3.3.1 - number bases

• Binary (base 2)


  A number system with only 2 unique digits: 0 and 1
• How binary numbers work

  1. The weighting of the columns increases by a factor of 2 each time you move one space to the left

  2. Numbers are read as the sum of the column values, not as a single number
• Hexadecimal (base 16)


  A number system with 16 unique digits: 0-9 and A-F
• Hexadecimal numbers can be expressed more compactly than binary numbers, which is one of the reasons it is used
• Number systems


  • Decimal (base 10)
  • Binary (base 2)
  • Hexadecimal (base 16)
• Computers and computer science use different base number systems: binary for on/off states, decimal for human use, and hexadecimal for more compact representation
• All data is represented as binary digits, whether it is numbers, text, images or sound. Calculations are also made in binary.
• Binary


  A number system that contains two symbols, 0 and 1. Also known as base 2.
• Bit


  The smallest unit of data in computing represented by a 1 in binary.
• Byte


  A unit of data containing 8 bits.
• Binary unit system


  • 8 bits = 1 byte (B)
  • 1,000 bytes (1,000 B) = 1 kilobyte (KB)
  • 1,000 kilobytes (1,000 KB) = 1 megabyte (MB)
  • 1,000 megabytes (1,000 MB) = 1 gigabyte (GB)
  • 1,000 gigabytes (1,000 GB) = 1 terabyte (TB)
  • 1,000 terabytes (1,000 TB) = 1 petabyte (PB)
• When calculating storage space for disk drives, it is common to use multiples of 1,000.
• Nibble


  Four bits or half a byte.
• All data is represented as binary digits, whether it is numbers, text, images or sound. Calculations are also made in binary.
• Binary

  A number system that contains two symbols, 0 and 1. Also known as base 2.
• Decimal


  Another name for the number system that contains the digits 0 to 9. Also known as denary or base 10.
• Converting binary to decimal

  Take each place value that has a 1, and add them together.
• Binary is also used within truth tables.
• Hexadecimal


  Base 16 number system used in computer science
• Computers don't really use hexadecimal
• Relationship between hexadecimal and binary nibble

  Hexadecimal is useful for representing large binary numbers in a smaller number of digits
• Uses of hexadecimal in computer science

  • Representing colors
  • Memory addresses
  • MAC addresses
• Hexadecimal


  • 16 numbers, 0 to 15
  • Can represent numbers 0 to 15 in binary using 4 bits
• Hexadecimal is a more compact and human friendly way to represent long sequences of binary numbers
• Typical examples of hexadecimal use

  • Physical address (MAC address)
  • 24-bit colors