Logic and Gates
Logic is an organized method of reasoning.Therefore, logic must be used when making decisions,or when calculating or processing data. One logical methodology used in the design of all digital computers is called Boolean Algebra. It was developed by anEnglishman George Boole around 1947．In 1938，Claude E．Shannon, a research assistant at MIT,published a paper describing how Boolean algebra could be used to represent two-state, or binary, circuits used in today's modem digital computers．
Boolean algebra uses three basic opcrators：logical multiplication,called the AND function;logical add1tion, called the OR function; and logical complementation，called the NOT function. The variables in Bolean algebra is binary. That is, the resulting Vaiiable of an operation or a set of operations can have only one of two values: 1 or O.Varlables may also be interpreted as being true or false, or yes or no.
Gates and inverters are circuits that are used to implement the basic logic functions. An inverter is alogic circuit that has one input and one output. A gate is a logic circuit that has at least two input and one output. These gates and inverters are made up of transistors diodes，and resistors．In the present tech-nology they are always packaged as integrated circults, and there are anywhere from two to many thou-sand gates and/or inverters in a single chip. All the Flip-flops，registers，counters, adders, and otherlogic circuits in a computer arc made up of these basic circuits．
To develop all understanding of how gates and inverters are used in a computer，we must first de-velop an understanding of the logic functions they canperform. All input and output variables can have only one of two possible states-true or false. Because this true, Boolean algebra becomes a valuable tool tothe designer and to the technician because we canutilize the laws and theorems of Boolean algebra to simplify complex circuits and to help us understand existing circuits and systems.
翻译:
逻辑及逻辑门
逻辑是推理的一种有组织的方法，因此，当做决定或者计算或处理数据时，必须采用逻辑，在设计所有数字计算机时所采用的一种逻辑方法（学）叫做布尔代数。 它是由英国人乔治布尔于1847年左右研究出来的。 1938年，麻省理工学院的一位研究助教克劳德香农发表了一篇文章，其中论述了布尔代数如何可被用来表示在当今现代数字计算机中所用的两态（或二进制）电路。
布尔代数采用三种基本运算，逻辑乘也叫做“与”函数；逻辑加也叫做“或”函数；逻辑补，也叫 做“非”函数，布尔代数中的变量是二进制的，就是说，一种或一组运算的最终变量，仅能具有二值之一：I或0.变量也可被解释为真或 假，是或否（非）。
门和反相器是用来实现基本逻 辑函数的电路，反相器是具有一个输入（端）和一个输出（端）的逻辑电路。门是至少具有两个输入 （端）和•个输出（端）的逻辑毛路。这些门和反相器是由晶体管、 二极管及电阴器组成的，在现代技 术中，它们总是以集成电路的形式加以封装，总是集成了从两个到数千个门和（或）反相器在单个芯片上。在计算机中，所有的触发器、 寄存器、计数器、加法器以及其他逻辑电路，都是由这些电路构成的。
为了提高对在计算机中怎样天用门和反相器的理解，首先，我们必须提高对门和反相器所能执行色 逻辑函数的理解，所有的输入和转出变量只能具有两个可能状态之一真或假。这一点是对的．所以布尔代数对于设计师和技术人员成为有价值的工具。因此我们可以利用布尔代数的定律和定理简单复杂的电路，并且帮助我们理解现存的电路及系统。
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