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# Why not consistently round values halfway between two

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Unformatted text preview: set the bias this way for denormlized values? Having the exponent value be × rather than simply × might seem counterintuitive. We will see shortly that it provides for smooth transition from denormalized to normalized values.End Aside. ½ Denormalized numbers serve two purposes. First, they provide a way to represent numeric value 0, since with a normalized number we must always have Å ½, and hence we cannot represent 0. In fact the ﬂoating-point representation of ·¼ ¼ has a bit pattern of all 0s: the sign bit is 0, the exponent ﬁeld is all 0s (indicating a denormalized value), and the fraction ﬁeld is all 0s, giving Å ¼. Curiously, when the sign bit is 1, but the other ﬁelds are all 0s, we get the value ¼ ¼. With IEEE ﬂoating-point format, the values ¼ ¼ and ·¼ ¼ are considered different in some ways and the same in others. A second function of denormalized numbers is to represent numbers that are very close to 0.0. They provide a property known as gradual unde...
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