1. Data Representation

2. The binary system
Processing and storage devices have two states –on or off
1 = “on” and 0 = “off”
Binary number = 1 or 0
Inside the computer:-
0 volts represents 0
1-5 volts represents 1

3. Advantages and Disadvantages of binary
Simple rules for arithmetic
Slight drop in voltage still works as any voltage greater than 0 counts as a 1
Storage devices can represent 2 states e.g. CD-ROM
Lots of digits needed to represent numbers

4. Bits Bit = Binary digit Column headings for binary are:-
= 43

5. Bytes 8 bits = 1 byte Largest number shown by 1 byte?
= 255
Smallest number is = 0
How many different numbers?
256 (which is 28)

6. More bytes 1 Kilobyte = 1024 bytes 1 Megabyte = 1024 Kb
1 Gigabyte = 1024 Mb
1 Terabyte = 1024 Gb
Typical main memory = 2Gb
Typical hard disk = 320 Gb

7. Converting between units
Bits to bytes ?
÷ 8
Bytes to bits ?
x 8
Bytes to Kb ?
÷ 1024
Kb to bytes ?
x 1024

8. Place values (column headings)
Leftmost bit = most significant bit
Rightmost bit = least significant bit

9. See the table on Pages 4 & 5 28 = 256 210 = 1024 220 = 1 Mb
28 = 256
210 = 1024
220 = 1 Mb
224 = no of colours in “true” colour
230 = 1 Gb
240 = 1 Tb

10. Calculating the largest integer & range
No of bits
Max Number in binary
Max number in decimal
Easy calculation
Range 3
111 7
23 - 1
0 to 7
8 numbers 32
4,294,967,295
0 to 4,294,967,295
4,294,967,296 numbers

11. Changing between binary & decimal
Write down place values
Binary to decimal:-
where there is a 1 add the place value
Decimal to binary:-:-
Write a 1 in each place that you want and add them up to make your number

12. Example Convert 00110101 to decimal 128 64 32 16 8 4 2 1
In decimal = 53
Convert 67 to binary
In binary =

13. For you to do Page 20 Questions 1 and 2 1.a) 1011 b.) 1001 1111
c.)
d.)

14. Answers Q1
a) 1011 = 11
b) = 159
c) = 170
d) = 254 Q2
a) 122 =
b) 193 =
c) 256 =
d) 1023 =

15. Representing integers
Size of positive integers depends on the number of bytes available in memory to store it
E.g. using 16 bits to
0 to 65,535 (65,536 different numbers)
Negative integers –
Signed bit notation
Two’s complement

16. Signed bit notation Use leftmost bit to indicate sign + or –
E.g. using 16 bits only 15 bits are left for the number
is –(215-1) is
to 32767
Rule:- –(2n-1-1) to 2n-1-1

17. Disadvantage of signed bit notation
2 zero’s - aaaargh!
e.g is –ve zero
is +ve zero
It’s just mathematically WRONG!

18. Two’s complement
Represents +ve and -ve integers and doesn’t have 2 zeros
Write -7 :-
+7 using 8 bits
Change 1’s and 0’s
Add

19. Advantages of two’s complement
1 zero
Arithmetic is correct
Leftmost bit indicates the sign (0 is +ve and 1 is –ve)
Same procedure to read a –ve number i.e.
change the 1’sand 0’s then add 1

20. For you to do – small class
Page 20 Question 3

21. Representing real numbers
Decimal Fractions:-
1/10 1/100 1/ /10,000 1/100,000 …. ….
Binary Fractions:-
½ ¼ / / / / /128
Questions only have combinations of these fractions – don’t panic, Megan!

22. For you to do
Page 20 Question 4

23. Floating point representation
From Maths we know that:-
= x 102
M x Base e
Mantissa x Base Exponent
In binary :-
= = x 2 101
5 in decimal is 101 in binary

24. Floating point representation
Store the mantissa & exponent only:-
x 2 101
Mantissa =
Exponent = 101

25. For you to do
Page 20 Question 5,6

26. Text - ASCII American Standard Code for Information Interchange
Character set = all the characters which a computer can store & process
8 bits available in ASCII
Using 7 bits allows 27 characters
28 (extended ASCII) allows 256 characters

27. Text - Unicode Universal Character Set
Represents characters from writing schemes of all major languages
16 bits available
216 allows 65,536 characters

28. For you to do Page 20 Question 11, 12, 13, 14
11. a) What is a character?
B)What is a character set
C)What is a control character?
12. a) What does ASCII stand for?
B) How many characters can extended ASCII represent?
13) a)What is Unicode?
B) State one advantage of Unicode over ASCII?
C) State one disadvantage of Unicode over Ascii and explain.

29. Graphics resolution
Monitors – no. of pixels across x no. of pixels down
SVGA uses 800 x 600
XGA uses 1024 x 768
Which resolution is lower?
Which requires more storage space?
Digital cameras – total no. of pixels
E.g. 7 Megapixels

30. Bit mapped graphics – Paint packages
Number of bits = bits across x bits down
= 8 x 8 = 64
Changes the colour of pixels
Stores information about the colour of every pixel

31. Vector graphics – Draw packages
Draw objects on the screen
Descriptions of objects stored as a file – called object attributes
See p13

32. Differences between bit mapped and vector graphics - 1
When overlapping shapes are separated they behave differently

33. Differences between bit mapped and vector graphics - 2
Bit mapped files are larger – as the colour of every pixel is stored instead of descriptions of shapes

34. Differences between bit mapped and vector graphics - 3
Bit mapped graphic’s resolution is fixed when it is created – a printer with a higher resolution will not improve the image
Vector graphics can be printed at a higher resolution by a great printer – called resolution independence

35. Page description languages
Some printers have a processor and high level language interpreter to understand the page set up and objects
E.g.
moveto
lineto
lineto
closepath fill
showpage

36. Differences between bit mapped and vector graphics - 4
Bit mapped graphics allow you to zoom in and change individual pixels
Vector graphics can be enlarged to look at but changes involve editing the object attributes

37. 15,16, 18, 19, 20 15) Why are bit-mapped graphics so called?
16) How are vector graphics stored?
18) a) a) With respect to graphics, what is:
A) resolution
B) resolution independence
C) What type of graphics use resolution independence?
19) Which of the following are true of
a) bit-mapped b) vector graphics
Pixels can be edited
Resolution independence
Overlapping parts can be separated cleanly
File size is fixed regardless of complexity of image

38. Bit depth
Number of bits used to represent colours or shades of grey is known as the bit depth or colour depth.

39. Storage requirements (bit mapped)
Storage req’s = no of pixels x bit depth
Example 1 –
Graphic is 1 inch by 2 inches
Resolution is 90 dpi
256 colours
Pixels = 1 x 90 x 2 x 90 = 16200
Bit depth (no of bits for 256 colours) = 8 (28=256)
Storage req’s = x 8 = bits = bytes = Kb

40. storage requirements – example 2
A 4 page (10 inches x 8 inches)
Scanned at 300 dpi
65,536 colours
Pixels = 10 x 300 x 8 x 300 =
Bit depth = 16 (216= 65,536)
Storage req’s = x 16 = bits = bytes = Mb Kb

41. True colour
Bit depth = 24
i.e. 24 bits are used for each pixel to represent a range of 16,777,216 different colours
More colours in real life (analogue)
Real colours chopped into separate values (sampling)
Eyes can’t distinguish between 200 shades between black and white
8 bits per pixels are used (256 available)

42. True colour - continued
Colours are made by combining Red, Green and Blue
True colour uses 256 shades of red, 256 shades of green and 256 shades of blue

43. RGB Model
Red, green and blue - additive colours as they combine to create white
Mixing them creates most of the visible spectrum
Additive colours - used for lighting, video and monitors

44. True colour = 24 bit RGB colour
Each colour has 256 possibilities
Range from 0 to 255
See how pink is created

45. 17
A) What is true colour
B) How many bits are used to represent true colour
25) Which colours are represented by:
(0,255,0)
(0,0,255)
(0,0,0)
(255,255,255)

46. Lossless data compression
None of the original data is lost
1 method:-
Count the repeating pixels
More storage space saved when there are lots of pixels of the same colour beside each other

47. Lossy data compression
Sacrifices some of the data to reduce the file size
Uses:-
complex mathematical encoding
Losses info that we ignore
Saves more space than lossless compression
Not suitable for all file types e.g. program files

48. JPEG (Joint photographic experts group)
File type - compresses bit mapped files
Uses lossy compression
Some data is lost – detail may be lost
Images may acquire artefacts
Slow to compress large files
Repeatedly compressing and uncompressing may reduce quality
Common on flash cards in cameras
See page 19

49. 25, 27, 28, 30, 32