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Unformatted text preview: e the set Û ½ Û ¾ ¼ of all strings of 0s and 1s having length Û, and Û denote the string consisting of Û repetitions of symbol , then one can see that the resulting algebras: ¼ ½ Û | & ˜ ¼Û ½Û and ¼ ½ Û ˆ & Á ¼Û ½Û form Boolean algebras and rings, respectively. Each value of Û deﬁnes a different Boolean algebra and a different Boolean ring.
Aside: Are Boolean rings the same as modular arithmetic? The two-element Boolean ring ˆ&Á is identical to the ring of integers modulo two ¾ ¾ ¾ ¾ The generalization to bit vectors of length Û, however, however, yields a very different ring from modular arithmetic. End Aside. ¼½ ¼½ · ¢ ¼½. Practice Problem 2.5:
Fill in the following table showing the results of evaluating Boolean operations on bit vectors. 2.1. INFORMATION STORAGE
¼½½¼½¼¼½ ¼½¼½¼½¼½ 37 ˜ ˜ & | ˆ One useful application of bit vectors is to represent ﬁnite sets. For example, we can denote any subset ¼½ Û ½ as a bit vector Û ½ ½ if and only if ¾ . For example, ½ ¼ , where (recalling that we write Û ½ on the left and ¼ on the...
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