Representation of Data in Computer Systems
Name: Adriano Fernades
Key words and DefinitionsKey WordDefinition
Denary/DecimalBase 10The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations
BinaryBase 2A negative base may be used to construct a non-standard positional numeral system. Like other place-value systems, each position holds multiples of the appropriate power of the system's base.
BitShort forbinary digit, the smallest unit of information on a machine.
NibbleIn computer terms a nibble = 4 bits = 1/2 byte.
ByteByte = 8 bits
Kilobyte1KB = 1024bytes
Megabyte1MB=1024KB
Gigabyte1KB=1024MB
Terabyte1TB=1024GB
Hexadecimal
oforpertainingtoanumberingsystemthatuses16astheradix,employingthenumerals0through9andrepresentingdigitsgreaterthan9withthelettersAthroughF.
ASCIIA standard for assigning numerical values to the set of letters in the Roman alphabet and typographic characters.
Unicode
Astandardfor representingcharactersasintegers. UnlikeASCII, which uses 7bitsfor each character, Unicode uses 16 bits, which means that it can represent more than 65,000 unique characters.
Overflow Error
The condition in which the numerical result of an operation exceeds the capacity of the register.
Lesson 1: Binary to Decimal.and back againBinary to Denary Conversion1286432168421
00010001
Denary answer: 17
1286432168421
00100011
Denary answer: 35
1286432168421
01001001
Denary answer: 73
1286432168421
00111001
Denary answer: 57
1286432168421
10010111
Denary answer: 151
1286432168421
10111011
Denary answer: 187
My method for converting Binary to Denary isCreate a table whose leftmost column is the greatest power of 2 less than the number you want to convert. If the number is between 64 and 127, the leftmost column will be 64. If the number is between 128 and 255, the leftmost column will be 128. Each column in the table is a power of 2. The rightmost column is 20 (= 1), the next one to the left is 21 (= 2), the next is 22 (= 4), etc. Instead of thinking about powers of 2, you can just think about doubling each number to get the value for the next column to the left.
Denary to Binary conversion1286432168421
00011000
Denary answer: 24
1286432168421
01000110
Denary answer: 70
1286432168421
00010011
Denary answer: 19
1286432168421
10011100
Denary answer: 156
1286432168421
00111111
Denary answer: 63
1286432168421
11111111
Denary answer: 255
My Method for converting Denary to Binary isFind its quotient then dividing the number by two, taking away one if the number is odd and to continue to do this until the number is 0
My progress this lesson:I attempted ___6_ out of 6 in the binary to denary conversion. I got __6___ out of 6 correctI attempted __6__ out of 6 in the denary to binary conversion. I got __6___ out of 6 correctMy top score on the binary game was___6_____
This lesson I have been working at a ______ level.
Extension activity:Below are a number of statements. Decide whether each is true or false and tick the correct box.TRUEFALSE
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
0111
0100
Lesson 2: Adding Binary Numbers
0011
1100
1000
0101
0111
0011
0101
0011
0100
0111
Rules0 + 0 = 00 + 1 = 11 + 1 = 101 + 1 + 1 = 11
It is likely that in your exam you will have to add together two 8bit binary numbers
Example00011101
10011011
10111000
11111
Row 1 and 2 contains the binary numbers to be addedRow 3 contains the answerRow 4 is the carry over rowTask 101111101
01100010
Task 211010010
00000110
Task 301100110
00100001
Task 410101010
01000111
Task 510110001
00011010
Task 600011101
10001011
Task 701100011
01100111
Task 810010101
00011011
I got _____ out of 8 correct. This lesson I have worked at a ______grade. Lesson 3: HexadecimalIn your exam you will have to convert 2 digit hex numbers into denary, and vice versaDen0123456789101112131415
Hex0123456789ABCDEF
DenHexDenHexDenHex
453216
7854108
2618255
2013618
2076126
8AA3B2
BB3B1F
9FD1AA
0B038A
45FF2C
In your exam you may also have to convert hex, binary and denary numbers.HexadecimalBinaryDenary
A1010
7111
2F101111
4C1001100
D1
10019
1000117
1101127
10001100140
212
10011110
11110010
162
99
Extension task: Complete this crossword. SOME ANSWERS ARE EXPRESSED IN DENARY, OTHERS IN HEXADECIMAL
My method for working out Denary to Hex conversions is
Extension: My method for working out Binary to hex is
Lesson 4: Representing Characters
My name in DENARY is _____ _____ _____ _____ _____ _____ _____ _____ _____ _____My name in BINARY is ____________________________________________________________________________________________________________________________________My coded message:
The answer to my coded message:
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 question1. 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 6Extension task:Below is a section of theory written by a teacher about characters and binary codeUnfortunately, the teacher made a number of mistakes. Read through the text and correct their mistakes. There are 12 mistakes can you find them all?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 character will appear on the screen when a certain key on the keyboard is pressed.
Lesson 5: Binary ImagesStarter:Here is the completed crossword. It is your job to write the clues!
AcrossDown2.
1.
5.
3.
6.
4.
8.
7.
9.
10.
BinaryHEX
BinaryHEX
00000000
00011100
00100010
01000001
01001001
01000001
00100010
00011100
BinaryHEX
00
24
00
00
42
24
18
00
BinaryHEX
Fill in the missing gapsDisplayResolutionImages25616.8 million
BinaryPixelLargeClearerColour
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 correctlyExtension 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 data00000000001000000000
00000000001010000000
00000000001010100000
00000000001010000000
00000000001000000000
00000000001000000000
00010101010101010100
00000101010101010000
11111111111111111111
11111111111111111111
11110001001111001111
11000101010000010000
11000101010001010100
11000101010101010100
11000001101001010011
11110001101001001111
11000101010101010011
11010101010101010100
11010101010001010000
11000101001100010011
SoundDraw an example analogue and digital sound wave belowAnalogue soundDigital sound
Define: An analogue sound is
An example isDefine: 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 waveIntervalMeasurementIntervalMeasurement
16
27
38
49
510
Draw the digital signal here.
What is sample rate? __________________________________________________________________________________________________________________________________________________How does the sample rate effect - a) The quality of the sound file __________________________________________________________________________________________________________________________________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 __________________________________________________________________________________________________________________________________________6