Lesson Objectives

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# Lesson Objectives - PowerPoint PPT Presentation

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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Presentation Transcript
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

x10

x2

x2

x10

x10

x2

1000

8

100

4

2

10

1

1

1

1

2

0

1

3

1

4

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

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…

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)

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?

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

You do it in exactly the same way

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

255
• Denary
• 255
• Binary
• 11111111
• FF

Large binary numbers are hard to remember

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

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

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!