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Lesson Objectives. Understand the hexadecimal numbering system Convert numbers between hexadecimal and denary, and vice versa ALL students be able to count in hex from 1 to 16 MOST students will convert hex numbers into denary

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lesson objectives
Lesson Objectives
  • Understand the hexadecimal numbering system
  • Convert numbers between hexadecimal and denary, and vice versa
  • ALL students be able to count in hex from 1 to 16
  • MOST students will convert hex numbers into denary
  • SOME students will convert numbers between hex, denary and binary
slide2

x10

x2

x2

x10

x10

x2

1000

8

100

4

2

10

1

1

1

1

2

0

1

3

1

4

You already know about base 10 (Decimal/Denary)

And you’ve just learnt about base 2 (Binary)

why do we need binary numbers
Why do we need binary numbers?

Because computers work on the principle of 2 states, that something is either ON/TRUE or OFF/FALSE.

This can only be done with base 2 (binary)

If it was done with decimal/base 10 there would be 10 different states!

the problem with binary
The problem with binary…

There is one big problem with binary…numbers can become VERY long!

In order to make it easier for a human programmers to work with binary numbers, they use the hexadecimal system (like a binary shortcut)

hexadecimal
Hexadecimal

As we move left, the column headings increase by a factor of sixteen

x16

x16

x16

4096

256

16

1

0

1

2

3

This number is:

1 x 256 + 2 x 16 + 3 x 1 = 291

It’s still two hundred and ninety-one, it’s just written down differently

How can there be sixteen possible digits in each column, when there are only ten digits?

http://www.advanced-ict.info/interactive/hexadecimal.html

hexadecimal1
Hexadecimal

Notice how 0 is classed as a digit, so there are 16 numbers in total from 0 to 15

Hexadecimal uses the digits 0-9 and the letters A-F to represent the denary numbers 0-15

making bigger numbers
Making bigger numbers

You do it in exactly the same way

where is it used
Where is it used?

When have you seen numbers being represented as letters?

Hex is often used for 32-bit colour values, especially on web pages

FF00EE99 instead of 11111111000000001110111010011001.

http://www.advanced-ict.info/interactive/colours.html

slide9
255
  • Denary
    • 255
  • Binary
    • 11111111
  • Hexadecimal
    • FF
slide10

Large binary numbers are hard to remember

Programmers use hexadecimal values because:

each digit represents exactly 4 binary digits;

hexadecimal is a useful shorthand for binary numbers;

hexadecimal still uses a multiple of 2, making conversion easier whilst being easy to understand;

converting between denary and binary is relatively complex;

hexadecimal is much easier to remember and recognise than binary;

this saves effort and reduces the chances of making a mistake.

you convert denary to hex in the same was as binary
You convert denary to hex in the same was as binary

2

Convert the denary number 45 into a hex number

Step 1: How many times does 16 go into 45?

45 / 16 = 2 (with 13 remaining)

Step 2: How many times does 13 go into 1?

13! 13 in hex is D

let s do another one
Let’s do another one

C

Convert the denary number 199 into a hex number

Step 1: How many times does 16 go into 199?

199 / 16 = 12 (with 7 remaining)

Step 2: 12 in hex is C

Step 2: How many times does 7 go into 1?

7! 7 in hex is 7!

lesson task
Lesson task:

Complete the denary to hex conversions in your workbook.

Extension: If you complete, have a go at the cross word task in your booklet.

hex to binary

To convert from hexadecimal to binary treat each digit separately. It may be easier to go via denary to get a binary number.

So DB in hexadecimal is 11011011 in binary.

Hex to binary