Good Learning Co.
SavannahYear 8
← Computing
ComputingHow computers work20 min★★ difficulty

Binary: how computers count

Inside a computer, everything (numbers, words, photos, music) is stored as 1s and 0s. Here's how that works.

Part of your national curriculum
  • Data and representation: Understand how numbers can be represented in binary, and be able to carry out simple operations on binary numbers

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

  • • Why 0 and 1
  • • Binary place values
  • • Denary to binary
  • • Adding in binary

This lesson at a glance

  • 20 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 · Intro5%
1

Introduction

Part 1 of 19

Binary: how computers count illustrationVisual introduction

Picture this

Binary: how computers count

Inside a computer, everything (numbers, words, photos, music) is stored as 1s and 0s. Here's how that works.

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 know place value: units, tens, hundreds.

3

Key words

Part 3 of 19

Key words

Words you'll need today

binary
A number system that only uses 0 and 1.
bit
A single 0 or 1.
byte
8 bits. It can store numbers from 0 to 255.
denary
Our normal base-10 number system.
4

Learning cycle

Part 4 of 19

Learning cycle 1 of 2

Part 1: Place values

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

5

Explore the idea

Part 5 of 19

Learn

Why 0 and 1

Computers are made of billions of tiny switches that are either off (0) or on (1). Two states are simple and reliable.

6

Explore the idea

Part 6 of 19

Learn

Binary place values

In denary, each column is 10 times bigger. In binary, each column doubles: 128, 64, 32, 16, 8, 4, 2, 1. So binary 101 = 4 + 0 + 1 = 5.

7

Quick check

Part 7 of 19

Quick check

What is binary 101 in denary?

8

Quick check

Part 8 of 19

Quick check

How many bits in a byte?

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

Part 2: Converting and adding

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

11

Explore the idea

Part 11 of 19

Learn

Denary to binary

To write 13: which columns add to 13? 8 + 4 + 1. So 13 = 1101. Work from the biggest column that fits, then the next.

12

Explore the idea

Part 12 of 19

Learn

Adding in binary

0+0=0, 0+1=1, 1+1=10 (write 0, carry 1), and 1+1+1=11 (write 1, carry 1). For example, 0101 + 0011 = 1000, which is 5 + 3 = 8.

13

Quick check

Part 13 of 19

Quick check

What is 6 in binary?

14

Quick check

Part 14 of 19

Quick check

What is 1 + 1 in binary?

15

Common mix-ups

Part 15 of 19

Common mix-ups

Things people often get wrong

  • Binary 10 isn't ten. It's 2.
  • Columns double from right to left: 1, 2, 4, 8, not 1, 10, 100.
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.

Two states are ____ and reliable.

In ____, each column doubles: 128, 64, 32, 16, 8, 4, 2, 1.

18

Mastery quiz

Part 18 of 19

Marked quiz

End of lesson quiz: Binary: how computers count

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

  1. 1. Binary columns go:

  2. 2. What is binary 1111 in denary?

  3. 3. Why do computers use binary?

  4. 4. What is the denary value of the binary number 1011?

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 · Introduction

How this is going

  • Not looked at yet

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

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