Thẻ ghi nhớ: iGCSE - Unit 1 - Data representation - GCSE

Character set

A defined list of characters recognised by the computer hardware and software.

Denary System

Number system with base 10

Binary

The binary number system is base 2, using only bits 0 and 1.

Analogue data

Non-discrete, Continuous data

e.g. a sound wave

Digital data

Discrete data that has only two values

By example, e.g. binary data / 1's and 0's

Binary headings

128 64 32 16 8 4 2 1

Binary to Denary Conversion

Each time

a 1 appears in a column, the column value is added to the total.

Denary to Binary Conversion

1. Starting left to right on the binary table

2. Does 128 go into our number

3. If no write a 0 and move onto 64

4. If yes, write 1 and subtract 128 from the number and move onto 64 with the new number

PNG

Lossless picture file format

.WAV

uncompressed audio files

.FLAC

lossless compressed audio files

1KB (kilobyte)

1,000 bytes

1MB (megabyte)

1,000 kilobytes

1GB (gigabyte)

1,000 megabytes

1TB (terabyte)

1,000 gigabytes

1PB (petabyte)

1,000 terabytes

Hexadecimal Number System

Number system with base 16.

Hex uses

HTML colours

• e.g. blue 0000FF

Display machine code/programs/memory dump

• e.g. 5F 3A 09 F1

Display (MAC) addresses

• e.g. 01-23-45-67-89-AB-CD

Display ASCII/Unicode values

• e.g. %41 for A

Display error codes

• e.g. error #404 page not found

IPv6 addresses

e.g. 2001:0db8:85a3:0000:0000:8a2e:0370:7334

When using machine code, do programmers use hexadecimal or binary? Why?

Hex, because it is easier to read and remember with less symbols. - 16 bit number = 4 hex digits

Easier to convert binary to hex and vice versa

Less likely to make errors

Easier to spot errors with fewer characters

Would hexadecimal mainly be used in a high-level language or a low-level language?

Low-level

How many binary bits does one character in hexadecimal represent?

4

ASCII

American Standard Code for Information Interchange is a character set.

Each letter on the keyboard has a unique value that can be represented in hexadecimal or decimal.

Bit

Binary Digit. Either 1 or 0, On or Off.

Byte

A collection of 8 bits.

What are the 16 hex digits?

0-9

A - 10

B - 11

C - 12

D - 13

E - 14

F -15

Memory Dump

Output of memory contents onto the printer or screen.

Usually represented in hexadecimal.

JPG

Joint Photographic Experts Group

1. LOSSY

2. Photograph compression to a reduced size.

3. Rely on properties of the human eye (inability to see certain colour differences etc)

ADC

Analogue to Digital Converter

Converts physical values into discrete digital values.

Could be used in speech recognition.

Logic Gates

These take in binary inputs and produce a binary output using gates to regulate the output

Logic Circuits

These are made up of several logic gates and are designed to carry out a specific function.

Truth Tables

Logically work out the output of a logic circuit by writing a table.

AND logic gate

OR logic gate

NOT logic gate

NAND logic gate

NOR logic gate

XOR logic gate

DAC

Converts digital data in a computer into an analogue item, like what happens in speakers

MP3

Uses lossy audio compression

90% smaller than uncompressed CD music files

Quality of sound retained by using perceptual music shaping.

Perceptual music shaping

Refers to the process of removing inaudible sounds in order to make a file size smaller.

e.g.

Noises at frequencies that humans cannot hear

Quiet sounds that cannot be heard over louder sounds

MP4

Lossy video file format

How to convert denary - hexadecimal

Divide the denary number by 16 to get the number of full 16s that go into the number

Then put the remainder on the end

Denary 19 becomes:

19 / 16 = 1 r 3 so the hex value for 19 is 13

"one, three" not "Thirteen"

Binary to hex conversion

Take a binary word of 8 bits

1 1 0 0 1 1 0 1

Divide into two nibbles of 4 bits

1 1 0 0 1 1 0 1

Convert each nibble into hex and put back together

1 1 0 0 = 12 = C in Hex + 1 1 0 1 = D in Hex

So 1 1 0 0 1 1 0 1 = CD in Hex

Hex to denary conversion

16 1

A 6

Multiply the left-hand digit by 16, then add the units

Hex to binary conversion

Split the two hex characters

4 = 0100

C = 1100

So 4C = 0100 1100 in binary

Binary Addition Rules

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 0 Carry 1

1 + 1 + 1 = 1 Carry 1

Overflow error

When the result of an addition is too big for the number of bits the computer works with

Pixels

The smallest identifiable area of an image

Each pixel is a single colour and is given a binary value which represents that colour e.g. 11000000 might equal Red

A pixel's colour can be changed by changing this value

The image resolution

The concentration of pixels within a specific area

The area is defined by the image width and height in pixels e.g. 1920x1080

Colour (or bit) depth

Each pixel can represent a finite number of colours

A pixel can be n bits

The number of combinations = 2n

A higher bit depth gives a greater range of colour and a better quality/accurate of image

Metadata

data that describes other data (i.e.: dimensions)

How to calculate image file size

1) Find the total number of pixels

2) Work out how many bits per pixel given the number of colours (colour depth)

3) Find the file size in bits. Resolution x Bit Depth

4) Convert this to bytes

MIDI

Musical Instrument Digital Interface file

• Stores a set of commands / instructions for how the sound should be played

• Does not store the actual sounds

• Data in the file has been recorded using digital instruments

• Specifies pitch of the note // specifies the note to be played

• Specifies when each note plays and stops playing // Specifies key on/off

• Specifies duration of the note

• Specifies volume of the note

• Specifies the tempo

• Specifies the type of instrument

MIDI benefits and drawbacks

The full sound signal does not need to be transmitted, only the instructions to play the sound

It is up to the instrument to create the sound

This significantly reduces the amount of data transmitted

Drawback

As sounds are synthesised, they may be less realistic

Sample resolution

The number of bits (audio bit depth) used to record each measurement

More bits used per sample enables the height of the wave to be more accurately measured but increases file size

Sampling rate

The frequency (rate) at which samples are taken

Sample rate is usually measured in Hertz (Hz)

1Hz = 1 sample per second

Correlates with sound quality.

Higher sampling rate = more accurate the representation of sound

Calculating sound file sizes

File size (bits) = sample rate x resolution x seconds

Compression

a method or protocol for using fewer bits to represent the original information

Lossy Compression

Reduction of file size by removing certain, redundant information from the file

The eliminated data is unrecoverable.

Tries to recreate an file without the omitted data

Much smaller file sizes but there will be some loss of quality

Lossy Image Compression

A compression algorithm is used

Permanently deleting some data // file cannot be restored to original

Colour depth / colour palette can be reduced

Resolution can be reduced // number of pixels can be reduced

Less bits will be required for each pixel / colour

Lossless compression

Every bit of the original data can be recovered from the compressed file.

the uncompressed image will be the same as the original with no loss of data

Works by looking for patterns in the data

Larger compressed file sizes than lossy

Lossless text compression

Finds patterns in original text.

Encodes each pattern in a dictionary

File is recovered from dictionary

Lossless image compression

A compression algorithm is used

No data is removed in the compression process

An index/dictionary of pixels is created

The number of times a pixel is repeated in a row is stored

Run length encoding

Reasons to Compress data

Download/buffering times decrease

Smaller files = fewer packets = faster transmission time

Reduces traffic over the Internet

Less chance of collisions or transmission errors

Data allowances do not run out as quickly = Saves money

Voice can be transmitted fast enough to keep up with speech in a video

Saves spending more money on data storage e.g. hard drives, cloud etc

Faster to back-up data

Frame rate

The number of images / frames processed per second

Higher frame rates can decrease motion blur from high speed objects

Run Length Encoding (RLE)

Lossless compression technique

Summarises consecutive patterns of the same data

Works well with image and sound data where data could be repeated many times

RLE of sound

Sound recordings can have many thousands of samples taken every second

The same sound or note played for a fraction of a second could result in hundreds of identical samples

RLE records one example of the sample and how many times it consecutively repeats

Dynamic range

Difference between the largest and smallest signal a system can record or reproduce

Unicode

Uses 16, 24 or 32 bits / two, three or four bytes

Unicode is designed to be a superset of ASCII

Designed so that most characters (in other languages) can be represented

Bitmap images

Defines a display space and the colour for each pixel or "bit" in the display space