This structure is no longer a boolean algebrain fact

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Unformatted text preview: n algebra still plays a central role in digital systems design and analysis. There are many parallels between integer arithmetic and Boolean algebra, as well as several important differences. In particular, the set of integers, denoted , forms a mathematical structure known as a ring, denoted · ¢ ¼ ½ , with addition serving as the sum operation, multiplication as the product operation, negation as the additive inverse, and elements 0 and 1 serving as the additive and multiplicative identities. The Boolean algebra ¼ ½ | & ˜ ¼ ½ has similar properties. Figure 2.7 highlights properties of these two structures, showing the properties that are common to both and those that are unique to one or the other. One important difference is that ˜ is not an inverse for under |. 36 CHAPTER 2. REPRESENTING AND MANIPULATING INFORMATION Aside: What good is abstract algebra? Abstract algebra involves identifying and analyzing the common properties of mathematical operations in different domains. Typically, an algebra is c...
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