Hexadecimal and Conversions

• Computing
• Lower Secondary (Key Stage 3)

Hexadecimal and Conversions

Connect on your whiteboards

2. What is the binary number for the denary digits:

17?

1. What is the decimal number for the binary digits:

1011?

3. Name two ways to communicate without using electricity

4. Name one way to stop or prevent online bullying

Drag the text on to the pictures that you think

best represent that number system

Binary

(base 2)

Denary

(base 10)

Hexadecimal

(base 16)

Key objective

1. Understand the hexadecimal number system
2. Convert between hexadecimal and decimal
3. Convert between binary and hexadecimal 

Hexadecimal

• "Hexa" - comes from the Greek word "six"
• "Decimal" - comes from the Latin word "Decimus"                                                - which means "10th"
• "6 and 10" - "Base 16"

However we only have 10 digits:

0,1,2,3,4,5,6,7,8,9

What do we do now?

Review this picture and guess what they have done to represent numbers greater than 9:

Hexidecimal System

We know Binary is base 2 and uses: 0 and 1.

We know Denary/Decimal is base 10 and uses: 0 up to 9.

Hexidecimal is base 16 and uses:

0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F - 0 to 15 where 10 is A and 15 is F.

Hexadecimal or "Hex" is used to compact values, so instead of "1111" in binary, we can just write "F".

Bringing it all together

Consider how we want to start moving from one base to another.

Knowing your times tables and this counting system will help.

If in doubt, have a pen and paper about, show your workings out!

Bases

What is the pattern -

How is each column growing?

Bases

Each column is a multiple of the base.

 

Example: Representing 11

How would we represent the digits 11 in each base?

Converting Hexadecimal to Denary

How do we convert C9 to Denary

Multiple by columns

12 x 16 = 192

9 x 1 = 9

Add together

192 + 9 = 201

We know 9 = 9

Break it up by column

C | 9

We know C = 12

We know 9 = 9

Hex -> Denary Game

https://bellamywood.github.io/number-rain-game/

Look on the monitor for "purple" themed game.

ViPos for top 3

Make sure to tell students who are struggling to use slower speeds and tell them to review the helper text that appears when they attempt to answer.

Converting Denary to Hexadecimal

How do we convert 201 to Hexadecimal

Divide by Base (16)

201 / 16 =  12 with 9 remainder.

Put it together

C | 9 -> C9

Break it up by column

We know C = 12

And the remainder can be

directly translated to 9 = 9

Converting Denary to Hexadecimal

How do we convert 316 to Hexadecimal

Divide by Base (16)

316 / 256 =  1 with 60 remainder.

60 / 16 = 3 with 12 remainder.

Put it together

1 | 3 | C -> 13C

Break it up by column

We know 1 = 1 and 3 = 3

so the remainder can be

directly translated from 12 = C

Denary -> Hex Game

https://bellamywood.github.io/number-rain-game/

Look on the monitor for "blue" themed game.

ViPos for top 3

Make sure to tell students who are struggling to use slower speeds and tell them to review the helper text that appears when they attempt to answer.

Converting Binary to Hexadecimal

How do we convert 000111101100 to Hexadecimal

Separate the nibbles (4 bits)

0001 | 1110 | 1100

Put it together

1 | E | C -> 1EC

Look up the column or count the bits

We know 0001 = 1

We know 1110 = E

We know 1100 = C

Binary-> Hex Game

https://bellamywood.github.io/number-rain-game/

Look on the monitor for "teal" themed game.

ViPos for top 3

Make sure to tell students who are struggling to use slower speeds and tell them to review the helper text that appears when they attempt to answer.

Converting Hexadecimal to Binary 

How do we convert F1A to Hexadecimal

Separate the nibbles (4 bits)

F | 1 | A

Put it together

1111 | 0001 | 1010 -> 111100011010

Look up the column or count the bits

We know 1111 = F

We know 0001 = 1

We know 1010 = A

Hex-> Binary Game

https://bellamywood.github.io/number-rain-game/

Look on the monitor for "pink" themed game.

ViPos for top 3

Make sure to tell students who are struggling to use slower speeds and tell them to review the helper text that appears when they attempt to answer.

Stretch: Go for the high score!

Look on the monitor for "purple" themed game.

ViPos for top 1

This is probably the hardest mode.

How confident are you with converting between base numbers?

😒🙁😐🙂😃