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# 2 the complemented bit vector has numeric value

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Unformatted text preview: y truncating the representation to Û bits. The result is not as familiar mathematically as modular addition, however. The Û-bit two’s complement sum of two numbers has the exact same bit-level representation as the unsigned sum. In fact, most computers use the same machine instruction to perform either unsigned or signed 2.3. INTEGER ARITHMETIC x +y 57 +2w Case 4 Positive Overflow x +t y +2w –1 Case 3 +2w –1 0 –2w –1 Negative Overflow 0 Case 2 –2w –1 Case 1 –2w Figure 2.17: Relation Between Integer and Two’s Complement Addition. When Ü · Ý is less than ¾Û ½, there is a negative overﬂow. When it is greater than ¾Û ½ · ½, there is a positive overﬂow. addition. Thus, we can deﬁne two’s complement addition for word size Û, denoted as +tÛ on operands and Ý such that ¾Û ½ Ü Ý ¾Û ½ as Ü Ü +t Ý Û Í¾Ì Û ´Ì¾Í Û ´Üµ +u Ì¾Í Û ´Ý µµ Û (2.11) By Equation 2.3 we can write Ì¾Í Û ´Üµ as ÜÛ ½ ¾Û · Ü, and Ì¾Í Û ´Ý µ as ÝÛ ½ ¾Û · Ý . Using the pro...
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