computer

• Binary


  Base two number system based on the values 0 and 1 only
• Bit


  Abbreviation for binary digit
• One's complement

  Each binary digit in a number is reversed to allow both negative and positive numbers to be represented
• Two's complement


  Each binary digit is reversed and 1 is added in right-most position to produce another method of representing positive and negative numbers
• Sign and magnitude


  Binary number system where left-most bit is used to represent the sign (0 = + and 1 = –); the remaining bits represent the binary value
• Hexadecimal


  A number system based on the value 16 (uses the denary digits 0 to 9 and the letters A to F)
• Memory dump


  Contents of a computer memory output to screen or printer
• Binary-coded decimal (BCD)


  Number system that uses 4 bits to represent each denary digit
• ASCII code


  Coding system for all the characters on a keyboard and control codes
• Character set


  A list of characters that have been defined by computer hardware and software. It is necessary to have a method of coding, so that the computer can understand human characters
• Unicode


  Coding system which represents all the languages of the world (first 128 characters are the same as ASCII code)
• Every one of us is used to the decimal or denary (base 10) number system. This uses the digits 0 to 9 which are placed in 'weighted' columns.
• Designers of computer systems adopted the binary (base 2) number system since this allows only two values, 0 and 1. No matter how complex the system, the basic building block in all computers is the binary number system.
• Bit


  Each of the binary digits are known as bits
• Binary number system column weightings


  • 128
  • 64
  • 32
  • 16
  • 8
  • 4
  • 2
  • 1
• Converting from binary to denary


  Each time a 1 appears in a column, the column value is added to the total
• Converting from denary to binary


  Successive division by 2; the remainders are then written from bottom to top to give the binary value
• One's complement


  Each digit in the binary number is inverted (0 becomes 1 and 1 becomes 0)
• Two's complement


  Each digit in the binary number is inverted and a '1' is added to the right-most bit
• Two's complement 8-bit number representation


  • -128
  • 64
  • 32
  • 16
  • 8
  • 4
  • 2
  • 1
• Two's complement


  Method used to represent negative numbers in binary
• Converting a denary number to its negative equivalent using two's complement

  1. Invert the digits

  2. Add 1
• Converting denary numbers to binary using two's complement


  • +114
  • +61
  • +96
  • -14
  • -116
• Binary addition


  1. Convert numbers to binary

  2. Add the binary numbers

  3. Ignore any additional bits beyond the 8-bit representation
• Binary addition examples


  • 0 0 1 1 1 0 0 1 + 0 0 1 0 1 0 0 1
  • 0 1 0 0 1 0 1 1 + 0 0 1 0 0 0 1 1
  • 0 1 0 1 1 0 0 0 + 0 0 1 0 1 0 0 0
  • 0 1 1 1 0 0 1 1 + 0 0 1 1 1 1 1 0
  • 0 0 0 0 1 1 1 1 + 0 0 0 1 1 1 0 0
• Binary subtraction


  1. Convert numbers to binary

  2. Find two's complement of number being subtracted

  3. Add the two binary numbers
• Binary subtraction examples


  • 0 1 1 0 0 0 1 1 - 0 0 1 1 0 0 0 0
  • 0 1 1 1 1 1 1 1 - 0 1 0 1 1 0 1 0
  • 0 0 1 1 0 1 0 0 - 0 1 0 0 0 1 0 0
  • 0 0 0 0 0 0 1 1 - 0 1 1 0 0 1 0 0
  • 1 1 0 1 1 1 1 1 - 1 1 0 0 0 0 1 1
• Byte


  Smallest unit of memory in a computer
• Memory size units


  • Kilobyte (KB)
  • Megabyte (MB)
  • Gigabyte (GB)
  • Terabyte (TB)
  • Petabyte (PB)
• IEC memory size system

  Based on powers of 2, more accurate than SI system
• IEC memory size units


  • Kibibyte (KiB)
  • Mebibyte (MiB)
  • Gibibyte (GiB)
  • Tebibyte (TiB)
  • Pebibyte (PiB)
• Hexadecimal number system


  Base 16 system using digits 0-9 and A-F
• Converting binary to hexadecimal


  1. Split binary into groups of 4 bits

  2. Convert each group to equivalent hexadecimal digit
• Binary to hexadecimal conversion examples


  • 1 0 1 1 1 1 1 0 0 0 0 1
  • 1 0 0 0 0 1 1 1 1 1 1 1 0 1
• Converting hexadecimal to binary


  Take each hexadecimal digit and write the corresponding 4-bit binary code
• Hexadecimal to binary conversion examples


  • 4
  • F
  • A
  • 8
• Memory dumps


  Displaying the contents of computer memory in hexadecimal format
• Binary-coded decimal (BCD)


  1. bit code to represent each denary digit
• BCD representation examples


  • 3 1 6 5
  • 2 7 1
  • 5 0 0 6
  • 7 9 9 0
• Uses of BCD


  • Representing digits on calculator/clock displays
  • Storing monetary values accurately