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Unformatted text preview: Examples. Although the bit-level representations of the full products may differ, those of the truncated products are identical. As illustrations, Figure 2.21 shows the results of multiplying different 3-bit numbers. For each pair of bitlevel operands, we perform both unsigned and two’s complement multiplication. Note that the unsigned, truncated product always equals Ü ¡ Ý ÑÓ , and that the bit-level representations of both truncated products are identical. Practice Problem 2.20: Fill in the following table showing the results of multiplying different 3-bit numbers, in the style of Figure 2.21 Mode Unsigned Two’s Comp. Unsigned Two’s Comp. Unsigned Two’s Comp. Ü Ý Ü ½½¼ ½½¼ ¼¼½ ¼¼½ ½½½ ½½½ ¼½¼ ¼½¼ ½½½ ½½½ ½½½ ½½½ ¡ Ý Truncated Ü ¡ Ý We can see that unsigned arithmetic and two’s complement arithmetic over Û-bit numbers are isomorphic— the operations +u , -u , and *u have the exact same effect at the bit level as do +tÛ , -tÛ , and *tÛ . From this Û Û Û Û ½ we can deduce that two’s complement arithmetic...
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