Chapter 3: Data Representation

• Number base

  Defines how many unique digits are used within a number system
• Number bases

  • Decimal (base 10)
  • Binary (base 2)
  • Hexadecimal (base 16)
• Decimal (base 10)


  Number system with 10 unique digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• Binary (base 2)


  Number system with 2 unique digits: 0 and 1
• Bit


  A binary digit
• Bit pattern


  Combination of bits used to represent data
• Binary number

  A bit pattern that represents a number
• Hexadecimal (base 16)


  Number system with 16 unique digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
• Each hexadecimal digit can be used to represent a 4-bit binary number (nibble)
• Hexadecimal is used to simplify the representation of long bit patterns
• Hexadecimal values representing colours

  • Each pair of hexadecimal digits represents RED, GREEN and BLUE values from 0 to 255 or 0 to FF
• This makes it much easier to represent long bit patterns
• You will often see hexadecimal values used to represent colours
• Each pair of hexadecimal digits represents each colour RED, GREEN and BLUE which each have values from 0 to 255 or 0 to FF
• Each binary and hexadecimal number has a decimal equivalent
• For AQA GCSE Computer Science the maximum values you will be tested on are: Decimal: 255, Binary: 1111 1111, Hexadecimal: FF
• Binary to decimal conversion

  Use the binary line to calculate the decimal equivalent of a binary number
• Hexadecimal

  Base 16, has 16 digits: 0 1 2 3 4 5 6 7 8 9 A B C D E F
• Hexadecimal to decimal conversion

  The first 10 digits (0 - 9) are the same as hexadecimal, then A is 10, B is 11, up to F which is 15
• The hexadecimal system is based on powers of 16
• Binary to hexadecimal conversion

  Each 4-bit pattern (nibble) represents a single hexadecimal digit
• Decimal to binary conversion

  Divide the decimal number by 2 repeatedly and read the remainders from bottom to top
• Hexadecimal to binary conversion


  Convert each hexadecimal digit to decimal and then to binary
• Bits


  Electrical signals which can be either on (1) or off (0)
• Byte

  A group of 8 bits, the smallest bit pattern that can be used to represent data in a computer system
• Units of information

  • Bits
  • Bytes
  • Kilobytes (kB)
  • Megabytes (MB)
  • Gigabytes (GB)
  • Terabytes (TB)
• Kilobyte (kB)

  1,000 bytes
• Megabyte (MB)


  1,000 kilobytes (1,000,000 bytes)
• Gigabyte (GB)


  1,000 megabytes (1,000,000,000 bytes)
• Terabyte (TB)

  1,000 gigabytes (1,000,000,000,000 bytes)
• Adding binary numbers

  1. 0 + 0 = 0

  2. 1 + 0 = 1

  3. 0 + 1 = 1

  4. 1 + 1 = 10 (carry 1 to next column)
• Computers use bits and bytes to represent data and instructions
• Bits and bytes can be combined into larger units like kilobytes, megabytes, gigabytes and terabytes
• Adding binary numbers follows the same principles as adding decimal numbers, with carrying to the next column when the sum exceeds the base (2 for binary)
• Binary shifts

  Used for multiplication and division
• Binary multiplication

  Shift left and add zeros to multiply by 2, 4, 8
• Binary shift left

  Add zero to right side, discard bit at left
• Binary division

  Shift right and add zero to left, discard bit at right
• Computers only work with binary bits, so all characters need to be represented by a binary number
• ASCII

  
  

  American Standard Code for Information Interchange, a set of bit patterns used for standard characters and control codes