section 2 Data representation

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Units

binary digit (or bit) is unit of data storage, and will have a value of 0,0 or 1. 

Four bits called a nible

Data converted by binary as computer ony processed two inputs - on and off , or 0 and 1

NameNotationPower of 10Value kilobyte kB 10, cubed,103 1, comma, 000,1,000 bytes megabyte MB 10, to the power 6 ,106 1, comma, 000, comma, 000,1,000,000 bytes gigabyte GB 10, to the power 9 ,109 1, comma, 000, comma, 000, comma, 000,1,000,000,000 bytes terabyte TB 10, to the power 12 ,1012 1, comma, 000, comma, 000, comma, 000, comma, 000,1,000,000,000,000 bytes

1,

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binary numbers

Denary numbers = base 10

Binary numbers = base 2

place values are powers of two

e.g  128,64,32,16   8,4,21

number 66

0,1,0,0   0,0,1,0

64+2 = 66

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binary addition

  • 0+0=0
  • 0, plus, 1, equals, 1,0+1=1
  • 1, plus, 0, equals, 1,1+0=1
  • 1, plus, 1, equals, 0,1+1=0 and carry 1,1
  • 1, plus, 1, plus, 1, equals, 1+1+1=1 and carry 1,1

Overflow error - when extra bit adding eigth place value e.g  1+1+1 = 1,1 

one is carried to ninth place holder

Programme either ignore error so calculation made emits different outcome

or programme crashes

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Binary shifts

want to multiple - shift to left

want to divide - shift to right

left shift - left most bit discarded , rightmost bit replaced by a zero

e.g 0001,0001 =  17 shift 2 places left

0100,0100 = 68

shift two places = 2*2=4 the numebr times by 4  17*4=68

Right shift - right most bit discarded , leftmost bit replaced by zero

e.g 1100,1000 = 200

0001,1001

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hexadecimal

hexadecimal - base 16

made up of  16 characters . 0-9 and a-f. Each character corresponds to a nibble

0 - 0000 - denary 0

4- 0100 - denary 4

8- 1000 - denary 8

A- 1010 - denary 10

C - 1100 - denary 12

F- 1111 - denary 15

hexadecimal format two numbers - e.g AF

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why is hexadecimal used

hexadecimal used by people because

 - easier to read

fewer digits represent the same value

- less likely digit written incorrectly

Hexadecimal used in colours - graphic designers chose colour they want by typing in hexadecimal

most use RGB colour coordinator - requires 24 bits as 8*3 = 24 but it is easier to remember colour with  digits e.g FFA445

also used MAC address and memory dumps

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convert denary and binary to hexadecimal

convert binary to hexadecimal

step 1 - split binary into nibbles

2 - covert nibbles corresponding hexadecimal

e.g 1100, 0100

1100 - C ,  0100 - 4

C4

Convert denary to hexadecimal

1. covert denary into binary

2. convert binary to hexadecimal 

e.g number 67 - 0100 , 0011

0100 = 4    0011 = 3   -> HD = 43

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convert hexadecimal into binary and denary

convert into binary

1, split up each character

2. find corresponding nibble

e.g 4C   4 = 0100 C = 1100

0100 , 1100

covert into dinary

1. Convert into binary first , then convert into denary

5E    5 = 0101     E = 1110

0101 1100   -> 64+16+8+4 = 92

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characters

binary used to represent characters from different languages

know letter - use binary calculate storage space and size of text file required

each character unique bit-pattern .  Pattern used for each character becomes numeric character code.

ASCII - american standard code for imformation interchange - use 7 bits - allow 128 charcters represented. Character include letter , numbers , symbols.  Eigth byte is used to store each character in a set and used as a parity bit for checking errors during execution of data

Extended ASCII - eight bits , used to represent more characters. Extended set varies in different countries - not useful global communications

Unicode -  represents characters from all international langauges. examples UTF-16 and UTF-32 : 16 and 32 bits used per character . More bits allow more representation of symbols , arrows , signs. 

Calculate file size - characters * 8 = 3 characters * 8 = 24 bits =  3 bytes

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images

pixel - smallest element of bitmap image , only is one colour. All data is stored in 1s and 0s and each colour needs binary code assigned to it. 

Bitmap image - image made by grid of pixels

colour depth - how much bits required to code for one colour . Depends on how much colours . 2 colours - one bit. 4 coulours - two bits . 8 colours - 3 bits. you root the number of coulours by two and find indicies . eg 16 is 2^4. 

Image resolution - refers to how clear an image is . When you zoom in on an image , poor quality as pixels streched into larger blocks.  Resolutione measured how mang pixels per ince e.g 330ppi -  330 pixels per inch. Image resolution also measure in area , by width of pixels * heigt of pixels.

Image file size =  image resolution (width * heigth) * colour depth

e.g  4 * 6* 4 = 96 bits - 12 bytes

covert bited in KB or GB

Higher the colour depth - larger storage space required to save the image. 

Smaller file size allows image download more quickly and images in emails less time to transmit.

Meta data - additional data stored along with pixel data in file size.  Extra data

- Image data - width and height 

- file format

- date and time of creation

- file formats - PNG , JPEG

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sound

sampling - convert sound to analoque to digital

Analogie - sound waves : Digital - binary patterns

Computer takes measurements of analogue symbols regular time intervals - unique binary pattern identified each interval.  Digitised sound processed by sequences 1's and 0's .

sample rate - how much signals pass through per second - equivalent to frequency - measure in hertz.

sample rate =  number of samples * 1(seconds) = hertz

sample rate increase , improve sound quality

sample resolution (bit depth) - how much bits are required to store a sample e.g 4 bits - colour depth 4.  2^4 = 16 . 16 different samples stored. Higher bit depth , more accurate sound will be recorded, results higher quality audio file ,  leads to larger file size. 

Bit rate - number of bits used to encode or transmit audio file over communication channel per second

Channel = time period

Bit rate = sampling rate * sample resolution * channel

e.g 30hz * 4 * 5s = 600 bits

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compression

compression used for reducing file size e.g memory card or wireless communication link. 

storage space limited so image uploaded to cloud storage or web server

store JPEG format - highly compressed

Sound compressed MP3 file - some people uncompressed audio format - WAV

Lossy compression - compression result loss of data. File compressed , data is removed and re-created from orginal data . Re-created data not the same copy but approximation of original data. 

used for sound and images because data is lost without noticeable quality

files including words and numbers unsuitable for lossy compression because contents need to be exactly the same and noticeable differences will be spotted

Risks - original data is lost. 

lossless compression - no data is lost in the process. Contents are identical to original file

Appropriate for data that cannot be approximated - such as documents containing numbers and letters. 

Useful for PNG and GIFs

risks - produce low quality and result in bit depth quality lowering - not suitable for picture. 

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