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SavannahYear 8
← Computing
ComputingYear 8 Computing: data, logic and programs30 min★★★ difficulty

Binary numbers and representing text

A computer stores everything as two states. Once you can convert between denary and binary, file sizes and character sets stop being mysterious.

Lesson overview

What you'll learn in this lesson

Understand how numbers can be represented in binary, and be able to carry out simple operations on binary numbers

Key learning points

  • • Place value in base two
  • • Binary addition
  • • Overflow
  • • From numbers to text

This lesson at a glance

  • 30 minutes
  • 19 parts to scroll through
  • 4 quick checks
  • Marked quiz at the end
  • Gentle pace: short sittings with pauses

Words to know

numbersrepresentedbinarysimpleoperations

Scroll down — the lesson carries on below

Part 1 of 19 · Discover5%
1

Watch & discover

Part 1 of 19

Watch first

Binary numbers and representing text

Discover how a string of 1s and 0s becomes the letters you type.

In a nutshell

Understand how numbers can be represented in binary, and be able to carry out simple operations on binary numbers

2

What you already know

Part 2 of 19

Before we start

What you already know

You should already know place value in base ten and that computers use switches that are on or off.

3

Key words

Part 3 of 19

Key words

Words you'll need today

Bit
A single binary digit, 0 or 1.
Byte
Eight bits, enough for 256 different patterns.
Denary
Ordinary base-ten counting.
Overflow
When a result needs more bits than are available.
Character set
An agreed mapping from characters to binary codes, such as ASCII.
4

Learning cycle

Part 4 of 19

Learning cycle 1 of 2

Counting in twos

A short piece of teaching, then a check to make sure it has landed.

5

Explore the idea

Part 5 of 19

Learn

Place value in base two

In an eight-bit number the column headings are 128, 64, 32, 16, 8, 4, 2, 1. To convert 37 you take the biggest heading that fits (32), then 4, then 1: 00100101. Converting back is simply adding the headings above each 1.

6

Explore the idea

Part 6 of 19

Learn

Binary addition

The rules are 0+0=0, 0+1=1, 1+1=10 (write 0, carry 1) and 1+1+1=11 (write 1, carry 1). Line up the columns exactly as you would in denary, working right to left.

7

Quick check

Part 7 of 19

Quick check

What is 00101101 in denary?

8

Quick check

Part 8 of 19

Quick check

What is 1011 + 0110 in binary?

9

Reset break

Part 9 of 19

Pause

That's sitting 1 of 2 done

Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.

Stop here for now
10

Learning cycle

Part 10 of 19

Learning cycle 2 of 2

Adding, overflow and characters

A short piece of teaching, then a check to make sure it has landed.

11

Explore the idea

Part 11 of 19

Learn

Overflow

If you only have eight bits, 11111111 + 1 needs a ninth. The carry falls off the end and the answer wraps to 00000000, which is wrong. Real systems detect this with an overflow flag; it is a limit of the storage, not of the arithmetic.

12

Explore the idea

Part 12 of 19

Learn

From numbers to text

Characters are stored as numbers. In ASCII, 'A' is 65 and 'a' is 97, so the gap between an upper- and lower-case letter is always 32. Unicode extends the idea to tens of thousands of characters, which is why one emoji can take more bytes than one letter.

13

Quick check

Part 13 of 19

Quick check

Overflow happens when...

14

Quick check

Part 14 of 19

Quick check

In ASCII, if 'A' is 65 then 'C' is...

15

Common mix-ups

Part 15 of 19

Common mix-ups

Things people often get wrong

  • Binary 10 is two, not ten.
  • Eight bits give 256 patterns (0–255), not 255 patterns.
  • Text is not stored 'as letters' — it is stored as numbers using an agreed character set.
16

Challenge round

Part 16 of 19

Game · Sort it

Which of these are true?

Drag each card into the right column. Tap a card first if dragging is fiddly.

True

Not true

17

Challenge round

Part 17 of 19

Game · Fill the gaps

Finish the sentences

Choose the word that belongs in each gap.

Characters are stored as ____.

18

Mastery quiz

Part 18 of 19

Marked quiz

End of lesson quiz: Binary numbers and representing text

6 questions, marked with the reasoning shown. No timer.

  1. 1. How many patterns can 8 bits hold?

  2. 2. Denary 9 in binary is...

  3. 3. A byte is...

  4. 4. 1 + 1 in binary gives...

  5. 5. Unicode exists because...

  6. 6. Lower-case 'a' in ASCII is...

19

Lesson round-up

Part 19 of 19

Lesson round-up

Ready when you are

Quiz score

Not sat

Games

Not played

Points this lesson

0

Best run

0 in a row

Luna: 0 out of 4 on the practice checks. Only if you feel up to it — one more?

Ask Luna

Do the work

Your written work for this lesson

This is the part you'd do in your book at school. Pick the pieces below, write here or on paper, and photograph anything you draw or work out.

Article

How a supermarket checkout knows the price

When a barcode is scanned, the checkout does not store the price itself. It sends the barcode number to a database and reads back a record: product name, price, whether it needs an age check. The record is the single place the price lives, so changing one row changes every till in the shop at once.

Problems come from bad data, not bad scanners. If two products share a barcode, or a price update reaches the shop overnight but the till holds an old copy in its cache, customers are charged the wrong amount. Shops check this with test transactions: scan a known item, expect a known price, record what actually happened.

Good systems also log every scan. If a customer complains, the log shows exactly which record was used and when.

Written for Good Learning Co.

Reading questions

  1. Write in your own words what the checkout sends and what it receives back.
  2. Explain one way bad data could cause a wrong price, and how logging helps find it.
  3. Design a test table with four tests for a new checkout, with expected and actual results.

  • Reading and notes

    Reading

    Read the lesson text again and note the key terms and how each one is used, in your own words — as you would for revision.

    Half a page of notes

  • Extended writing

    Writing

    Explain a real system that uses this idea — how it works, where it can go wrong, and how you would make it safer or better.

    250–350 words

  • Algorithm on paper

    Diagram

    Write your steps out as pseudocode or a flowchart before you type anything, then photograph it.

    1 flowchart or 10 lines

  • Code write-up

    Writing

    Copy your code in, then explain underneath what each part does and what you had to fix.

    Code + 5 sentences

  • Test table

    Working out

    Make a test table: what you tried, what you expected, what actually happened.

    4–6 tests

Saved as you type.

Part 1 of 19 · Watch & discover

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