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# Representing and manipulating information we compiled

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Unformatted text preview: r product Ü ¡ Ý can range between ¾Û ½ ¡ ´¾Û ½ ½µ ¾¾Û ¾ · ¾Û ½ and ¾Û ½ ¡ ¾Û ½ ¾¾Û ¾. This could require as many as ¾Û bits to represent in two’s complement form—most cases would ﬁt into ¾Û ½ bits, but the special case of ¾¾Û ¾ requires the full ¾Û bits (to include a sign bit of 0). Instead, signed multiplication in C is generally performed by truncating the ¾Û-bit product to Û bits. By Equation 2.8, the effect of the Û-bit two’s complement multiplication operation *tÛ is: Ü *t Ý Û Í¾Ì Û ´´Ü ¡ Ý µ ÑÓ ¾ Û µ (2.15) We claim that the bit-level representation of the product operation is identical for both unsigned and two’s complement multiplication. That is, given bit vectors Ü and Ý of length Û, the bit-level representation of the unsigned product ¾Í Û ´Üµ *u ¾Í Û ´Ý µ is identical to the bit-level representation of the two’s complement Û product ¾Ì Û ´Üµ *tÛ ¾Ì Û ´Üµ. This implies that the machine can use a single type of multiply instruction to multi...
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