Year 8 · Spring 1

Representations: from clay to silicon · Lesson 5 of 5

Units and an introduction to hexadecimal

TheoryTopic 2 Bits and bytesTopic 3 Binary, denary and hex

Year 8 · Representations: from clay to silicon · Lesson 5 of 5

You will learn to

  • Convert between bits, bytes, KB, MB and GB, using × 8 and × 1000.
  • Explain why one hex digit stands for exactly four bits, called a nibble.
  • Convert a byte to two hex digits by splitting it into two nibbles.
  • Explain that a colour code like #FF8800 is three bytes: red, green and blue.

Year 8 · Representations: from clay to silicon · Lesson 5 of 5

Success criteria

You have got it when you can say:

  • I can convert 3 MB to bytes and to bits.
  • I can convert 10011100 to 9C, and 9C back to binary.
  • I can read #FF8800 as red 255, green 136 and blue 0.

Year 8 · Representations: from clay to silicon · Lesson 5 of 5

Retrieval starter

Questions from before. Write your answers, then show them.

  1. Last lesson

    A = 65 and a = 97. Which bit is different between them?

    A The 128s bitB The 32s bitC The 1s bit

    B. The 32s bit

  2. Last unit

    The web and the internet are…

    A The web is a service that runs on the internetB The internet runs on the webC The same thing

    A. The web is a service that runs on the internet

  3. Earlier this year

    A 100 Mbps connection downloads at most…

    A 800 MB per secondB 12.5 MB per secondC 100 MB per second

    B. 12.5 MB per second

Year 8 · Representations: from clay to silicon · Lesson 5 of 5

Key words (1 of 2)

Hexadecimal
Base 16: digits 0–9 then A–F. One digit = 4 bits.
Bit
One binary digit, 0 or 1. One switch.
Byte
8 bits. 256 possible patterns.
Nibble
4 bits. One hex digit.

Year 8 · Representations: from clay to silicon · Lesson 5 of 5

Key words (2 of 2)

Denary
Base 10. Our everyday numbers.
Binary
Base 2. Digits 0 and 1. Columns 128 64 32 16 8 4 2 1.
Overflow
A result too big for the bits available.

The explanation · step 1 of 3 · part 1 of 2

Converting between units

★Remember

Going to a bigger unit: divide. Going to a smaller unit: multiply.

?Why?

Why? Think of money. 3 euros = 300 cents. Cents are smaller, so you need more of them. More = bigger number = multiply.

The explanation · step 1 of 3 · part 2 of 2

Converting between units (continued)

e.g.Example

3 MB → bytes: 3 × 1000 = 3,000 KB. Then 3,000 × 1000 = 3,000,000 bytes. Then × 8 = 24,000,000 bits.

The explanation · step 1 of 3

The maths: Changing units

The explanation · step 2 of 3 · part 1 of 2

Hexadecimal: why it exists

Binary is hard for people to read: 1001110011110101. Hexadecimal is a shorthand.

?Why?

Why 16? 4 bits make 16 patterns (2⁴ = 16). So one hex digit = exactly 4 bits. One byte = exactly 2 hex digits.

Denary101112131415
HexABCDEF

The explanation · step 2 of 3 · part 2 of 2

Hexadecimal: why it exists (continued)

!Watch out

Hex doesn't change how the computer stores anything. It's only a way for humans to write binary.

The explanation · step 3 of 3

Converting with hex

  • Binary → hex: split into groups of 4. 1001 | 1100 → 9 | 12 → 9C.
  • Hex → binary: each digit becomes 4 bits. 3F → 0011 1111.
  • Hex → denary: first digit × 16, plus second digit. 9C = 9 × 16 + 12 = 156.
  • Denary → hex: divide by 16. 200 ÷ 16 = 12 remainder 8 → C8.
e.g.Example

Web colours are hex: #FF0000 is pure red.

The explanation · step 3 of 3

The maths: Hex to denary

Year 8 · Representations: from clay to silicon · Lesson 5 of 5

Quick quiz · 1 of 3

What is 1011 in denary?

  1. A 13
  2. B 11
  3. C 7

B. 11

8 + 2 + 1 = 11. Add the columns that hold a 1.

Year 8 · Representations: from clay to silicon · Lesson 5 of 5

Quick quiz · 2 of 3

What is 200 in 8-bit binary?

  1. A 11001000
  2. B 10011000
  3. C 11010000

A. 11001000

128 fits (72 left), 64 fits (8 left), then 8 fits: 11001000.

Year 8 · Representations: from clay to silicon · Lesson 5 of 5

Quick quiz · 3 of 3

Hex F is…

  1. A 16
  2. B 10
  3. C 15

C. 15

Hex digits run 0–9 then A = 10 up to F = 15.

Year 8 · Representations: from clay to silicon · Lesson 5 of 5

Exit ticket

Answer on paper before you go. Then check.

  1. 1 + 1 in binary is…

    A 2B 11C 10

    C. 10 Write 0, carry 1. Say 'one zero', not 'ten'.

  2. Shifting a binary number one place right…

    A Adds 1B Doubles itC Halves it

    C. Halves it Each column is worth half the one to its left. The bit that falls off is lost.

Year 8 · Representations: from clay to silicon · Lesson 5 of 5

Homework and the challenge

Homework

Study pages 3 and 4; Bit Maths Lab 'Convert' section.

End-of-unit challenge

A binary escape room: each solved conversion unlocks the next door.