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# The high order bits have matching numeric values thus

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Unformatted text preview: perty that +u is simply addition modulo ¾Û , along with the properties of modular addition, we then have Û Ü +t Ý Û Í¾Ì Û ´Ì¾Í Û ´Üµ +u Ì¾Í Û ´Ý µµ Û Û Í¾Ì Û ´ ÜÛ ½ ¾ · Ü · ÝÛ ½ ¾Û · Ý µ ÑÓ Í¾Ì Û ´Ü · Ý µ ÑÓ ¾Û ¾ Û The terms ÜÛ ½ ¾Û and ÝÛ ½ ¾Û drop out since they equal 0 modulo ¾Û . To better understand this quantity, let us deﬁne Þ as the integer sum Þ Ü · Ý , Þ ¼ as Þ ¼ Þ ÑÓ ¾Û , and Þ ¼¼ as Þ ¼¼ Í¾Ì Û ´Þ ¼ µ. The value Þ ¼¼ is equal to Ü +tÛ Ý . We can divide the analysis into four cases as illustrated in Figure 2.17: 1. Þ 2. ¼ . Then we will again have Þ ¼ Þ · ¾Û , giving ¾Û ½ · ¾Û ¾Û ½ Þ ¼ ¾Û . ¼ is in such a range that Þ ¼¼ Þ ¼ ¾Û , and therefore Þ ¼¼ Examining Equation 2.6, we see that Þ Þ ¼ ¾Û Þ · ¾Û ¾Û Þ . That is, our two’s complement sum Þ ¼¼ equals the integer sum Ü · Ý. ¾ Û negative overﬂow. We have added two negative numbers Ü and Ý (that’s the only way we can have ¾...
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## This note was uploaded on 09/02/2010 for the course ELECTRICAL 360 taught by Professor Schultz during the Spring '10 term at BYU.

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