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Unformatted text preview: Equation 2.12, we can see that ÌÅ Ü Û +tÛ ½ is one of the positive overﬂow cases, yielding ÌÅ Ò Û . ¼ Û ½, i.e., Ü 3. When Û ½, i.e., Ü ÌÅ Ü Û and Ü ½, we can see that the low-order · ½ bits of Ò Ö ´Üµ È ½ has numeric value ¾ , while the low-order · ½ bits of Ü has numeric value ¾ ½. The ¼¾ high-order Û · ½ bits have matching numeric values. Thus, Ò Ö ´Üµ has numeric value Ü · ½. In addition, for Ü ÌÅ Ü Û , adding 1 to Ü will not cause an overﬂow, and hence Ü +tÛ ½ has numeric value Ü · ½ as well. As illustrations, Figure 2.20 shows how complementing and incrementing affect the numeric values of several four-bit vectors. 2.3.4 Unsigned Multiplication
Û Integers Ü and Ý in the range ¼ Ü Ý ¾ ½ can be represented as Û-bit unsigned numbers, but their Û product Ü ¡ Ý can range between ¼ and ´¾ ½µ¾ ¾¾Û ¾Û·½ · ½. This could require as many as ¾Û bits to represent. Instead, unsigned multiplication...
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