Binary Numbers and Data Representation

• newEditor
• Computing
• Lower Secondary (Key Stage 3)

Binary: How Computers Use 0s and 1s

This KS3 computing lesson explores Binary Numbers and Data Representation. Students learn why computers use binary, convert between binary and denary numbers and explore how simple data can be represented using bits and bytes. It provides a clear introduction to the topic and can be used for classroom teaching, homework or revision.

Binary, Binary Numbers, KS3 Computing, Computer Science, Base 2, Denary, Bit, Byte, Place Values, Binary Addition, ASCII, Character Sets, Overflow Error, MCQs, Open Questions, Polls, Emoji Polls, Exit Tickets

What comes to mind when you hear 0s and 1s?

Use this to surface prior ideas such as computers, code, numbers, on/off, games, robots or maths. Briefly connect student words to the lesson goal.

What is binary?

• Binary is a number system with only two digits: 0 and 1.

• Computers use binary because electronic switches can be off or on.

• So binary matches the simple states a computer can detect.

Link 0 and 1 to low/high or off/on without going deeply into electronics.

Bits: the smallest unit

• A bit is one binary digit.

• A bit can hold 0 or 1.

• Bits are the smallest units of data in computing.

• Groups of bits can represent more complex information.

You may mention that 8 bits make a byte, but keep the main focus on bits.

Binary and decimal

• Uses 10 digits: 0 to 9

• The system people use every day

• Place values grow in powers of 10

Binary system

• Uses 2 digits: 0 and 1

• Used inside computers

• Place values grow in powers of 2

Decimal system

Emphasise that the idea of place value is the same in both systems; only the base changes.

Place value in binary

In binary, each place is worth twice the place to its right.

From right to left, the first few place values are:

1, 2, 4, 8, 16, 32

A 1 means that value is included.

A 0 means that value is not included.

This is a key mechanism slide. Keep attention on the pattern of doubling.

Reading a binary number

1011 means:

• 1 eight

• 0 fours

• 1 two

• 1 one

So 1011 = 8 + 2 + 1 = 11

Students often read 1011 as 'one thousand and eleven'. Remind them it is a binary value, not a decimal one.

What is one bit?

A

one binary digit

B

ten binary digits

C

one decimal digit

D

two decimal digits

Checks the key term from the first subtopic. Distractors target confusion between binary and decimal, and between one bit and larger groups of bits.

Complete the summary

Binary uses only 0 and 1. A bit is one binary digit. In binary, place values grow in powers of 2, not 10.

0 and 1

bit

2

0 to 9

byte

10

100

This reinforces the core vocabulary and the binary/decimal contrast after slides 2 to 6.

Decimal to binary: small examples

• 1 in decimal = 1 in binary

• 2 in decimal = 10 in binary

• 3 in decimal = 11 in binary

• 4 in decimal = 100 in binary

• 5 in decimal = 101 in binary

Show how each new place appears when the value reaches the next power of 2.

How to convert small numbers

To change a small decimal number into binary:

• Find the biggest binary place value you need

• Write 1 if you use it

• Write 0 if you do not

• Add the chosen values to check the answer

Example: 6 = 110 because 4 + 2 = 6

Keep examples small and concrete. KS3 A2 learners benefit from repeated use of 1, 2, 4, 8.

What is 110 in decimal?

A

4

B

5

C

6

D

7

Students should use place values 4, 2 and 1. 110 means 4 + 2 + 0.

Fill in the conversion steps

To change 6 into binary, use the place values 4 and 2. Write 1 for used values and 0 for unused values. So 6 is 110 in binary.

4

2

1

110

8

1

10

101

Echoes the worked example on slide 8 and checks that students can connect place values to the binary answer.

Binary represents numbers

• Computers store numbers as patterns of bits.

• Different bit patterns mean different values.

• The same place value rules let a computer represent quantities using 0s and 1s.

Do not go into signed numbers or floating point; keep it at basic whole-number representation.

Binary represents text

Letters and symbols can also be stored in binary.

A computer uses a code that gives each character a number. That number is then stored in binary.

So text on a screen is also built from patterns of 0s and 1s.

You may mention ASCII as an example of a code, but it is not necessary for this lesson.

Binary represents images

• Digital images are made of tiny parts called pixels.

• Each pixel stores colour or brightness as numbers.

• Those numbers are stored in binary.

• So an image is a very large set of bits.

Keep this at a basic level: pixels store values, and values are stored in binary.

One system, many kinds of data

Numbers, text and images may look different to us, but a computer stores them in the same basic way:

patterns of bits

That is why binary is a foundation of computing.

This slide resolves the lesson's central question by unifying the examples.

How does a computer store text?

A

as spoken sounds

B

as bit patterns

C

as pencil marks

D

as paper lines

Builds on slides 9 to 12: text is first given a number by a code, then stored in binary as patterns of bits.

Complete the paragraph

Computers can store numbers, text and images. Images are made of pixels, and each pixel stores colour or brightness as numbers. In the end, all of these are stored as patterns of bits.

text

pixels

brightness

bits

sound

letters

screens

bytes

Reinforces the final unifying idea that many kinds of data are stored in the same basic way.

How can binary store text and images?

Expected elements: computers store different kinds of information using the same basic system of bit patterns; examples may include numbers, text and images.

To what extent do you feel your understanding of binary has increased over this lesson?

Glossary

binary - a number system that uses only 0 and 1

bit - one binary digit

decimal - a number system that uses the digits 0 to 9

place value - the value of a digit because of its position

data - information stored or used by a computer

text - letters, numbers and symbols used as writing

pixel - a tiny part of a digital image