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# This analysis shows that for a twos complement

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Unformatted text preview: in C is deﬁned to yield the Û-bit value given by the low-order 62 CHAPTER 2. REPRESENTING AND MANIPULATING INFORMATION Ü ¼½¼½ ¼½½½ ½½¼¼ ¼¼¼¼ ½¼¼¼ ˜Ü ½¼½¼ ¼ ½¼¼¼ ¼¼½½ ½½½½ ¼½½½ ¿ ½ Ò Ö ´˜Üµ ½¼½½ ½¼¼½ ¼½¼¼ ¼¼¼¼ ½¼¼¼ ¼ Figure 2.20: Examples of Complementing and Incrementing four-bit numbers. The effect is to compute the two’s value negation. Û bits of the ¾Û-bit integer product. product modulo ¾ Û By Equation 2.7, this can be seen to be equivalent to computing the . Thus, the effect of the Û-bit unsigned multiplication operation *u is: Û Ü *u Ý Û ´ Ü ¡ Ýµ ÑÓ ¾ Û (2.14) It is well known that modular arithmetic forms a ring. We can therefore deduce that unsigned arithmetic Û over Û-bit numbers forms a ring ¼ ¾ ½ +uÛ *uÛ -uÛ ¼ ½ . 2.3.5 Two’s Complement Multiplication Integers Ü and Ý in the range ¾Û ½ Ü Ý ¾Û ½ ½ can be represented as Û-bit two’s complement numbers, but thei...
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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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