Session Objectives#8
Justify why 8 bits don’t always make a byte!
explain the use of code to represent a character set (ASCII, EBCDIC and UNICODE)
express numbers in binary, octal and hexadecimal
Create a colour scheme using hex codes in html
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Number Systems
Starter Number Puzzle:
Find a 10-digit number where the first digit is how many zeros
in the number, the second digit is how many 1s in the number
etc. until the tenth digit, which is how many 9s in the number.
6210001000
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Number Systems
We already know that computers like to use 0 and 1 to count due
to the fact an electrical charge = 1 and no charge = 0.
This forms the base 2 or binary system. Instead of base 10, the
decimal system (denary) where you have Units, Tens, Hundreds,
Thousands etc, we have use multiples of 2:
128
0
64
1
32
0
16
0
8
1
4
0
2
1
1
1
Using a column diagram like this it is easy to turn denary into
binary. In this example, 75 is 1 lot 64, 1 lot 8, 1 lot of 2 and
1 lot 1.
So the denary number 75 expressed in 8 bit binary is
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01001011
Number Systems
TASK
Now express the following denary numbers as 8 bit binary numbers
and show your working.
a) 13
b) 56
c) 143
a) 00001101
b) 00111000
c) 10001111
EXTENSION:
Create your own 8 bit binary number and convert back to denary.
What is the largest denary number you can create in 8 bit
binary?
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Position Valued Representation
Position valued representation (PVR) is a system to represent
any value with a limited number of symbols. Take the decimal
system for example, we can represent any value that we need with
only 10 symbols (0....9).
Examples:100=1......Any number to the 0th power is 1
101=10............Any number to the 1th power is that number
102=100..........10*10
103=1000........10*10*10
104=10000......10*10*10*10
With the PVR system there are a number of rules
• The number of digits needed for the system is equal to the
base. (i.e. decimal (base 10) has 10 digits)
• The value of the largest digit is one less than the base.
• The first position to the left of the "base point" is worth 1.
(i.e. the decimal point is the base point of the decimal
system.)
• Every other position is worth base times the position value to
its immediate right.
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Octal
If binary is a base 2 number system, what would the base be of
an octal system?
8
In the octal system the column headings are now changed to:
and denary 75 is:
512
0
64
1
8 1
1 3
These larger base systems are needed for computing larger
numbers.
TASK: Convert the following denary numbers into octal and
remember the PVR rule: The value of the largest digit is one less than the base
a) 263
b) 482
c) 4095
0407
0742
7777
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Hexadecimal
Some information is stored in computers as numbers in base 16.
This is called hexadecimal (or hex for short). The principles
are the same except that the digits above 9 are represented by
capital letters A – F.
Binary
Hex
Decimal
Binary
Hex
Decimal
0000
0
0
1000
8
8
0001
1
1
1001
9
9
0010
2
2
1010
A
10
0011
3
3
1011
B
11
0100
4
4
1100
C
12
0101
5
5
1101
D
13
0110
6
6
1110
E
14
0111
7
7
1111
F
15
TASK: As you can see decimal 10 is A in Hex, so what would the
decimal value of hex 10 be?? Discuss...
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Hexadecimal
The column headings in hex (base 16) would now be:
256
16
1
And 75 denary will be: 4 lots of 16 and 11 ones or
4B.
TASK: What will the hex value of 128 be?
DISCUSSION ACTIVITY:
What is the connection between binary and octal, and between
binary and hexadecimal? Try calculating the answers to some more
denary number conversions in pairs of binary and octal and then
binary and hex. Prepare to discuss anything that you notice.
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Why use different systems?
This is an obvious question since we know computers like the use
of binary. Well, the reason is down to the application or use of
the computer.
For example, the common QWERTY keyboard is often used for typing
text and numbers etc and to enable computers to understand each
other a common standard was agreed in the 1960s and the ASCII
character set was formed (American Standard Code for Information
Interchange). This accounts for all letters + capitals + digits
+ punctuation etc, 127 characters in total are represented by
ASCII codes, within the capability of 8 bits (one byte, used to
represent a single character).
TASK: Investigate why do we need 8 bits per character, why not
7?
ASCII is not always relevant for some applications.
HWK – Research the meaning and application of the EBCDIC and
UNICODE character sets.
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The Application of HEX
Why does the 256 (in hex, base 16 to power 2) sound familiar?
Each pixel you see in your display is either Red, Green or
Blue (RGB) The light intensity of each is changed from 0 to
255 (a byte for each) to determine the colours you see.
Colour codes are represented in Hex in a set of 6 digits, 2
for R, 2 for G and 2 for B.
Follow the link to see codes for the various colours and
then attempt the quiz
http://www.nameacolor.com/RGB.HTML
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HTML
<HTML>
<BODY BGCOLOR="#FFFF00">
<P>This is my very first web page!</P>
</BODY>
</HTML>
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