FloatingPointNumbersandArithmetic

# 49999 same w ith rounding if y ou w ant to simulate

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Unformatted text preview: . (exactly ) and this is truncated to 12.49999 (same w ith rounding) (If y ou w ant to simulate binary machines do this: a. D o the operation EX A CT LY (in binary). b. T ake this result, KEEP the binary point, but truncate (or round) all bits follow ing the leading 24.) F or double precision simulation use 16 decimal digits or 52 binary bits. 3 . So, other than keeping track of w here the decimal point belongs, the decimal point (or binary point) has no effect on the calculation? T his simple simulation is actually exactly correct EX CEPT for w hat happens if overflow or underflow occurs: the number is above the overflow level or beneath the underflow level. In those cases w hat happens (stop, set result to zero, use an &quot;Inf&quot;, ...) depends upon the computing e nvironment. T his happens so rarely (look at those underflow and overflow values up above) that w e w ill ignore it here. 4 . What does &quot;precision&quot; mean? Suppose an exact calculation results in v and the floating point calculations results in v . T he v v e rror is v v , the absolute...
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