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Unformatted text preview: recision and ½¼¾¾ to ·½¼¾¿ for double precision. The fraction ﬁeld frac is interpreted as representing the fractional value , where ¼ ½, having binary representation ¼ Ò ½ ¡ ¡ ¡ ½ ¼ , that is, with the binary point to the left of the most signiﬁcant bit. The signiﬁcand is deﬁned to be Å ½ · . This is sometimes called an implied leading 1 representation, because we can view Å to be the number with binary representation ½ Ò ½ Ò ¾ ¡ ¡ ¡ ¼ . This representation is a trick for getting an additional bit of precision for free, since we can always adjust the exponent so that signiﬁcand Å is in the range ½ Å ¾ (assuming there is no overﬂow). We therefore do not need to explicitly represent the leading bit, since it always equals 1. Denormalized Values When the exponent ﬁeld is all 0s, the represented number is in denormalized form. In this case, the exponent value is ½ × , and the signiﬁcand value is Å , that is, the value of the fraction ﬁeld without an implied leading 1.
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