IEEE Floating Point

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IEEE Floating Point

• Standards
• Special Values

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• Condition
•  exp 0000
• Cases
• exp 0000, frac 0000
• Represents value?0?(zero)
• Both positive and negative
• exp 0000, frac ? 0000
• De-normalized Form
• Fills in gap around zero
• Referred to as gradual underflow

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• Condition
•  exp 1111
• Cases
• exp 1111, frac 0000
• Represents value???(infinity)
• Operation that overflows
• Both positive and negative
• E.g., 1.0/0.0 ?1.0/?0.0 ?, 1.0/?0.0 ??
• exp 1111, frac ? 0000
• Not-a-Number (NaN)
• Represents case when no numeric value can be
  determined
• E.g., sqrt(1), ?????

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OPERATION ON SPECIAL VALUES ? /-/ any
number ? -? /-/ any number - ? Any
number / ? 0 Any operation on NAN yields
NAN /- of infinities yields NAN divide by
0 yields NAN ? div by ? yields NAN x REM
0 or ? REM x yields NAN ? -x yields NAN