Chapter 1

• 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 denary to binary using two's complement

  1. Invert the digits

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


  • +104 becomes 1 0 0 1 1 0 0 0
  • -104 becomes 1 0 0 1 1 0 0 0
• Two's complement makes binary addition and subtraction more straightforward
• The byte is the smallest unit of memory in a computer
• Memory size units


  • Kilobyte (KB)
  • Megabyte (MB)
  • Gigabyte (GB)
  • Terabyte (TB)
  • Petabyte (PB)
• SI (base 10) system of units


  1 kilo = 1000
• IEC (binary) system of units

  • 1 kibibyte (KiB) = 1024
  • 1 mebibyte (MiB) = 1,048,576
  • 1 gibibyte (GiB) = 1,073,741,824
• Internal memories should be measured using the IEC system
• Hexadecimal


  Base 16 number 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
• Converting hexadecimal to binary


  Take each hexadecimal digit and write the 4-bit binary code
• Converting binary to hexadecimal

  • 1 0 1 1 1 1 1 0 0 0 0 1 becomes B E 1

  1 0 0 0 0 1 1 1 1 1 1 1 0 1 becomes 2 1 F D
• Converting hexadecimal to binary

  • 4 becomes 0 1 0 0

  F becomes 1 1 1 1

  0 8 becomes 0 0 0 0 1 0 0 0
• Memory dump


  Output of a computer's memory contents, often in hexadecimal
• Binary-coded decimal (BCD)


  1. bit code to represent each decimal digit
• BCD representation


  • 0 0 0 0 = 0

  0 1 0 1 = 5

  1 0 0 1 = 9
• Uses of BCD


  Representation of digits on calculator/clock displays

  Storing monetary values accurately
• ASCII code
• Binary addition


  1. 0 + 0 = 0

  2. 0 + 1 = 1

  3. 1 + 0 = 1

  4. 1 + 1 = 1 with carry 1