Monash University > School of Computer Science and Software Engineering > CSE1303 > Part B > Lectures > Lecture B04 notes

CSE1303 Computer Science
Semester 2, 2003
Part B
Lecture B04 notes: Floating point

In this lecture

• Real numbers
• Alternative representation
  • Rational numbers
  • Fixed point
• Floating point
  • Approximation of scientific notation
  • Sign
    • Signed magnitude
    • 0 = positive, 1 = negative
  • Mantissa (significand)
    • Fixed point
    • Implicit leading 1
  • Exponent
    • Excess notation
  • Normalized representation
• C support for floating point
  • float (8-bit exponent, 23-bit mantissa)
  • double (11-bit exponent, 52-bit mantissa)
  • long double (15-bit exponent, 64-bit mantissa)
• Limitations of floating point
  • Exponent size is fixed: limits range
  • Mantissa size is fixed: limits precision
  • Addition not associative
• Comparing floating-point numbers
  • Compare sign
  • Then compare exponent
  • Then compare mantissa
• Multiplying floating-point numbers
  • Sign (exclusive OR)
  • Exponent (add)
  • Mantissa (multiply)
  • Renormalize result
• Adding floating-point numbers
  • Examine signs, possibly switch to subtraction
  • sign: same as of larger number
  • exponent: same as of large number
  • mantissa: temporarily denormalize, then add
  • Renormalize result

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Last modified 2002-12-04