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Unformatted text preview: the style of Figure 2.18. Give the integer values of the 5-bit arguments, the values of both their integer and two’s complement sums, the bit-level representation of the two’s complement sum, and the case from the derivation of Equation 2.12.
Ü Ý Ü ·Ý Ü +t Ý Case ½¼¼¼¼ ½¼¼¼¼ ½½¼¼¼ ½½½½¼ ¼½¼¼¼ ½¼½¼½ ½¼¼¼¼ ¼¼½½½ ¼¼½¼½ ¼½¼¼¼ 2.3.3 Two’s Complement Negation
We can see that every number Ü in the range ¾Û ½ Ü ¾Û ½ has an additive inverse under +tÛ as follows. First, for Ü ¾Û ½, we can see that its additive inverse is simply Ü. That is, we have Û ½ Û ½ ¾ Ü ¾ and Ü +tÛ Ü Ü · Ü ¼. For Ü ¾Û ½ ÌÅ Ò Û , on the other hand, Ü ¾Û ½ cannot be represented as a Û-bit number. We claim that this special value has itself as the additive inverse under +tÛ . The value of ¾Û·½ +tÛ ¾Û·½ is given by the third case of Equation 2.12, since ¾Û ½ · ¾Û ½ ¾Û . This gives ¾Û·½ +tÛ ¾Û·½ ¾Û · ¾Û ¼. From...
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