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Unformatted text preview: haracterized by a set of elements, some of its key operations, and some important elements. As an example, modular arithmetic also forms a ring. For modulus Ò, the algebra is denoted , with components deﬁned as follows: Ò Ò Ò Ò · ¢ ¼½ · Ò Ò Ò ¢ Ò ¼½ ½ · ÑÓ ¢ ÑÓ ¼ ¼ ¼
Ò Ò Ò Ò Even though modular arithmetic yields different results from integer arithmetic, it has many of the same mathematical properties. Other wellknown rings include rational and real numbers. End Aside. If we replace the O R operation of Boolean algebra by the E XCLUSIVE O R operation, and the complement operation ˜ with the identity operation Á —where Á ´ µ for all —we have a structure ¼ ½ ˆ & Á ¼ ½ . This structure is no longer a Boolean algebra—in fact it’s a ring. It can be seen to be a particularly simple form of the ring consisting of all integers ¼ ½ Ò ½ with both addition and multiplication performed modulo Ò. In this case, we have Ò ¾. That is, the Boolean A ND and E XCLUSIVE O R operations correspon...
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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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