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Unformatted text preview: ., set the bit with negative weight but clear all others) having integer value ÌÅ Ò Û ¾Û ½. The greatest ÈÛ ¾ Û ½ value is given by bit vector ¼½ ¡ ¡ ¡ ½ , having integer value ÌÅ Ü Û ¾ ½. Again, one ¼¾ Û Û ½ Û ½ can see that ¾Ì Û is a bijection ¾Ì Û ¼ ½ ¾ ¾ ½ , associating a unique integer in the representable range for each bit pattern. Figure 2.9 shows the bit patterns and numeric values for several “interesting” numbers for different word sizes. The ﬁrst three give the ranges of representable integers. A few points are worth highlighting. First, the two’s complement range is asymmetric: ÌÅ Ò Û ÌÅ Ü Û · ½, that is, there is no positive counterpart to ÌÅ Ò Û . As we shall see, this leads to some peculiar properties of two’s complement arithmetic and can 2.2. INTEGER REPRESENTATIONS 43 be the source of subtle program bugs. Second, the maximum unsigned value is nearly twice the maximum two’s complement value: ÍÅ Ü Û ¾ÌÅ Ü Û · ½. This follows from the fact that two’s complement notation reserves half of the bit patterns to represent negati...
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- Spring '10
- The American