电气工程与自动化专业英语PPT课件2-2.ppt

* Chapter 2 Electronics Section 2 Boolean Algebra for Digital Systems Text New Words and Expressions Exercises End Selection of Word Meaning Section 2 Boolean Algebra for Digital Systems Introduction The mathematics of computers and other digital electronic devices have been developed from the decisive work of George Boole (l815～l864) and many others, who expanded and improved on his work. The body of thought that is known collectively as symbolic logic established the principles for deriving mathematical proofs and singularly modified our understanding and the scope of mathematics. Section 2 Boolean Algebra for Digital Systems Only a portion of this powerful system is required for our use. Boole and others were interested in developing a systematic means of deciding whether a proposition in logic or mathematics was true or false, but we shall be concerned only with the validity of the output of digital devices. True and false can be equated with one and zero, high and low, or on and off. These are the only two states of electrical voltage from a digital element. Thus, in this remarkable algebra performed by logic gates, there are only two values, one and zero; any Section 2 Boolean Algebra for Digital Systems algebraic combination or manipulation can yield only these two values. Zero and one are the only symbols in binary arithmetic. The various logic gates and their interconnections can be made to perform all the essential functions required for computing and decision-making. In developing digital systems the easiest procedure is to put together conceptually the gates and connections to perform the assigned task in the most direct way. Boolean algebra is then used to reduce the complexity of the system, if possible, Section 2 Boolean Algebra for Digital Systems while retaining the same function. The equivalent simplified combination of gates will probably be much less expensive and less difficult to assemble. Rules of Bool