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通信与信息工程学院

二〇一五年

Passage B Binary System and Logic Systems

1.Binary System

A digital system functions in a binary manner.It employs devices which exist only in two possible states.A transistor is allowed to operate at cutoff or in saturation, but not in its active region.A node may be at high voltage of, say, 4±1V or at a low voltage of, say, 0.2±0.2V, but no values are allowed.Various designations are used for these two quantized states, and the most common are listed in Table 3.1.In logic,a statement is characterized as true or false, and this is the first binary classification listed in the table. A switch may be closed or open, which is the notation under 9, etc.Binary arithmetic and mathematical manipulation of switching or logic functions are best carried out with classification 3, which involves two symbols, 0(zero) and 1 (one).

The binary system of representing numbers will now be explained by making reference to the familiar decimal system.In the latter the base is 10(ten), and ten numerals,0,1,2,3···,9, are required to express an arbitrary number.To write numbers larger than 9, we assign a meaning to the position of numerals in an array of numerals.For example, the number 1264 (one thousand two hundred sixty four) has the meaning

1264=1×103＋2×102＋6×101＋4×100

Thus the individual digits in the number represent the coefficients in an expansion of the number in powers of 10.The digit which is farthest to the right is the coefficient of the zeroth power; the next is the coefficient of the firth power.and so on.

In the binary system of representation the base is 2, and only two numerals 0 and 1are required to represent a number.The numerals 0 and 1 have the same meaning as in the decimal system ,but a different interpretation is placed on the position occupied by a digit.In the binary system the two rather than ten as in the decimal system.For example, the decimal number 19 is written in the binary representation as 10011 since

10011=1×24＋0×23＋0×22＋1×21＋1×20 =16＋0＋0＋2＋1=19

A short list of equivalent numbers in decimal and binary notations is given in Table

3.2.

A general method for converting from a decimal to a binary number is indicated in Table 3.3.The procedure is the following.Place the decimal number (in this illustration,19) on the extreme right.Next divide by 2 and place the quotient (9) to the left and indicate the remember (1) directly below it.Repeat this process (for the next column 9÷2=4 and a remainder of 1) until a quotient of 0 is obtained.The array of 1’s and 0’s in the second row is the binary representation of the origin decimal number.In this example, decimal 19=10011 binary.

A binary digit (a 1 or a 0) is called a bit.A group of bits that has the same significance is called a byte, word, or code.For example, to represent the 10 numerals (0,1,2,3···,9) and the 26 letters of the English alphabet would require 36 different combinations of 1’s and 0’s.Since 25<36<26, then a minimum of 6 bits per bit are

required in order to accommodate all the alphanumeric characters.In this sense a bit is sometimes referred to as a character and a group of one or more characters as a word.

2. Logic Systems

In a DC, or level-logic, system a bit is implemented as one of two voltage levels.If, as in Figure 3.6(a), the more positive voltage is the 1 level and the other is the 0 level, the system is said to employ DC positive logic.On the other hand, a DC negative-logic system,as in Figure 3.6(b),i s one which designates the more negative voltage state of the bit as the 1 level and the more positive as the 0 level.It should be emphasized that the absolute values of the two voltages are of no significance in these definitions.In particular, the 0 state need not represent a zero voltage level (although in some systems it might).

The parameters of a physical device (for example,VCE·sat of a transistor) are not identical from sample to sample,and they also vary with temperature.Furthermore, ripple or voltage spikes may exist in the power supply or ground leads, and other sources of unwanted signals, called noise,may be present in the circuit.For these reasons the digital levels are not specified precisely, but as indicated by the shaded region in Figure 3.6,each state is defined by a voltage range about a designated level, such as 4±1V and 0.2±0.2V.

In a dynamic,or pulse-logic,system a bit is recognized by the present or absence of a pulse.At 1 signifies the existence of a positive pulse in a dynamic positive-logic system; a negative pulse denotes a 1 in a dynamic negative-logic system a 0 at a particular input (or output) at a given instant of time designates that no pulse is present at that particular moment.

B篇二进制系统和逻辑系统

1.二进制系统

一个数字系统作用以二进制方式。它采用只存在两种可能状态的设备。晶体管允许运行在截止或饱和，但不是在其活跃的区域。一个节点可以在高电压4±1V 或者在低电压下0.2±0.2V，但允许没有值。各种名称用于这两个量化状态，在表3.1中列举出了最常见的，声明定性为真或假，这是表中列出的第一个二进制分类。一个开关可能会被封闭或开放，这是在9以下的符号等。二进制算术和数学操作的开关或逻辑功能最好进行分类3，其中涉及2个符号，0（零）和1（1）。

代表数字的二进制系统现在可以通过对熟悉的十进制系统的引用来解释。在后者的基础是10（十），和十个数字，0、1、2、3···，9，需要表示任意数量。写数字大于9，我们分配一个意义的数字在数字数组的位置。例如，数字1264（一千二百六十四）的含义

1264=1×103＋2×102＋6×101＋4×100

因此在个人数的数字代表权为10数量的膨胀系数，数字的最右边是第零权系数；其次是第一权系数等。

在表象的基础上二进制是2，只有两个数字0和1被要求代表一个数字。数字0和1具有相同的含义，在十进制系统，但一个不同的解释放在一个由数字所

占据的位置。在二进制系统中表示的权为二而不是十进制系统中的十。例如，十进制数19用二进制表示为10011

10011=1×24＋0×23＋0×22＋1×21＋1×20 =16＋0＋0＋2＋1=19

在表3.2中给出了一个在十进制和二进制符号中的等效数字的简短列表。

在表3.3中表示一个将十进制转换为二进制数的一般方法。步骤如下，将十进制数（在这个例子中的19）放在最右边。然后除以2，把商（9）放在左侧和指示记住（1）在正下方。重复这个过程（下一列9÷2 = 4余1）直到得到一个商数为0。1和0阵列的第二行是原点十进制数的二进制表示。在这个例子中，十进制数19 = 10011二进制数。

一个二进制数字（1或0）称为一位。一组比特具有相同的意义被称为一个字节，字，或代码。例如，要表示10个数字（0、1、2、3···，9）和英文字母表中的26个字母，就0和1的36种不同的的组合。因为 25<36<26，，为了能表示所有的字母和数字，要求每个字节最少要有6个比特。在这个意义上，有时被称为一个字符和一组一个或多个字符作为一个字。

2.逻辑系统

在直流或层面逻辑,系统被实现为两个电压水平。如果,如图3.6(a)所示,把比特较高的电压记为1电平,较低的电压状态记为0电平,这样的系统称为直流正逻辑系统。另一方面，如图3.6（b）所示，把比特的较低的电压状态记为1电平，较高的电压状态记为0电平，这样的系统称为直流负逻辑系统。应该强调的是，这两个电压的绝对值是在这些定义处没有意义。特别是,0状态不需要代表零电压水平(尽管在一些系统中它可能).

物理元件的参数（例如，晶体管VCE·sat）是不相同的样品，他们也随温度的变化而变化。此外，电源和地线中还有可能有电压脉动和电压尖峰，电压中还有可能有其他不需要的被称为噪声的信号源。由于这些原因，我们不能把数字电平规定得太死，而要像图3.6的阴影所标示的那样，规定每一个状态都在指定电平附近的一段电压范围，例如4±1V及0.2±0.2V。

在一个动态的、或脉冲逻辑系统中一位被认为是一个脉冲的有无在。在动态正逻辑系统中，1表示有正脉冲存在，而在负逻辑系统中，负脉冲表示为1，不管哪种系统，某一时刻在某一输入（或输出）的0，均表示此刻无脉冲。