Transcript Higher Computing

Intermediate 2 Computing
Computer Systems
How we count in decimal
• Remember how we count.
Decimal
Thousands Hundreds Tens
Units
104
Number of
10000
combinations
103
102
101
1000
100
10
• Each column can have 10 different values in it. Making
Decimal a Base 10 number system.
• Binary can only have 2 different values.
• Binary is a Base 2 number system.
Binary representation of positive
numbers (Cont.)
Binary
27
26
No. of
Combinations
128
64 32 16
232
230
220
25
24
216
23 22 21 20
8 4
2
1
210
29
28
4294967296 1073741824 1048576 65536 1024 512 256
• Using a table like this you can work out the
values of binary numbers.
Binary ranges
No of
Digits
Max Number and Range
Calculation
8
256 numbers, from 0 to
255
28= 256
16
65536 numbers, from 0
to 65535
216 = 65 536
24
16 777 216 numbers,
from 0 to 16 777 215
224 = 16 777 216
32
4 294 967 296 numbers, 232 = 4 294 967
from 0 to 4 294 967 295
296
Conversion from binary to
decimal
• E.g. an 8- bit binary number 10010011
27 26 25 24 23 22 21 20
1 0 0 1 0 0 1 1
= 27 + 2 4 +
= 128 + 16 +
= 147
21+20
2+1
Conversion from decimal to
binary
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Given the binary number 150.
Divide by 2 = 75 r 0
Divide by 2 = 37 r 1
Divide by 2 = 18 r 1
Divide by 2 = 9 r 0
Divide by 2 = 4 r 1
Divide by 2 = 2 r 0
Divide by 2 = 1 r 0
Divide by 2 = 0 r 1
The binary value is = 10010110
Conversion to and from a
byte, Kilobyte, Megabyte
• There are 1024 bytes in a kilobyte and
1024 kilobytes in a megabyte so to turn
bytes into megabytes you divide once by
1024 to turn them into kilobytes and again
by 1024 to turn them into megabytes.
• 1 048 576 bytes = 1 048 576/1024 = 1024
kilobytes
• 1024 kilobytes = 1024/1024 = 1 Megabyte
Conversion between bytes,
Kilobytes, Megabytes, Gigabytes
• There are 1024 megabytes in a gigabyte so
we calculate the number of megabytes and
then dive by 1024 to turn them into
gigabytes.
• 4 294 967 296 bytes = 4 294 967 296/1024
= 4 194 304 kilobytes
• 4 194 304 kilobytes = 4 194 304/1024 =
4096 megabytes
• 4096 megabytes = 4096/4 = 4 gigabytes
Conversion between Gigabytes
and Terabyte.
• There are 1024 gigabytes in a terabyte so
we calculate the number of gigabytes and
then dive by 1024 to turn them into
terabytes.
• 512 gigabytes = 512/1024 = 0.5 terabytes
Floating point numbers
• First of all look at a real number in decimal.
• 15.25 = .1525 x 100 = .1525 x 102
• Any number can be written as:
Mantissa x baseExponent
• The above example can be written as:
• 1111.01 = .111101 x 24 = .111101 x 2100
=15
. =0.25
• Decimal numbers are base 10.
• Binary numbers are base 2. This is always the case
so the computer doesn’t need to store this.
Floating point numbers (Cont.)
• 1111.01 = .111101 x 24 = .111101 x 2100
• If the decimal point is always in the same
position all that needs stored is the
mantissa and the exponent.
• This leaves us with
• 111101 100
Exponent
mantissa
Precision and range of floating
point numbers
• Precision
– The more bits set aside for the mantissa, the
more precise the number will be.
– If there are not enough bits then the system
has to round down loosing precision.
Precision and range of floating
point numbers
• Range
– Increasing the number of bits used to represent
the exponent increases the range of numbers
that can be represented.
ASCII
• American Standard Code for Information
Interchange is a method of representing all the
characters in memory.
• Each character is given it’s own ASCII code.
• ASCII is a 7-bit code with the 8th bit being used
as a parity bit.
• The 7 bit provide 128 possible values for the text.
• This gives us 96 characters and 32 control codes.
• Many systems use extended ASCII code which is
an 8-bit code giving a range of 256 characters
The bitmap method of graphics
representation
• Bitmap representation of graphics means that
each pixel in a graphic is represented by a series
of bits / bytes. Bitmaps are typically used for
creating realistic images, e.g. photographs, the
output of paint packages.
• In the simplest example each pixel is represented
by 1 bit.
=
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
=
1110111 00000000
1110111 1110111
1110111 1110111
1110111 1110111
Bit depth
• The more bits assigned to represent each
pixel the greater the range of colours or
shades of gray that can be represented.
• This is known as the colour bit depth.
• Here the bit depth is 2 giving 22= 4 colours
01 01 01 00 01 01 01 01
00 00 00 00 00 00 00 00
=
10 10 10 00
11 11 11 11
10 10 10 00
11 11 11 11
10 10 10 00
11 11 11 11
10 10 10 00
11 11 11 11
10 10 10 00
11 11 11 11
10 10 10 00
11 11 11 11
=
01010100 01010101
00000000 00000000
10101000 11111111
10101000 11111111
10101000 11111111
10101000 11111111
10101000 11111111
10101000 11111111
Bit depth (Cont.)
Number of bits per pixel
1
2
Colours, or shades of grey,
represented
2 (black and white)
4
8
16
256
65 536
24
16 777 216 (true colour)
Relationship between bit depth
and file size
• Let's look at the file sizes of a tiny 1 inch square
graphic.
Resolution
(pixels per
square inch)
Pixels per 1 Number of bits
inch square representing
graphic
each pixel
File size
in bytes
File size in
megabytes
600 x 600
360000
8 bits(1 byte)
360000
0·343
600 x 600
360000
16 bits(2 bytes)
720 000
0·687
600 x 600
360000
24 bits(3 bytes)
1 080 000 1·030
• The more bits that are used to represent a pixel
the more colours you get but the greater the file
size.
Relationship between bit depth and
file size.
• If the graphic was larger, say 6 inches square
then the table looks like this:
Resolution
(pixels per
square inch)
Pixels per 6 Number of bits
inch square representing
graphic
each pixel
File size in
bytes
File size in
megabytes
600 x 600
12960000
8 bits(1 byte)
12960000
12·36
600 x 600
12960000
16 bits(2 bytes)
25920000
24·72
600 x 600
12960000
24 bits(3 bytes)
38 800 000 37·8
Advantages of bit-mapped
graphics
• They allow the user to edit at pixel level.
• Storing a bit-mapped graphic will take the
same amount of storage space no matter
how complex you make the graphic.
Disadvantages of bit-mapped
graphics
• They demand lots of storage, particularly
when lots of colours are used.
• They are resolution dependent.This means
the resolution of the graphic, the number of
pixels per inch, is set when the bitmap is
produced. If you reduce the resolution, the
system reduces the size of the pixel grid and
eliminates pixels. This reduces the quality of
the image.
• You cannot isolate an individual object in a
graphic and edit it.
Why is compression needed?
• You can see from the table that sizes for bitmapped graphics can be very large.
• This means that they demand lots of storage
space, and can take quite a time to transmit
across a network.
• Compressing the files means that less space
is required for storage and transmission
times are less.