Number Systems

• Denary (Base 10, 0-9) 

• Binary (Base 2, 0 -1) (2024)

• Hex(Base 16, 0 -9 and A-F) (2024)

Binary Manipulations

• • Binary Addition

    • 0+0=0

    • 0+1=1

    • 1+0=1

    • 1+1=10

    • Overflow error

      • When two binary numbers are added by a computer and an overflow error may occur due to:

      • The result of the calculation is greater than 255 // The value generated is larger than can be stored in the register

      •  The result of the calculation would require more than 8 bits to be represented // A register has a predetermined number of bits and there are too many bits for it

  • Negative Binary numbers

    • Two's complement

      • Invert all the values in the binary numbers (1s to 0s and vice versa)

      • Add 1 to the result

Logical shift left (2024)

• Each/All/Every value/digit/bit in the binary number is shifted/moved to the left

• The left most/most significant bit is lost

• A 0 is added as the right most/least significant bit

• The binary integer is multiplied by 2

Text, images & sound

• Converting text to binary

  • Uses Character set (2024)

  • ASCII (represents up to 256 characters, 7-bit encoding, limited/fewer characters/limited set of languages)

  • Unicode (represents up to 65000 characters, 8/16/32-bit encoding, more characters/includes many languages/emojis) (2024)

• Converting images to binary

  • An image is made up of pixels

  • Pixels- One square/circle of one colour // the smallest component of the image

  • Each image has

    • Resolution: The number of pixels per set area/cm/inch // the number of pixels wide by the number of pixels high // number of pixels in an image

    • Colour depth: Represents each colour, 8-bit/32-bit (greater number of bits- greater the quality)

• Converting sound to binary

  • Sound is made up of sound waves

  • When sound is recorded, this is done at set time intervals called Sound Sampling

  • Number of samples taken in a second is called the Sample rate (measured in Hertz, 1 Hz= 1 sample/second)

  • Number  of bits that represents each sample is called the Sample Resolution

  • Example (How analogue sound is recorded and converted to digital):

    • • (The analogue sound is) recorded using a microphone

      • The sound wave is sampled (measuring the height/amplitude)

      • Each amplitude has a unique binary value

      • The sample rate is set(number of samples taken per second)

      • The sample resolution is set(number of bits used for each sample)

      • Each sample taken is converted to binary

Data Storage

• Bit (Smallest unit) [2024]

• Nibble (1 Nibble = 4 bits) [2024]

• Byte (1 Byte = 8 bits)

• kibibytes (KiB) 

• mebibytes (MiB)

• gibibytes (GiB)

• tebibytes (TiB)

• pebibytes (PiB)

• exbibytes (EiB)

Calculating file size

Image

Image width * Image height * Colour depth * number of images

Sound

Sample rate * sample resolution * length of soundtrack (in seconds)

Data Compression

• Benefits (2024)

  • Reduce the file size

  • Reduce storage space required

  • Increase transmission speed // Reduce transmission time//Takes less time to transmit

  • Quicker to upload/download

  • Less bandwidth is required for transmission

  • More likely to meet file size limits set by email clients/apps

Types

• • Lossy

    • Finds unnecessary/redundant data

    • used by image or sound files

    • Images

      • Colours that the human eye can not distinguish

      • reduces color depth/resolution/pixels

      • permanently removed

    • Sound

      • sounds that can not be heard by the human ear (using perceptual music shaping)

      • soft sounds

      • reducing sampling rate/resolution

  • Lossless

    • mainly used for text files

    • reduces size without permanently removing any data

    • Find repeating data

    • Group them

    • Lossless Compression in Images

      • Uses Run Length encoding (RLE) that finds, groups, and stores similar pixels

      • Image can be recreated without any loss