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Unformatted text preview: numeric value is therefore Î ¾ ¾ ½ ·¾. The value ½ ¼ has a bit representation with all but the most signiﬁcant bit of the exponent ﬁeld equal to 1 and all other bits equal to 0. Its signiﬁcand value is Å ½ and its exponent value is ¼. The largest normalized value has a bit representation with a sign bit of 0, the least signiﬁcant bit of Ò , giving the exponent equal to 0, and all other bits equal to 1. It has a fraction value of ½ ¾ Ò (which we have written ¾ ¯). It has an exponent value ½ ½, a signiﬁcand Å ¾ ¾ ¾ Ò µ ¢ ¾¾ ½ ½ ´½ ¾ Ò ½ µ ¢ ¾¾ ½ . giving a numeric value Î ´¾ ¾ Practice Problem 2.26:
A. For a ﬂoating-point format with a -bit exponent and an Ò-bit fraction, give a formula for the smallest positive integer that cannot be represented exactly (because it would require an Ò · ½-bit fraction to be exact). , Ò ¾¿)? B. What is the numeric value of this integer for single-precision format ( 2.4.4 Rounding
Floating-point arithmetic can only approximate real arithmetic, since the representation has limited range and precision. Thus, for a value Ü, we generally want a systematic method of ﬁnding the “closest...
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- Spring '10
- The American