Question

自动化专业英语翻译

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.
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 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,
while retaining the same function. The equivalent simplified combination of gates will probably be much less expensive and less difficult to assemble.
Rules of Boolean algebra for digital devices
Boolean algebra has three rules of combination, as any algebra must have: the associative, the commutative, and the distributive rules. To show the features of the algebra we use the variables A, B, C, and so on. To write relations between variables each one of which may take the value 0 or l, we use to mean “not A,” so if A = l , then = 0. The complement of every variable is expressed by placing a bar over the variable; the complement of = "not B". Two fixed quantities also exist. The first is identity, I = l; the other is null, null = 0.
Boolean algebra applies to the arithmetic of three basic types of gates: an OR-gate, an AND-gate and the inverter. The symbol and the truth tables for the logic gates are shown in Fig.2-3, the truth table illustrate that the AND-gate corresponds to multiplication, the OR-gate corresponds to addition, and the inverter yield the complement of its input variable.
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Answer 1

以下结果来自百度，希望能够帮点忙！认真学习吧！！！
布尔代数的数字系统

景区简介

数学计算机及其他电子设备已开发的决定性的工作从布尔（l815～l864）和许多其他人，谁扩大和改进他的工作。主体思想是统称为符号逻辑建立的原则所产生的数学证明和奇修改我们的理解和数学的范围。

只有一部分这一强大的系统需要使用。布尔和其他有兴趣的发展有系统的手段决定是否在逻辑或数学命题是真或假，但我们应该只关注的有效性，输出的数字设备。真和假可以等同于一个零，高，低，或上下。这些仅是两国的电压从一个数字元件。因此，在这一非凡的代数的逻辑大门，仅有2值，一个零；任何代数组合或操纵可以产生的价值。零和一个是唯一在二进制算术符号。

各种逻辑大门和它们之间可以进行所有的基本职能所需要的计算和决策。发展数字系统最简单的程序，把概念的大门和连接以执行指定的任务，以最直接的方式。布尔代数是用来降低系统复杂度，如果可能的话，

同时保留了同样的功能。等效简化组合的大门可能会更昂贵和更难集合。

布尔代数的数字器件

布尔代数有三个组合规则，任何代数必须有：联想，交换，和分布的规律。显示功能的代数我们使用变量，乙，丙，等等。写变量之间的关系，每一种可能的值为0或1，我们使用的是“不，“所以如果=我，然后=0。补充变量是由放置一个酒吧在变；补充=“乙”。固定数量也存在。首先是身份，我=我；另一是空，空=0。

布尔代数的算法适用于三个基本类型的大门：一个或门，与门和逆变器。符号和事实表的逻辑大门都显示在fig.2-3，事实表说明，与门相当于乘法，或门相当于增加产量，以及逆变器的补充其输入变量。

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。。。。。不管怎么说，谢啦

追答

OK！

Answer 2

用于数字系统的布尔代数
概述
计算机数学和其它数字电子设备的发展是基于乔治·布尔决定性的研究成果，其他科学家在此基础上进行了拓展与完善。象征逻辑思想建立了数学证明的原则，使我们对数学的理解和视野发生了不可思议的改变。
强大的体系中只有一部分为我们所用。布尔和其它科学家想发展出一套体系方法，可以判断逻辑或数学假设是否正确，但我们只应该关注数字设备输出的效量。正确和错误可以对应1和0，高和低，开和关，这些只不过是数字元件电压的两种状态。所以，用逻辑门控制的代数学中只有两个值——1和0。一切代数组合与操作只能得出这两个数值。在二进制算术中，0和1仅仅是两个象征性数字。各种各样的逻辑门和相互关联可以为计算和制定决策产生极为重要的功能。在发展各种数字系统中，最简单的过程就是把各种概念性的逻辑门和关联组合在一起，以最直接的方式执行所分配的任务。如果可能的话，布尔代数在保证功能不变的同时，还可以减少这些系统的复杂性。这些功能相同，被简化了的逻辑门组合很有可能会成本下降，组装起来更容易些。

用于数字设备的布尔代数的规则

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还有一小段嘛