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# X y 2w1 2w 0 overflow x u y figure 215 relation

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Unformatted text preview: ¾ For a two’s complement number Ü, a similar argument shows that ¾Ì Û ´ ÜÛ ÜÛ ½ Ü¼ µ ÑÓ ¾ ¾Í ´ Ü Ü ½ Ü¼ µ. That is, Ü ÑÓ ¾ can be represented by an unsigned number having bit-level representation Ü ½ Ü¼ . In general, however, we treat the truncated number as being signed. This will have numeric value Í¾Ì ´Ü ÑÓ ¾ µ. Summarizing, the effects of truncation are: ¾Í ¾Ì Ü Ü ½ ´Ü Ü ½ ´ Ü¼ µ Ü¼ µ ¾Í Û ´ ÜÛ ÜÛ ½ Í¾Ì ´ ¾Ì Û ´ ÜÛ Ü¼ µ ÑÓ ¾ Ü ½ Ü¼ µ ÑÓ Û (2.7) ¾µ (2.8) Practice Problem 2.15: Suppose we truncate a four-bit value (represented by hex digits 0 through F) to a three-bit value (represented as hex digits 0 through 7). Fill in the table below showing the effect of this truncation for some cases, in terms of the unsigned and two’s complement interpretations of those bit patterns. Hex Original 0 3 8 A F Truncated 0 3 0 2 7 Unsigned Original Truncated ¼ ¿ ½¼ ½ Two’s Complement Original Truncated ¼ ½ ¿ Explain how Equations 2.7 and 2.8 apply to these cases. 2.2.7 Advi...
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