FloatingPointRepresentation

The ideas are all the same only the eld widths and

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Unformatted text preview: same only the eld widths and exponent bias are di erent. Clearly, a number like 1=10 with an in nite binary expansion is stored more accurately in double precision than in single, since b1 : : : b52 can be stored instead of just b1 : : : b23. There is a third IEEE oating point format called extended precision. Although the standard does not require a particular format for this, the standard implementation used on PC's is an 80-bit word, with 1 bit used for the sign, 15 bits for the exponent and 64 bits for the signi cand. The leading bit of a normalized number is not generally hidden as it is in single and double precision, but is explicitly stored. Otherwise, the format is much the same as single and double precision. We see that the rst single precision number larger than 1 is 1 + 2;23, while the rst double precision number larger than 1 is 1+2;52. The extended precision case is a little more tricky: since there is no hidden bit, 1 + 2;64 cannot be stored exactly, so the rst number larger than 1 is 1+2;63. Thus the 10 Table 3: W...
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This note was uploaded on 02/12/2014 for the course MATH 4800 taught by Professor Lie during the Spring '09 term at Rensselaer Polytechnic Institute.

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