data representation

• label

  A) k

  B) M

  C) G

  D) T

  E) P

  F) B

  G) kB

  H) MB

  I) GB

  J) TB

  K) 3

  L) 6

  M) 9

  N) 12

  
• label

  A) 50 kB

  B) 100 kB

  C) 100 MB

  
• binary is base 2 (0-1), denary is base 10 (0-9), hexadecimal is base 16 (0-9, A-F)
• • binary <=> denary: use 256, 128, 64, 32, 16, 8, 4, 2, 1
  • binary <=> hex: split binary into nibbles (8, 4, 2, 1) and turn into hex based on added value (0-9 or A-F if it's 10-15)
  • denary => hex: with binary each number to the left increases in multiples of 2. But with hexadecimal it increases by powers of 16. So our columns are as follows: 4096, 256, 16, 1. Under each column, write how many times it fits into that power (if it is 10-15 write A-F)
  • hex => denary: shove the hexadecimal into 4096, 256, 16, 1 columns and multiply the hex by the column and add them all together
• binary addition

  • 0 + 0 = 0
  • 1 + 0 = 1
  • 1 + 1 = 0 carry 1
  • 1 + 1 + 1 = 1 carry 1
  • If the number of bits required to store the answer is bigger than the number of bits in the available range, then this is an overflow error.
• Multiply a number, a binary shift moves all the digits in the binary number along to the left and fills the gaps after the shift with 0 (XO easier to draw for right hand onto left):

  • x 2, all digits shift 1 place left (add 0 on right hence x 0 on left hand)
  • x 4, 2 places left (2 0s)
  • x 8, 3 places left (3 0s)

  To divide a number, a binary shift moves all the digits in the binary number along to the right (0 ÷ is on right cuz left hand draw on right hand is harder symbol):

  • ÷ 2, all digits shift 1 place right (add 0 on left)
  • ÷ 4, 2 places right (2 0s)
  • ÷ 8, 3 places right (3 0s)
• To represent text digitally, each character needs its own unique bit-pattern (combinations of 1s and 0s) called a character code.

  A character can be any of the following:

  • Letters (upper and lower case)
  • Punctuation (e.g. ?/|\£$)
  • Numbers (0–9)
  • Commands (e.g. Enter, Delete, F1)

  For computers to be able to communicate + exchange text, they must have an agreed standard that defines which character code is used for which character. A standardised collection of characters and the bit-patterns used to represent them is called a character set (eg ASCII, Unicode)
• • ASCII uses seven bits, giving a character set of 128 codes (32control codes and 96 characters). The characters are represented in a table, called the ASCII table.
  • Extended ASCII uses eight bits, giving a character set of 256 characters. This allows for special characters such as those with accents in languages.
  • While suitable for representing English characters, 256 characters is far too small to hold every character in other languages, such as Chinese or Arabic. Unicode uses 16 bits, giving a range of over 65,000 characters. 
• file size (bits) = bits per character x number of characters

  file size (bytes) = bits per character x number of characters / 8
• A bitmap is an image formed from pixels. A pixel is the smallest element that makes up an image (a single point in an image)
• The number of bits determines the range of colours. This is known as an image's colour depth. For example, using a colour depth of 3, ie 3 bits per pixel, would allow 8 possible colours (2^8)
• Meta data is data about data. For a file, metadata can include:

  • type of file (eg bitmap)

  • file size (eg 3 Mb)

  • date created (eg 20-12-2017)

  For images, metadata will include:

  • colour depth

  • image height and width (in pixels)

  • image resolution (in ppi)

  • image type (eg JPEG)
• Minimum Bitmap File Size (bits) = Width x Height x Colour Depth

  Size in bytes = size in bits ÷ 8
• Amplitude = A measurement of sound

  Sample = Measure of amplitude at a specific time

  Bit depth = Number of bits used for each sample

  Sample rate = Number of samples per second measured in Hz
• Sound begins life in an analogue format. This means it has no discrete (exact) value and varies continuously. It can be represented in the form of a wave. An ADC will capture a sound wave at regular time intervals. This recording is known as a sample.
• bit rate (bits per second) = sample rate x bit depth

  file size (bits) = sample rate x bit depth x seconds

  file size (bits) = bit rate x seconds
• • Lossy compression, some data is removed + discarded, reducing overall amount of data AND the file size.
  • Image can reduce colour depth (fewer shades of colour).
  • Audio file can be compressed by reducing the bit depth of the samples. MP3 is a lossy audio file format.

  Various lossy standards exist:

  • the JPEG file format works on this principle, which is why JPEG files tend to be smaller in size
  • the MPEG file format compresses audio and video, making it more suitable for streaming media
  • >MP3 is a lossy format for audio, including music
• There are some files that we would not want to lose data from eg

  • text files
  • spreadsheets
  • financial records
  • emails

  With lossless compression, files size reduce without loss of data. Lossless compression cannot compress files as much as lossy compression.

  • PDF - text documents
  • GIF - image file format
• label

  A) most

  B) overflow error

  C) least

  D) loss of

  E) precision

  
• label

  A) digital

  B) analog