1. Lesson Objectives Aims You should be able to:
Explain why data is represented in binary form
Define some basic binary storage terms
Understand that data needs to be converted to binary to be processed by a computer

2. Quick recap
Computers are binary devices
This means they are DIGITAL
The real world is ANALOGUE
This means computers can’t understand our world (data) without conversion

3. Digital V Analogue
Digital information is binary, that means it can be either off or on
1 or 0
Like a light switch.

4. Analogue
Analogue or real world data is, generally, constantly changing
Analogue values do not tend to jump from one to the other, there is a small, incremental movement

5. Therefore
Computers CANNOT understand analogue information
There is always a need for conversion
Most input and output devices do ADC or DAC
This enables to computer to process data in a form it understands – binary.

6. Useful
On its own, Binary doesn’t seem that useful
But we can combine strings of binary digits and interpret them as sound, images, text etc
We will investigate this in coming lessons

7. Learn to count
You should know this, but lets do it anyway.
How do you count to 10?
What happens we get to 9? This point is pivotal…

8. It’s all about the BASE. Geddit? See what I did there?
Our number system
Our number system is called Denary
It is BASE 10
Which means… we have 10 digits 0..9
It’s all about the BASE. Geddit? See what I did there?

9. Lets go through on the board:
Denary
Lets go through on the board:
How we count
What happens when we run out of digits
How we arrive at a value for each column
What a number really is

11. Denary Notes Number system rules
Any number system has a set of digits (in denary this is 0..9, 10 in total)
The number of available digits is the BASE of the number system
When all digits have been used and a higher number is required, simply reset the current column to 0 and start again at 1 in the next column
The first (units) column in any number system has a value of 1x the digit
Subsequent columns have a value of the base x previous column
A number is actually the sum of each digit, multiplied by it’s column value
= (4x1000) + (3x100) + (2x10) + (4x1) = 4324
Thousands
(x1000)
Hundreds (x100)
Tens (x10)
Units (x1) 4 3 2

12. Binary
The binary number system works in the same way
The ONLY difference is we only have 2 digits – 0 and 1

13. Lets go through on the board:
Binary
Lets go through on the board:
How we count
What happens when we run out of digits
How we arrive at a value for each column
How to work out the value of a binary number

15. Copy the example…
128 64 32 16 8 4 2 1
Binary numbers are simple to work out – they use the same rules as denary!
1 means ON so add up its value
0 means OFF so ignore it
So this number is:
(128x1) + (64x0) + (32x0) + (16x0) + (8x1) + (4x0) + (2x1) + (1x1)
Anything x0 = 0 and anything x1 is itself so…
= 139

16. Binary Quantities
The smallest piece of information a computer can understand is a 1 or a 0
This single digit is called a BIT.
Obviously, this isn’t too useful on its own.
If we group 4 BITS together, we have 16 possible combinations – a NYBBLE

17. Copy this in to your notes
Binary Quantities
1 or 0 = Bit
4 bits = Nybble
8 bits = Byte (most common grouping)
1024 bytes = 1 Kilobyte (Kb) (2^10)
1024Kb = 1 Megabyte (Mb) (2^20)
1024Mb = 1 Gigabyte (Gb) (2^30)
1024Gb = 1 Terabyte (Tb) (2^40)
1024Tb = 1 Petabyte (Pb) (2^50)
All are powers of 2

18. June 2015, Q8 (b)