Floating point Multiplication

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Floating point Multiplication

• Multiply mantissas and add exponents
• Steps
• Add exponents
• Multiply mantissas
• Normalise result
• Round results
• Fix sign of product

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Floating Accuracy

• Floating point Numbers are normally
  approximations for the numbers they represent
• IEEE-754 keeps two extra bits on the right during
  intermediate calculations called guard and round
  respectively
• Example add 2.56ten 100 to 2.34ten102
  assumming three significant digits
• First with guard and round digits and
• then without them

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Floating Point Accuracy

• Four Rounding modes
• round to nearest (default)
• round towards plus infinity
• round towards minus infinity
• round towards 0
• Special symbols used by IEEE-754
• ? or - ? (largest exponent with 0 mantissa)
  (result of divide by zero)
• NaN (Not a number) (largest exponent with 0
  mantissa) (0/0 or ? - ?)
• Unnormalised Numbers (no explicit 1 in MSB) (0
  exponent non-zero mantissa)
• Zero (zero Mantissa and zero expeonent)

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Summary
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Processor Design

• Clocking Methodology
• Defines when signals can be read and written
• Going to assume and edge triggered clocking
  methodology

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Control Step

• Each control step takes one clock cycle

Source registers output here
Destination registers read values here
Clock cycle
Signals propagate through system
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