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Unformatted text preview: right), we have ¼½½¼½¼¼½ representing the set ¼¿ , and ¼½¼½¼½¼½ representing the set ¼¾ . Under this interpretation, Boolean operations | and & correspond to set union and intersection, respectively, and ˜ corresponds to set complement. For example, the operation & yields bit vector ¼½¼¼¼¼¼½ , while ¼ . In fact, for any set Ë , the structure È ´Ë µ Ë forms a Boolean algebra, where È ´Ë µ denotes the set of all subsets of Ë , and denotes the set complement operator. That is, for any set , its complement is the set ¾ Ë ¾ . The ability to represent and manipulate ﬁnite sets using bit vector operations is a practical outcome of a deep mathematical principle. 2.1.8 Bit-Level Operations in C
One useful feature of C is that it supports bit-wise Boolean operations. In fact, the symbols we have used for the Boolean operations are exactly those used by C: | for O R, & for A ND, ˜ for N OT, and ˆ for E XCLUSIVE O R. These can be applied to any “integral” dat...
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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.
- Spring '10
- The American