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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 twoelement 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
Operation Result
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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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
 Schultz
 The American, Gulliver's Travels, 2.2.5 2.2.6 2.2.7 2.3 2.3.1 2.3.2 2.3.3 2.3.4 2.3.5

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