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