Lesson Objectives
Aims
You should be able to:
1. Explain why data is represented in binary form
2. Define some basic binary storage terms
3. Understand that data needs to be converted to binary to be
processed by a computer
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
Digital V Analogue
• Digital information is binary, that means
it can be either off or on
• 1 or 0
• Like a light switch.
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
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.
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
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…
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?
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
Denary Notes
• Number system rules
1.
2.
3.
4.
5.
6.
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
Thousands
(x1000)
Hundreds
(x100)
Tens (x10)
Units (x1)
4
3
2
4
= (4x1000) + (3x100) + (2x10) + (4x1) = 4324
Binary
• The binary number system works in the
same way
• The ONLY difference is we only have 2
digits – 0 and 1
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
Copy the example…
128
64
32
16
8
4
2
1
1
0
0
0
1
0
1
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…
• 128+8+2+1 = 139
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
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
June 2015, Q8 (b)