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The course provides the fundamental concepts used in the design of digital systems, including the methodology to design the combinational and sequential circuits with Boolean Algebra, Karnaugh map, and the logic elements, such as basic logic gates, latches, and flip-flops,etc.

本课程在提供数位系统设计所须具备的基础能力,包括学习以布林代数、卡诺图来设计组合逻辑与序向逻辑电路的方法,以及培养基础逻辑元件的应用能力,包括基本逻辑闸、栓锁器、与正反器等等元件。

As a logic optimization method,the Boolean algebra was introduced for the analysis and simplification of complicated logic diagram and on-off control system.

本文通过火电厂开关量控制系统优化设计的分析,对逻辑优化的基本方法进行初步探讨。1容错逻辑设计方法仅根据被控设备的工艺要求设计逻辑,往往经不起实际运行的考验。

The results obtained in the thesis are as follows: Firstly, the thesis proves that the inner measure and outer measure which defined by Fagin and Halpern are a kind of random sets, generalizes the concept of random sets to Boolean algebra's, and hence establishes the theory of the generalization of random sets.

本文的主要结果如下:①本文证明了Fagin和Halpern提出的内、外测度可表示为一种随机集合,并把随机集合的概念从幂集合推广到了布尔代数上,从而提出了广义随机集合理论。

In Chapter 3,we classify a binary-coded individual space equivalently withthe help of the ideals of Boolean algebra and analyze the search capabilitiesof a new kind of algebraic crossover operator in these equivalence classes,thenprovide the algebraic representation of a type of genetic algorithms by usingthe permutation group,therefore we can derive a lot of new forms of geneticalgorithms.

第三章运用Boole代数的理想将二进制编码的个体空间进行等价分类,分析了一类代数杂交算子在这些等价类上的搜索能力;然后利用置换群给出一类遗传算法的代数表示,由此导出多种新形式的遗传算法,并给出其中两类算法形式的收敛性结果。

8 Chapter 3 Number Systems and Boolean Algebra 3.1.2 Positional Notation The exponential powers of the positions are critical for understanding numbers in other numbering systems.

位的指数幂在理解其他计数制中的数时是个关键。基数小数位的指数幂在理解其他计数制中的数时是个关键。

11 Chapter 3 Number Systems and Boolean Algebra 3.1.2 Positional Notation Example 3-1 shows a 110.101 in binary (often written as 110.1012). It also shows the power and weight or value of each digit position.

给出了一个二进制数110.101(通常写成通常写成110.1012),也给出了这个数每例3-1给出了一个二进制数给出了一个二进制数通常写成,个位的幂,权和值。

The sufficient and necessary conditions which Fuzzy subalgebra of direct product Boolean algebra can be decomposed as direct product of two Fuzzy subalgebras are obtained.

进而分别定义了在对偶模意义下直觉模糊群的外直积与内直积。

Difference set is one kind of unbounded difference poset. The existenceof the tensor products of two cancellative difference sets are investigated. It isproved that the tensor product of a Boolean algebra and a cancellative differenceset always exists.

作为差分偏序集无界推广的差分集,我们研究了它的张量积问题,证明了任何消去差分集和布尔代数的张量积一定存在。

23 Chapter 3 Number Systems and Boolean Algebra 3.1.6 Complements Today, the radix -1 complement is not used by itself; it is used as a step for finding the radix complement. The radix complement is used to represent negative numbers in modern computer systems.

如今,反码已不单独使用,而作为求补码的一个步骤使用,如今,反码已不单独使用,而作为求补码的一个步骤使用,补码是当代计算机系统表示负数的方法(反码用于早期的计算补码是当代计算机系统表示负数的方法反码用于早期的计算技术中)。

24 Chapter 3 Number Systems and Boolean Algebra 3.1.6 Complements To form the radix complement, first find the radix -1 complement, and then add a one to the result.

为得到补码,先求反码,然后将加到结果上加到结果上。为得到补码,先求反码,然后将1加到结果上。

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