FloatingPointRepresentation

Consequently we can use the 23 bits of the signi cand

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Unformatted text preview: it. Consequently, we can use the 23 bits of the signi cand eld to store b1 b2 : : : b23 instead of b0 b1 : : : b22, changing the machine precision from = 2;22 to = 2;23 : Since the bitstring stored in the signi cand eld is now actually the fractional part of the signi cand, we shall refer henceforth to the eld as the fraction eld. Given a string of bits in the fraction eld, it is necessary to imagine that the symbols \1." appear in front of the string, even though these symbols are not stored. This technique is called hidden bit normalization and was used by Digital for the Vax machine in the late 1970's. Exercise 3 Show that the hidden bit technique does not result in a more accurate representation of 1=10. Would this still be true if we had started with a eld width of 24 bits before applying the hidden bit technique? Note an important point: since zero cannot be normalized to have a leading nonzero bit, hidden bit representation requires a special technique for storing zero. We shall see what this is sh...
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