system
Place values 1, 16, 256
Base 10
Answers

Round 1: Quiz Blitz

  1. 180 128 + 32 + 16 + 4 = 180.
  2. B4 180 is 10110100. 1011 is 11, which is B, and 0100 is 4.
  3. 00101111 2 is 0010 and F is 1111. Each hex digit becomes exactly four bits.
  4. Their components have two easily distinguishable states Two states can be told apart even when the signal is noisy.
  5. 4 A nibble is 4 bits, which is exactly one hex digit.
  6. False AQA uses 1000. Using 1024 will not match the mark scheme.
  7. 2 8 bits is two nibbles, and each nibble is one hex digit.
  8. 4000 4 x 1000 = 4000 bytes.
  9. Bit → Nibble → Byte → Kilobyte → Megabyte → Terabyte 4 bits, 8 bits, then 1000 times bigger at each step from kilobyte on.
  10. 180 B is 11, so (11 x 16) + 4 = 180.
  11. Denary to binary, then binary to hex Going through binary means you only need two conversions instead of six.
  12. True Each hex digit replaces four bits.

Round 2: Quick Fire

    • Their components have two states, such as on and off
    • Two states can be told apart reliably, even with noise
    Model answer

    Computer components, such as transistors, have two easily distinguishable states. Two states can be told apart reliably even when the signal is noisy, whereas ten states would need nine thresholds that interference could push a value across.

    • Working: 10110100, or 180 / 16 = 11 remainder 4
    • B4
    Model answer

    180 is 10110100 in binary. Split into nibbles: 1011 is 11, which is B, and 0100 is 4. So 180 is B4.

    • It is shorter: one hex digit is four bits
    • It is easier to read and compare, with fewer mistakes
    Model answer

    Hex is much shorter, because one hex digit stands for four bits, so a byte is just two digits. That makes addresses easier for people to read and compare without mistakes.

    • Divide by 1000 twice, or by 1,000,000
    • 3.5 MB
    Model answer

    3,500,000 / 1000 = 3500 kB, and 3500 / 1000 = 3.5 MB.

Round 3: Big Think

    • Takes the place values that fit: 128 + 32 + 16 + 4
    • Binary: 10110100
    • Splits it into nibbles from the right: 1011 and 0100
    • Hexadecimal: B4
    Model answer

    180 minus 128 leaves 52, 52 minus 32 leaves 20, 20 minus 16 leaves 4, and 4 minus 4 leaves 0, so 180 = 128 + 32 + 16 + 4, which is 10110100. Split into nibbles from the right: 1011 is 11, which is B, and 0100 is 4. So 180 is B4.

    • Divide by 8, because there are 8 bits in a byte
    • 3,000,000 bytes
    • Divide by 1000 for kilobytes: 3000 kB
    • Divide by 1000 again: 3 MB
    Model answer

    Divide by 8, because there are 8 bits in a byte: 24,000,000 / 8 = 3,000,000 bytes. Divide by 1000 to go up to kilobytes, as AQA uses 1000: 3000 kB. Divide by 1000 again to go up to megabytes: 3 MB.

This or That

  1. A Hex uses A to F for ten to fifteen, so every value is a single digit.
  2. Right to left The rightmost bit is worth 1, then 2, 4, 8 and so on to the left.
  3. Hex F F is 15.
  4. At F, which is 15 Sixteen digits: 0 to 9, then A to F.
  5. 16 8 bits in each byte.
  6. The right Starting from the left puts every digit in the wrong column when the bits do not divide evenly.
  7. 1000 AQA uses 1000 at every step.
  8. Only two states need telling apart With two states, a little noise cannot push a value across a threshold.

Memory Match

  • A 6 Binary 1111: 15
  • B 3 Hex FF: 255
  • C 4 Hex 10: 16
  • D 1 Binary 1000: 8
  • E 2 Hex B4: 180
  • F 5 Binary 100000: 32

Sort It

  1. Hexadecimal Base 16 Hexadecimal uses sixteen digits.
  2. Hexadecimal One digit stands for four bits Sixteen is two to the power four.
  3. Binary Base 2 Binary uses two digits.
  4. Binary Place values 1, 2, 4, 8 Binary place values double each time.
  5. Hexadecimal Uses A to F for ten to fifteen Hex needs six extra digits.
  6. Binary Only the digits 0 and 1 Binary has just two digits.
  7. Binary Used because components have two states On and off map onto 1 and 0.
  8. Denary Place values 1, 10, 100, 1000 Denary place values go up in tens.
  9. Denary The everyday number system Denary is what people normally use.
  10. Hexadecimal Place values 1, 16, 256 Hex place values go up in sixteens.
  11. Denary Base 10 Denary uses ten digits.