1. Intermediate 2 Computing
Computer Systems

2. How we count in decimal Remember how we count. Decimal Thousands
Hundreds
Tens
Units
104
103
102
101
Number of combinations
10000
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.

3. Binary representation of positive numbers (Cont.)27 26 25 24 23 22 21 20
No. of Combinations
128 64 32 16 8 4 2 1
232
230
220
216
210 29 28
65536
1024
512
256
Using a table like this you can work out the values of binary numbers.

4. Binary ranges 8 256 numbers, from 0 to 255 28= 256 16
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 = 24
numbers, from 0 to
224 = 32
numbers, from 0 to
232 =

5. Conversion from binary to decimal
E.g. an 8- bit binary number 27 26 25 24 23 22 21 20 1 = =
= 147

6. Conversion from decimal to binary
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 = r 0
Divide by 2 = r 1
Divide by 2 = r 0
Divide by 2 = r 0
Divide by 2 = r 1
The binary value is =

7. 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.
bytes = /1024 = 1024 kilobytes
1024 kilobytes = 1024/1024 = 1 Megabyte

8. 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.
bytes = /1024 = kilobytes
kilobytes = /1024 = 4096 megabytes
4096 megabytes = 4096/4 = 4 gigabytes

9. 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

10. Floating point numbers
First of all look at a real number in decimal.
15.25 = x 100 = x 102
Any number can be written as:
Mantissa x baseExponent
The above example can be written as:
= x 24 = 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.

11. Floating point numbers (Cont.)
= x 24 = 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
mantissa
Exponent

12. Precision and range of floating point numbers
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.

13. Precision and range of floating point numbers
Increasing the number of bits used to represent the exponent increases the range of numbers that can be represented.

14. 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

15. 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. = =

16. 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 = =

17. Bit depth (Cont.) Number of bits per pixel
Colours, or shades of grey, represented 1
2 (black and white) 2 4 8
256 16
65 536 24
(true colour)

18. 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 inch square graphic
Number of bits representing each pixel
File size in bytes
File size in megabytes
600 x 600
360000
8 bits(1 byte)
0·343
16 bits(2 bytes)
0·687
24 bits(3 bytes)
1·030
The more bits that are used to represent a pixel the more colours you get but the greater the file size.

19. 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 inch square graphic
Number of bits representing each pixel
File size in bytes
File size in megabytes
600 x 600
8 bits(1 byte)
12·36
16 bits(2 bytes)
24·72
24 bits(3 bytes)
37·8

20. 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.

21. 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.

22. Why is compression needed?
You can see from the table that sizes for bit-mapped 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.