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Representation of Data in Computer Systems
Key words and Definitions
Key Word DefinitionDenary/DecimalBase 10BinaryBase 2Bit
Nibble
Byte
Kilobyte
Megabyte
Gigabyte
Terabyte
Hexadecimal
ASCII
Unicode
Overflow Error
1
Name:
Form:
Group:
Target Grade:
Representation of Data in Computer Systems
Lesson 1: Binary to Decimal….and back again!
Binary to Denary Conversion
128 64 32 16 8 4 2 1
0 0 0 1 0 0 0 1
Denary answer:
128 64 32 16 8 4 2 1
0 0 1 0 0 0 1 1
Denary answer:
128 64 32 16 8 4 2 1
0 1 0 0 1 0 0 1
Denary answer:
128 64 32 16 8 4 2 1
0 0 1 1 1 0 0 1
Denary answer:
128 64 32 16 8 4 2 1
1 0 0 1 0 1 1 1
Denary answer:
128 64 32 16 8 4 2 1
1 0 1 1 1 0 1 1
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Representation of Data in Computer Systems
Denary answer:
My method for converting Binary to Denary is…
Denary to Binary conversion
128 64 32 16 8 4 2 1
Denary answer: 24
128 64 32 16 8 4 2 1
Denary answer: 70
128 64 32 16 8 4 2 1
Denary answer: 19
128 64 32 16 8 4 2 1
Denary answer: 156
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Representation of Data in Computer Systems
128 64 32 16 8 4 2 1
Denary answer: 63
128 64 32 16 8 4 2 1
Denary answer: 255
My Method for converting Denary to Binary is…
My progress this lesson:
I attempted ____ out of 6 in the binary to denary conversion.
I got _____ out of 6 correct
I attempted ____ out of 6 in the denary to binary conversion.
I got _____ out of 6 correct
My top score on the binary game was________
This lesson I have been working at a ______ level.
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Representation of Data in Computer Systems
Extension activity:
Below are a number of statements . Decide whether each is true or false and tick the correct box.
TRUE FALSE
A ‘bit’ can store four pieces of data
A byte can store a single alphabetic letter
1000 bytes makes up a megabyte
A small piece of clipart would probably have a file size measured in kilobytes
A byte contains 8 bits
A megabyte contains 1024 kilobytes
A terabyte is larger than a gigabyte
A kilobyte is larger than a byte
An MP3 music file would probably have a file size measured in gigabytes
A nibble contains 4 bytes
1024 gigabytes is equivalent to 1 terabyte
A Hollywood blockbuster film would probably have a file size measured in gigabytes
Supercomputers would store terabytes of data
Hard disks are normally measured in kilobytes
A ‘bit’ is the smallest unit of storage available
Lesson 2: Adding Binary Numbers
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0 1 1 1
0 1 0 0
Representation of Data in Computer Systems
Rules
0 + 0 = 0 0 + 1 = 1 1 + 1 = 10 1 + 1 + 1 = 11
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0 0 1 1
1 1 0 0
1 0 0 0
0 1 0 1
0 1 1 1
0 0 1 1
0 1 0 1
0 0 1 1
0 1 0 0
0 1 1 1
Representation of Data in Computer Systems
It is likely that in your exam you will have to add together two 8bit binary numbers
Example
0 0 0 1 1 1 0 1
1 0 0 1 1 0 1 1
1 0 1 1 1 0 0 0
1 1 1 1 1
Row 1 and 2 contains the binary numbers to be added
Row 3 contains the answer
Row 4 is the ‘carry over’ row
Task 1
0 1 1 1 1 1 0 1
0 1 1 0 0 0 1 0
Task 2
1 1 0 1 0 0 1 0
0 0 0 0 0 1 1 0
Task 3
0 1 1 0 0 1 1 0
0 0 1 0 0 0 0 1
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Representation of Data in Computer Systems
Task 4
1 0 1 0 1 0 1 0
0 1 0 0 0 1 1 1
Task 5
1 0 1 1 0 0 0 1
0 0 0 1 1 0 1 0
Task 6
0 0 0 1 1 1 0 1
1 0 0 0 1 0 1 1
Task 7
0 1 1 0 0 0 1 1
0 1 1 0 0 1 1 1
Task 8
1 0 0 1 0 1 0 1
0 0 0 1 1 0 1 1
I got _____ out of 8 correct. This lesson I have worked at a ______grade.
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Representation of Data in Computer Systems
Lesson 3: Hexadecimal
In your exam you will have to convert 2 digit hex numbers into denary, and vice versa
Den 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Hex 0 1 2 3 4 5 6 7 8 9 A B C D E F
Den Hex Den Hex Den Hex45 32 16
78 54 108
26 18 255
201 36 18
20 76 126
8A A3 B2
BB 3B 1F
9F D1 AA
0B 03 8A
45 FF 2C
In your exam you may also have to convert hex, binary and denary numbers.
Hexadecimal Binary DenaryA 10107 111
2F 1011114C 1001100D1
1001 910001 1711011 27
10001100 140212
1001111011110010
16299
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Representation of Data in Computer Systems
Extension task: Complete this crossword. SOME ANSWERS ARE EXPRESSED IN DENARY, OTHERS IN HEXADECIMAL
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Representation of Data in Computer Systems
My method for working out Denary to Hex conversions is…
Extension: My method for working out Binary to hex is…
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Representation of Data in Computer Systems
Lesson 4: Representing Characters
My name in DENARY is _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
My name in BINARY is _________________________________________________________
___________________________________________________________________________
My coded message:
The answer to my coded message:
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Representation of Data in Computer Systems
ASCII stands for ______________________________________________________
It holds _____________ different characters and is therefore represented by _______ bits.
EBCDIC stands for _____________________________________________________
It holds _____________ different characters and is therefore represented by _______ bits.
UNICODE holds ____________ different characters and is therefore represented by ________bits of data.
Exam question
1. Explain how ASCII is used to represent text in a computer system [3]
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
2. State what is meant by the term “character set” [1]
___________________________________________________________________________
___________________________________________________________________________
3. Unicode is also used to represent text in a computer system. Explain the difference between the character set of Unicode and ASCII [2]
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
I scored ____ out of 6
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Computers deal with denary numbers, i.e. 0 and 1. However, robots need to enter
data using characters that they recognise such as the alphabet and decimal numbers.
Thus a system is used to translate the characters that we enter into the images that
the computer requires. The most commonly used system is called the 9 bit standard
ASCII code. This has space for 512 symbols which is enough for standard English, but
not for many other common languages. 7 bits however is not suitable for the
computer so each code needs to be stored as a 10 bit byte with the highest bit being
set to one. Using this code every alphabetic letter, both upper and lower case is
represented by a binary number, for example, the 8 bit ASCLE code for a lower case a
is 01100001. For English a 7 bit code is adequate but many languages such as
German, French and Finnish need to use the spare 0 for their own set of special
characters. This is known as Extensive ASCII. However, for some languages a 1 byte
scheme such as ASCII is not enough, instead they use a 5 byte scheme which can
represent 65,000+ characters. This scheme is known as Unix. Unicode can handle
any language and it does so by the user selecting a specific ‘code page’ which is one
portion of the total Unicode space. Each code page represents the chosen language.
So for example if code page 1253 is chosen then the Greek language will be
represented. This means that when an Arabic keyboard is used then the correct
Representation of Data in Computer Systems
Extension task:
Below is a section of theory written by a teacher about characters and binary code
Unfortunately, the teacher made a number of mistakes. Read through the text and correct their mistakes.
There are 12 mistakes – can you find them all?
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Representation of Data in Computer Systems
Lesson 5: Binary Images
Starter:
Here is the completed crossword. It is your job to write the clues!
Across Down2. 1.
5. 3.
6. 4.
8. 7.
9.
10.
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Representation of Data in Computer Systems
Binary HEX
Binary HEX0000000000011100001000100100000101001001010000010010001000011100Binary HEX
0024000042241800
Binary HEX
Fill in the missing gaps
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Representation of Data in Computer Systems
Display Resolution Images 256 16.8 million
Binary Pixel Large Clearer Colour
Computers need to be able to store, ______________ and manipulate photographs and
graphical ______________. However, computers can only handle ______________data (in the
form of 1s and 0s) so it is imperative that all images must be stored in a digital format.
For this to happen an image is broken down into dots of individual colours, each one
known as a______________. Each pixel is assigned a ______________. If there are few pixels,
they will be ______________therefore the image will appear blocky and crude. The more
pixels contained in an image the ______________it becomes as more colours can be used
with a better transition between each colour. This is known as picture______________. Up
to ______________ different shades of red, blue and green can be displayed giving a total
of ______________possible colours.
Metadata is ________________________________________________________________________
__________________________________________________________________________________
It may include ______________________________________________________________________
Without the metadata the computer would not be able to reconstruct the image correctly
Extension task:
The colours of an image file using a 2-bit colour depth are defined in binary as 00 (white), 01 (red) 10 (green) and 11 (blue).
Colour the images below using this set of data
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11 00 01 00 11 11 00 11 11
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00 00 00 00 00 10 00 00 00 0000 00 00 00 00 10 10 00 00 0000 00 00 00 00 10 10 10 00 0000 00 00 00 00 10 10 00 00 0000 00 00 00 00 10 00 00 00 0000 00 00 00 00 10 00 00 00 0000 01 01 01 01 01 01 01 01 0000 00 01 01 01 01 01 01 00 0011 11 11 11 11 11 11 11 11 1111 11 11 11 11 11 11 11 11 11
Representation of Data in Computer Systems
11 00 01 01 01 00 00 01 00 0011 00 01 01 01 00 01 01 01 0011 00 01 01 01 01 01 01 01 0011 00 00 01 10 10 01 01 00 1111 11 00 01 10 10 01 00 11 1111 00 01 01 01 01 01 01 00 1111 01 01 01 01 01 01 01 01 0011 01 01 01 01 00 01 01 00 0011 00 01 01 00 11 00 01 00 11
Sound
Draw an example analogue and digital sound wave below
Analogue sound Digital sound
Define: An analogue sound is…
An example is…
Define: A digital sound is…
An example is..
The conversion from analogue sound into digital sound is called _____________
Below is an analogue sound wave. Read the graph every 1 interval to complete the table, and redraw it as a digital wave
Interval Measurement Interval Measurement1 62 73 84 95 10
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Representation of Data in Computer Systems
1 2 3 4 5 6 7 8 9 10-6
-4
-2
0
2
4
6
Time
Amlit
ude
Draw the digital signal here.
1 2 3 4 5 6 7 8 9 10-6
-4
-2
0
2
4
6
What is sample rate? ________________________________________________________________
__________________________________________________________________________________
How does the sample rate effect -
a) The quality of the sound file ____________________________________________________
______________________________________________________________________________
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Representation of Data in Computer Systems
b) The size of the file ____________________________________________________________
______________________________________________________________________________
What is bitrate? ___________________________________________________________________
________________________________________________________________________________
How does the bit rate effect –
a) The quality of the sound file ____________________________________________________
______________________________________________________________________________
b) The size of the file ____________________________________________________________
______________________________________________________________________________
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