1.4.1

• When writing a program, it's essential to make sure data is being stored with the right data type, so that the right operations can be performed on it
• Integer


  A whole number
• Integers


  • 6
  • 47238
  • -12
  • 0
  • 15
• Real


  Positive or negative numbers which can, but do not necessarily, have a fractional part
• Real numbers


  • 0
  • -71.5
  • 5.01
  • -80.8
  • 15
• Character


  A single symbol used by a computer
• Boolean


  Values are restricted to True and False
• Boolean


  • True
  • False
• Bit


  A single binary digit
• Byte


  Eight binary digits
• Nybble


  Half a byte (four bits)
• Least significant bit


  The bit furthest to the right
• Most significant bit


  The bit furthest to the left
• Converting decimal to binary

  1. Find the largest power of two smaller than the number

  2. Write out place values in powers of two up to this power

  3. Place a 1 or 0 in each position so the total adds up to the original number
• Binary addition


  1. 0 + 0 + 0 = 0

  2. 0 + 0 + 1 = 1

  3. 0 + 1 + 1 = 10

  4. 1 + 1 + 1 = 11
• Sign magnitude


  Represents negative numbers by adding a leading 1 for negative and 0 for positive
• Two's complement


  Represents negative numbers by flipping all bits and adding 1
• Subtracting in binary using two's complement

  Subtracting a number is the same as adding the negative of that number
• Hexadecimal


  A base 16 number system that uses digits 0-9 and A-F
• Hexadecimal numbers


  • 4E7F
• 4E7F = 20095 in decimal
• • 12


  10100 in binary
• Minimum number of bits required to represent -12

  • Five
• Adding two's complement numbers

  1. Convert to binary

  2. Add using same technique

  3. Read off result
• The calculation -16 + 8 + 4 = -4 is correct
• Hexadecimal


  Base 16 number system
• Hexadecimal digits


  • 0-9
  • A-F
• Converting hexadecimal to decimal


  1. Convert each hexadecimal digit to decimal

  2. Combine using place values
• Converting hexadecimal to binary

  1. Convert each hexadecimal digit to decimal

  2. Convert decimal to binary nybble

  3. Combine binary nybbles
• Converting hexadecimal to decimal


  1. Convert to binary first

  2. Then convert binary to decimal
• Floating point binary


  Like scientific notation, with mantissa and exponent
• Floating point number structure


  • Sign bit
  • Mantissa
  • Exponent
• Converting floating point binary to decimal

  1. Convert sign bit

  2. Convert mantissa to decimal

  3. Convert exponent to decimal

  4. Combine to get final value
• Normalising floating point binary

  1. Adjust mantissa to start 01 or 10

  2. Adjust exponent accordingly
• Adding floating point binary numbers

  1. Ensure exponents are the same

  2. Add mantissas

  3. Normalise result
• Subtracting floating point binary numbers

  1. Ensure exponents are the same

  2. Convert subtrahend mantissa to two's complement

  3. Add mantissas

  4. Normalise result
• Logical shift


  Shifting bits left or right, adding/removing leading/trailing zeros
• Logical shift left


  Multiplies by 2 to the power of the number of places shifted
• Mask


  Applying a logic gate (AND, OR, XOR) to combine two binary numbers
• Character set


  Published collection of codes and corresponding characters for representing text