Data Representation Flashcards

Question

How can you quickly differentiate between even and odd numbers in binary?

Answer 1

If there is a 1 at the end, it is odd. If there is a 0, it is even.

Answer 2

1. 0 + 0 = 0 2. 0 + 1 = 1 3. 1 + 0 = 1 4. 1 + 1 = 0 Carry 1 5. 1 + 1 + 1 = 1 Carry 1

Answer 3

**An overflow error.** • Computers work with a fixed number of bits at a time • When the result of an addition is too large for the number of bits the computer works with there will be an overflow error Eg. If there is an extra 1 past the 8-bits, there is an overflow error.

Answer 4

**An overflow error.** • Computers work with a fixed number of bits at a time • When the result of an addition is too large for the number of bits the computer works with there will be an overflow error Eg. If there is an extra 1 past the 8-bits, there is an overflow error.

Answer 5

• A binary shift left of one bit moves all the bits one place to the left • The vacant bit spaces are filled with zeros. This doubles the binary number. A shift by 2 to the left would quadruple it, etc.

Answer 6

A binary shift right of one place results in halving the number and **rounding down** each time. Empty spaces are, again, replaced by a 0.

Answer 7

• Logical shifts can very quickly multiply or divide a binary number by a factor of two

Answer 8

Overflow error • If there’s a limited number of bits available to store the result, overflow can occur with logical shifts left.

Answer 9

Loss of precision • However, with right shifts a loss of accuracy can occur as bits are lost: • E.g. Right Shift by 2 places: 22 / 4 is not exactly 5

Answer 10

• Hexadecimal (or hex) is a number system which uses base 16 • As we only have 10 digits, it uses 0-9 and then the letters A to F 0 - 0 1 - 1 2 - 2 … 9 - 9 10 - A 11 - B … 15 - F

Answer 11

Hex uses base sixteen. You will only ever need to translate one or two digit hex. So… 16s Units 2 A 2 x 16 + 10 =42 in denary

Answer 12

27 = 1 x 16 r 11 (11 = B in hex) so = 1B

Answer 13

2 x 16 + 7 =39

Answer 14

Hex uses base sixteen. You will only ever need to translate one or two digit hex. So… 16s Units 2 A 2 x 16 + 10 =42 in denary

Answer 15

2 x 16 remainder 12 (12 is C in hex) = 2C

Answer 16

• Divide the denary number by 16 to get the number of 16s (the left-hand hex digit) • The remainder gives you the units Denary 18 becomes: 18 / 16 = 1 remainer 2 so the hex value for 18 is 12

Answer 17

1. take a binary word of 8 bits 11100101 2. Divide into two nibbles of 4 bits 1110 0101 3. Convert each nibble into its hex value and rejoin 1110 = 14 = E in hex + 0101 = 5 in hex So 11100101 = E5 in Hex

Answer 18

Split the two hex characters 3 = 0011 in binary and B = 1011 So 3B = 0011 1011 in binary

Answer 19

Use hex, it is entirely for human benefit

Answer 20

• It is much simpler to remember a hex value than a binary value • It is quicker to write or type since a hex digit only takes up one bit rather than 4 bits • People are less likely to make an error with fewer digits • It is easy to convert between hex and binary

Answer 21

- MAC Addresses - IP Addresses - Colours - hex colours use sixteen different values to represent a single shade of colour, whether it be red, green or blue. This is powerful because it gives you a broad range of shades for each colour - specifically 16.

Answer 22

• Every character on the keyboard is represented by a unique binary value • Uppercase letters (capitals) have different values from lowercase characters • Numbers have their own values • Punctuation symbols have their own character code

Answer 23

A common character set is required so that data is readable by ALL computer systems - for communicating and exchanging data with each other. The character set defines which character code (unique binary value) corresponds to each character. A standardised collection of characters and the bit patterns used to represent them is called a character set. There are two major character sets in use today: • ASCII • Unicode

Answer 24

• ASCII (American Standard Code for Information Interchange) has become the standard code, used worldwide • It encodes 256 characters into 8-bit binary codes • Characters include numbers 0 to 9, uppercase and lowercase letters A-Z, a-z, punctuation symbols and the space character In ASCII, character codes are commonly grouped and run in sequence. A-Z characters are from 65-90.

Answer 25

69 (0100 0101)

Answer 26

The ASCII character code for ‘7’ is 55 • 55 (0011 0111) is the ASCII character code that represents the character ‘7’ • This is clearly not the same as the equivalent binary value for 7 (00000111)

Answer 27

Arithmetic with ASCII

Answer 28

• Programming languages deal with the input of numbers in different ways • In some languages, variables have to be declared as type **char, string, integer, real** etc. at the beginning of the program • In other languages such as Python, all data is input as string, and if it is to be regarded as an integer, it has to be converted using an inbuilt function e.g. xString = input (“Enter an integer: ”) x = int(xString)

Answer 29

Ascii (actually extended ASCII) has 8 bits, meaning it can only represent 256 characters, which is not enough for many different alphabets (eg. Japanese, Mandarin, Arabic)

Answer 30

Unicode was developed to use 16 bits (= 65 536 possible characters): • Introduced to standardise the encoding of characters from all languages (e.g. Greek or Russian letters, Chinese characters and letters with accents) The first 256 characters of Unicode are the same as ASCII therefore ensuring backward compatibility

Answer 31

However, whilst Unicode enables many more characters to be represented, every character requires twice as much storage space (16 bits vs 8 bits). Strictly speaking Unicode is of variable length and can be as much as 32 bits per character.

Answer 32

• Digital images can be stored on a computer in many different file formats • BMP • JPG • GIF • PNG • TIFF

Answer 33

• Bitmap images are made up of pixels • A pixel is 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. 111100000000 might equal red • A pixel’s colour can be changed by changing this value

Answer 34

• Resolution is the concentration of pixels within a specific area: • Typically it is the number of pixels per inch: – e.g. 72 PPI (Pixels Per Inch) = typical screen resolution – Smartphones may have very high resolutions (300+ PPI) • Or it’s the size of the image (its dimensions - height and width)

Answer 35

The higher the image quality

Answer 36

• Each pixel is given a binary value • Each binary value represents a different colour • Using one bit per pixel allows only 2 values: • 0 and 1 1 = Black, 0 = White

Answer 37

The number of colour combinations 1 bit - 2 colours 2 bits - 4 colours 3 bits - 8 colours Where n is the number of bits per pixel: It is… 2^(n) colours

Answer 38

Colour Depth = the number of bits used to store the colour for each pixel Changing this affects the number of colours an image can display

Answer 39

• Each pixel can represent a finite number of colours • A pixel is attributed a number of n bits • The number of combinations (2^n) dictates the colour depth and therefore the number of colours that can be represented • A higher colour depth gives a greater range of colour and a better quality of image 8 bits per pixel = 2^8 = 256 colours 16 bits per pixel = 2^16 = 65,536 colours 24 bits per pixel = 2^24 = 16,777,216 colours

Answer 40

Resolution/ number of pixels x colour depth Remember 8 bits =1 byte

Answer 41

Means higher file size

Answer 42

Means higher file size

Answer 43

ppi = pixels per inch

Answer 44

Due to the metadata stored with the image

Answer 45

• Metadata is data about data • It is data other than image data that is stored with a file • This will include: • Colour depth in bits per pixel • Dimensions of the image (its height and width in pixels) • Date created • Author **NB: The 'name' of the file is not included**

Answer 46

• Analogue sound signals are continuous • Digital signals are discrete

Answer 47

by repeatedly measuring and recording the sound wave, ie. SAMPLING

Answer 48

• Sounds must be converted into a digital form in order to be stored and processed by a computer • An Analogue to Digital Convertor (ADC) is used to convert inputs to digital signals • A Digital to Audio Convertor (DAC) is used to convert digital signals to outputs Microphone —> ADC —> Processing —> DAC —> Speaker

Answer 49

• A sound sample is a measurement of amplitude of a sound wave at a given time • Sound is sampled using a bit depth and sample rate

Answer 50

= the number of bits available to store each sample - The more bits available, the more closely the wave is sampled on the y-axis

Answer 51

The higher the accuracy of the height of wave measurement, but also the higher the file size

Answer 52

= the number of samples taken per second - it is measured in hertz (Hz)

Answer 53

1 Hz = 1 sample per second 1 KHz = 1000 samples per second 1 MHz = 1 000 000 samples per second 1 GHz = 1 000 000 000 samples per second

Answer 54

The higher the accuracy, the higher the file size

Answer 55

File size (bits) = samples rate x bit depth x duration

Answer 56

• Recording quality improves: • the more frequently we sample the sound • the more accurately we record the wave height • Increasing the sampling rate means recording more data points • Increasing the bit depth improves the accuracy of each data point

Answer 57

• Compression is the name given to algorithms which reduce file sizes • Decompression is the process where compressed data is restored to its original format • Compression is heavily used with sound, image and video files

Answer 58

- lossy compression (JPG, GIF, MP3) - lossless compression (PNG, TIFF)

Answer 59

Lossy compression reduces the file size by permanently removing some data. The original **cannot be restored**.

Answer 60

Good: images, videos, sounds Bad: documents, computer programs

Answer 61

• Removes data permanently • Constructs the image minus the data which has been removed • Much smaller file sizes but some loss of quality

Answer 62

Similarly coloured pixels are all made the same -> essentially reducing the number of colours (reduces colour depth)

Answer 63

Lossy compression removes sounds that we can’t easily hear or that least affect the perceived playback quality

Answer 64

• Compresses data files by storing all of the same data, but in a different way • Therefore doesn’t lose any of the original information so is... • Reversible so that the original data can be reconstructed HOWEVER….not all data files can be compressed using Lossless compression AND the compressed data must be decompressed to be used, and this takes time, which may be detrimental to some applications

Answer 65

• Finds patterns in the original text • Encodes each pattern in a dictionary • Ie. multiple original characters are replaced With a single digit (stored in binary) Repeated words or numbers or symbols are stored as one binary digit

Answer 66

• Finds groups of repeating data and records the data only once along with the number of times it was repeated Eg. For this: ;;;;====—— It would do 4 x ; + 4 x = + 2 x — • When data is uncompressed it is restored exactly as it was in the original LOSSLESS COMPRESSION looks for patterns and substitutes these with something smaller but so that can recreate the original file (eg. repeating words / phrases in text files, repeating pixels in images)

Answer 67

Compression is often used for files and data that are sent via the internet • Download times are reduced • Data allowances go further • It is possible to transmit video and music data streams as fast as they are playing • Images inside web pages appear faster -> speeds up transmission of webpages • Reduces space on disk / servers

Answer 68

• Smaller files = fewer packets = faster transmission time • Quicker to complete transmission • Reduces traffic over the Internet • Reduces download times of video, sound (including speech used for VOIP systems) and image files • Streaming is also possible as the data can be sent as fast as the rate it is played • Images inside web pages appear faster -> speeds up transmission of webpages • Reduces storage requirements on disk / servers

Answer 69

• The files for video streaming are compressed • The TV or computer needs to decompress the data as it is playing the video • Before the video begins playing, it will buffer a sufficient amount to allow for the network occasionally being slow • If the website or server detects that the connection is slow, it may be able to start sending an alternative lower quality file

Answer 70

JPEG (photos), MP4 (videos), MP3 (music) are lossy PNG (images/photos), ZIP (documents), GIF (simple images, sometimes with animation) are lossless

Data Representation Flashcards

(103 cards)