Unit 3 Data representation

binary is

Base-2 number system using 0 and 1.

denary is

Base-10 system using 0-9

1 byte can represent

2^8

2^ 8 (bits)

can represent numbers between 0 & 255 = 256 no, in total

Hexadecimal is

Base-16 system.

0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

What is hexadecimal used for?

- address memory locations in computers

- easier to identify and locate data in memory

Advantages of hexadecimal

simpler to remember, quicker to write, easy to convert between hex & binary

Binary addition rules

0 + 0 = 0

0 + 1 = 1

1 + 1 = 0 (carry 1)

1 + 1 + 1 = 1 (carry 1)

ASCII

encodes 128 characters into 7-bit binary codes

A - Z: 065 - 090

a - z: 097 - 122

0 - 9: 048 - 057

space: 032

Extended ASCII

256 characters encoded.

8-bit character code

Disadvantages of ASCII

- Can' do arithmetic with characters

- if character represents a no., it must be converted to an integer before any arithmetic can be carried out

Unicode

- represents characters of all languages of the world.

- 2^16 and 2^32

- uses same codes as ASCII up to 127

Types of image file formats:

Bitmap image file format, vector image file format

types of bitmap image file formats

BMP, JPG, GIF, PNG, TIFF

types of vector image file formats

SVG

bitmap images

made up of pixels.

each pixel is a single colour and given a binary value which represents that colour

Image resolution

resolution is the concentration of pixels within a specific area.

area defined by image width and height in pixels.

Creating an image

1 = black

0 = white

Increasing the number of colours

more bits per pixel = more colour combinations

Higher bit depth

ex = 2^8

higher bit depth gives a greater range of colour and better quality of images

Higher colour depth

higher colour depth affects number of colours it can display

How does the number of colours affect the file size?

An increase in the number of colours that are used in an image (bit depth) will increase the file size.

How does the size of image affect the file size?

Increased no. of pixels in image, increases file size.

What are pbm monochrome images?

Portable bitmap images, use 0 for white, 1 for black. Monochrome image can be represents in binary as a bit pattern

Calculating image size in bits

width x height x colour depth

Calculating image size in bytes

width x height x colour depth/ 8

Calculating image size in MB

width x height x colour depth /8000,000

Sample resolution is

no. of bits used to store each sample.

Less accurately represented with 2-bit sample resolution, better in 4-bit sample resolution

2^2 = 4 -1 = 3

2^4 = 16 -1 = 15 colours

Number of bits used per sample

enables height of the wave to be more accurately measured but increases file size.

Sample rate

frequency/sample rate per second affects level of detail in digital representation. Greater the frequency, greater the accuracy & file size.

What are hertz?

Unit of frequency. Sample rate measured in Hz.

Calculating sound files sizes

file size (bits) = sampling rate x resolution x duration (s)

Recording quality of sound

recording quality improves more frequently we sample the sound, the more accurately we record the wave height.

How can we improve recording quality?

increasing sample rate/frequency, recording more data points. Increasing bit rate improves accuracy of each data point

What is bit rate?

storage of the resulting files and how large those files are.

What is image metadata?

information about data, includes colour depth in bits per pixel, resolution, date created, author.

What are sound waves?

Analogue; continuously changing. Has to be stored as a series of binary numbers. Sound digitalised by repeatedly measuring & recording sound waves.

How are Analogue sound waves converted into Digital

- analogue sound wave received by microphone.

- Converted into electrical analogue signal

- Signal amplitude measured at regular intervals

- Values rounded to a level

- Values stored as series of binary numbers

What is a sound sample?

a measurement of amplitude of a sound wave at a given time.

Sound is sampled using a sample resolution (bit depth) and sampling rate.

Lossy compression in sounds

removes sound we can't easily hear, leaves out some data from original; negatively affects sound quality

Lossless compression in sounds

able to reduce file size when compressed but does not lose any information.

Compression definition

algorithm which reduces file sizes

Decompression definition

process where compressed data is restored to it's original format.

Lossy compression in images

results in small mistakes known as digital artefacts. Blocks as a result from lossy compression.

Lossless compression in images

doesn't lose original data. Finds groups of repeating data & records it along with the no. of repetitions.

ex - run length encoding

Run length encoding

lossless compression. Uses frequency/data pairs to encode each run length of the same coloured pixels.

Lossless text compression

repeated patterns in original text. Encodes each pattern in a dictionary.

Dictionary compression example

'An eye for an eye, a tooth for a tooth.'

each word has its own binary value.

38 characters including spaces= 38 bytes.

using the "table" with binary values, there are 48 bits

48 bits= 6 bytes

6/38 x 100 = 15.7% of original size

Huffman trees

analyses frequency with characters in a body of text are used. DO A PRACTISE QUESTION ON THIS.

Example of a huffman tree

'She sells sea shells'

each letter has its own assigned binary value.

Using the bits (the binary value of the entire thing) = 49 bits.

20 characters including spaces.

7-bit ASCII code = 7 x 20 = 140 bits

49/140 x 100 = 35% of original size

Benefits of compression

Smaller files, faster transmission time. reduces download times of video/bandwidth, sound and image files. reduces space of disk/servers.

Buffering

download speed is slower than the playback speed

Types of lossy compression file formats

JPEG; photos , MP4; videos , MP3; music

Types of lossless compression file formats

PNG; images , ZIP; documents , GIF; images/animation , FLAC/ALAC; music