Transcrição 1/22/2026, 1:43:06 PM

Notes

**CHAPTER 8** **Boolean algebra and digital circuits** **8.1 Boolean algebra** In this chapter, we take a look at the branch of mathematics known as Boolean algebra. There are two main reasons for studying Boolean algebra at this point. Firstly, we will be able to see how Boolean algebra draws together into a unified theory many of the concepts in propositional logic and sets that we met in Chapters 4 and 5. The idea of incorporating two (or more) separate topics into a single theory is a powerful concept, which has played an important role in the development of mathematics. By identifying the common rules that underlie logic and sets, we will be able to derive results that can be applied to both areas. The second reason for studying Boolean algebra is that the notation of Boolean algebra is widely used in computing, especially in the design of digital circuits. In the latter part of this chapter, we will see how Boolean algebra is used in designing the circuitry needed to perform digital computations. Let us start by recalling the work we did in Chapter 4 on propositional logic. The objects we were working with there were logical expressions. When we used a variable such as ...