CH1

• Denary

  Base 10 with digits 0-9
• Binary

  • Base 2 system, represented with 1 and 0
  • All inputs need to be converted to binary for computers
• Decimal Prefixes


  • Kilobyte = 1000 bytes = 10^3
  • Megabyte = 10^6
  • Gigabyte
  • Terabyte
• Binary Prefixes (power of 2)


  • Kibibyte = 1024 bytes = 2^10
  • Mebibyte = 2^20
  • Gibibyte
  • Tebibyte
• Nibble


  4 bits
• Byte


  8 bits
• Converting Negative Decimal Numbers into Binary Numbers

  1. One's Complement: Turn all '0's to '1's and the '1's to '0's

  2. Two's Complement: Turn all '0's to '1's and the '1's to '0's, and add 1
• One's Complement


  • 01000011 → 10111100
• Two's Complement


  • 0111 → 1000 → 1001

  1111 → 0000 → 0001

  • 65 → 65 → 01000001 → 10111110 → 10111111
• Overflow


  The largest number of bits a register can hold at a time is exceeded
• CPU discards the overflow digit

  It will think it is 255 + 1
• Binary Arithmetic Overflow


  • 11111111 + 1 → 1 00000000 → 00000000
• Binary Coded Decimals (BCD)

  Binary encodings of decimal numbers where each digit is represented by a fixed number of bits
• BCD Types

  • Unpacked: A numeral encoded into one byte (8 bits, first 4 0s insignificant)

  Packed: A numeral encoded into a nibble (4 bits, most significant), typically used for transmission, can be made into 2 bytes
• BCD Examples

  • Unpacked: 8 5 0 3 → 00001000 00000101 00000000 00000011

  Packed: 8 5 0 3 → 1000 0101 0000 0011 → 10000101 00000011
• BCD Applications

  • Digital Calculator

  Digital Clock

  Digital Thermometer

  Currency Values
• Hexadecimal

  Base 16 system
• Why use Hexadecimal

  • Easier to debug as it is close to human language

  Reduces errors as less digits to write
• When to use Hexadecimal

  • MAC addresses

  RGB colors in HTML
• ASCII Code

  American Standard Code for Information Interchange

  Has a unique binary code for each character known as, Character Code

  1. bit code, uses 1 byte of memory per character

  Typically used for storing, displaying or printing text
• ASCII Limitations

  • Only supports up to 256 characters

  Does not support many symbols from international languages (not enough space to store)
• ASCII Special Features


  • Uppercase letters only differ from lowercase letters in bit 6

  Ex: a (01100001) → A (01000001)

  It is in alphabetical order
• Unicode


  Covers majority of different languages across the world

  Uses 16 bits (4 digits only, represents 2 bytes)
• Unicode Limitations


  • Requires more space compared to ASCII (16 bits instead of 8 bits)

  More bits are required for non-ASCII characters
• Unicode Special Features


  • Big enough to handle all existing characters and symbols

  Characters from the same language are grouped together and are in its natural order (if can be made possible)
• Image Types


  • Vectors: Made up of geometric shapes which requires attributes, to edit the design, need to change each of the geometric shapes, file size is small since made up of geometric shapes

  Bitmap: Consists of a matrix of individual dots (or pixels) that all have their own color (made up of binary), image built from pixel by pixel, final image are usually very realistic, can edit each pixel to change the design of the image, most images are typically stored as a bitmap
• Vector Advantages


  • Scalable and do not pixelate like a bitmap image therefore are used by corporations to create logos as they can resized without losing quality
• Bitmap Limitations


  • Very large file size because of pixel (accurate designs), poor quality when zoomed in,
  • decimation: throwing away pixels when zooming out which changes the image in an unacceptable manner, slow reading and rendering process (due to expansion of compressed data)
• Drawing List


  Set of commands used to define a property (thickness, style, colour, fill colour) of the object
• Pixel


  Small blocks of addressable areas & the color they have is represented by binary and stored as bits
• File Header


  A few bytes of binary and represents basic information about the graphic, such as image resolution, size, and number of colors
• Image Resolution


  The amount of pixels an image contains per inch
• Screen Resolution


  The number of pixels per row by the number of pixels per column
• Color Depth


  Number of bits used to represent the color of a single pixel
• The higher the color depth/image resolution, the better the color quality and file size
• Bit Depth


  The number of bits used to represent each pixel in an image
• Sound


  Vibrations that travels through a medium, continuous in nature
• Analogue to Digital Converter (ADC)

  Converts analogue sound to digital signals which can be digitally stored

  Analogue wave is picked up by a microphone and send to an ADC in the form of analogue electrical signals

  Once the sound wave is converted into a digital form it can be stored and manipulated
• Digital to Analogue Converter (DAC)


  Converts digital signals into analogue signal that can be output

  DACs take a binary number of the digital form of audio and turn it into an analog voltage or current that, when done, can create a wave of audio that represents the digital signal

  It creates the analog version of the digital audio in "steps" of each digital reading
• How Sampling Works


  Amplitude of the sound wave is first determined at set time intervals (sampling rate)

  Gives an approximate representation of the sound wave

  Sound wave is then encoded as a series of binary digits