1、number system 數字系統numerical nju(:) merikl adj. 數字的, 用數表示的numerical value 數字值decimal desiml adj. 十進制,十進的,小數的,以十為基礎的n. 小數decimal system 十進制系統binary bainri adj. 二進制的，二進位的, 二元的binary system 二進制系統octal ktl 八進制的octal system 八進制系統hexadecimal heksdesIm()l adj. 十六進制的n. 十六進制 hexadecimal system 十六進制系統digit did

2、it n. 阿拉伯數字base beis n. 底部, 基礎, 根據地, 基地, 本部, 基數 vt. 以.作基礎, 基于.adj.低級的weight weit n. 權重，位權，重量,分量power pau n. 數冪equivalent ikwivlnt adj. 相等的, 相當的, 同意義的n. 等價物, 相等物bit bit n. 位, 比特byte bait n.（二進制的）字節，位組word w:d n. 字, 詞succeeding sksi:diN adj. 以后的，隨后的logic 0 邏輯0logic 1 邏輯1programmable controller 可編程控制器t

3、humbwheel switch 指輪開關conversion of number 數字轉換BCD 二進制編碼的十進制multiply mltipli v.乘,增加remainder rimeind n. 余數adj. 剩余的Number System數字系統PLC is a computer. it stores information in the form of On or Off conditions (1 or 0), referred to as binary digits (bits). Sometimes binary digits are used individually

4、and sometimes they are used to represent numerical values.PLC就是一種計算機。它是以On或Off的形式（1或0）來存儲信息，也就是二進制（位）的方式。有時二進制數單獨使用，有時它們用來表示數字值。Decimal SystemVarious number systems are used by PLCs. All number systems have the same three characteristics: digits, base, weight. The decimal system, which is commonly u

5、sed in everyday life, has the following characteristics: Ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9Base 10Weights 1, 10, 100, 1000, .1十進制系統PLC中使用各種數制系統。所有的數制都有相同的三個屬性：數字、基數和權。十進制系統，也就是日常生活中經常用的，具有下面屬性：十個數字：0，1，2，3，4，5，6，7，8，9基數：10權：1，10，100，10002.Binary System The binary system is used by programmable

6、controllers. The binary system has the following characteristics:Two digits 0, 1Base 2Weights Powers of base 2 (1, 2, 4, 8, 16, .)2 二進制系統可編程序控制器中使用二進制。二進制系統具有下面的屬性：兩個數字：0，1基數：2基數為2的位權：1，2，4，8，16In the binary system 1s and 0s are arranged into columns. Each column is weighted. The first column has a

7、binary weight of 20. This is equivalent to a decimal 1. This is referred to as the least significant bit. The binary weight is doubled with each succeeding column. The next column, for example, has a weight of 21, which is equivalent to a decimal 2. The decimal value is doubled in each successive co

8、lumn. The number in the far left hand column is referred to as the most significant bit. In this example, the most significant bit has a binary weight of 27. This is equivalent to a decimal 128. 在二進制系統中的1s和2s排成列，每列對應一個權。第一列具有二進制權20。這個值等于十進制的1。這就是最低有效位。二進制中每列緊接的下一列的權是它的兩倍。例如，下一列的權是21，它相當于十進制中的2。相鄰著的下

9、一列的十進制值是這列的兩倍。一個數中最左邊的列意味著具有最高的有效“位”。在這個例子中，最高的有效權具有二進制位權27。它的值等于十進制數128。 3.Converting Binary to DecimalThe following steps can be used to interpret a decimal number from a binary value.1)Search from least to most significant bit for 1s2)Write down the decimal representation of each column containin

10、g a 1.3)Add the column values.3 二進制到十進制的轉換下面步驟是用來說明如何將二進制數轉換為十進制數。1）從最低到最高找到有效位1s。2）將所有各列為1的位權所代表的十進制都記下。3）將各列的值相加。In the following example, the fourth and the fifth columns from the right contain a 1. The decimal value of the fourth column from the right is 8,and the decimal value of the fifth colu

11、mn from the right is 16. The decimal equivalent of this binary number is 24. The sum of all the weighted columns that contain a 1is the decimal number that the PLC has stored. 在下面的例子中，從右數第四、第五個數為1。從右第四位的1相當于十進制數8，從右第五位的1相當于十進制數16。這個二進制數相應的十進制數是24。PLC中存儲的十進制數是所有的各列為1的位權的和。If the fourth and the sixth

12、columns from the right contain a 1. The decimal value of the fourth column from the right is 8,and the decimal value of the sixth column from the right is 32. The decimal equivalent of this binary number is 40. 如果從右數第四和第六列為1。右面第四位所對應的十進制值是8，右面第六位所對應的十進制值是32。這個二進制數相應的十進制數是40。4.Bits, Bytes, and WordsE

13、ach binary piece of data is a bit. Eight bits make up one byte. Two bytes, or 16 bits, make up one word.4位、字節和字二進制最小單位是一位。每八位組成一個字節。兩個字節或16位組成一個字。5.Logic 0,Logic 1Programmable controllers can only understand a signal that is On or Off. The binary system is a system in which there are only two number

14、s, 1 and 0. Binary 1 indicates that a signal is present, or the switch is On. Binary 0 indicates that a signal is not present, or the switch is Off. 5邏輯0，邏輯1可編程序控制器只能理解On或Off信號。在二進制系統中只有1和0兩個數字。二進制1表示有信號或開關為On.。二進制0表示沒有信號或開關為Off。6.BCDBinary-Coded Decimal are decimal numbers where each digit is repre

15、sented by a four-bit binary number. BCD is commonly used with input and output devices. A thumb wheel switch is one example of an input devices that uses BCD. The binary numbers are broken into groups of four bits representing a decimal equivalent. A four-digit thumb wheel switch, like the one shown

16、 here, would control 16(4x4) PLC input. 6BCD碼二進制編碼的十進制（BCD）是每位由四位二進制數表示的十進制數。輸入和輸出設備上通常使用BCD編碼。撥盤開關就是利用BCD編碼進行輸入的一個例子。二進制數被分成四位一組，每組表示一個等值的十進制數。如圖所示的四位撥盤開關，將控制16（44）個PLC的輸入。 7.HexadecimalHexadecimal is anther system used in PLCs. The hexadecimal system has the following characteristics.16 digits:Bas

17、e: 16Weights Powers of base 16: ：（1，16，256，4096） 7十六進制十六進制是PLC使用的另一種系統，十六進制有下列屬性：十六個數字：0，1，2，3，4，5，6，7，8，9，A，B，C，D，E，F基數：16基為16的位權：（1，16，256，4096）The ten digits of the decimal system are used for the first ten digits of the hexadecimal system. The first six letters of the alphabet are used for the r

18、emaining six digits.十進制中的十個數字被用作十六進制系統中的前十個數字，字母表中的開始六個字符用作十六進制系統中的其余六個數字。A=10D=13B=11E=14C=12F=15The hexadecimal system is used in PLCs because it allows the large number of binary bits to be represented in a small space such as on a computer screen or programming device display. Each hexadecimal d

19、igit represents the exact status of four binary bits. To convert a decimal number to a hexadecimal number is divided by the base of 16.to convert decimal 28, for example, to hexadecimal: 十六進制系統在PLC中被采用，是由于它可以把很多的二進制位的狀態表示在很小的空間中，比如表示在計算機屏幕或編程器的顯示屏上。每個十六進制數字可以表示四位二進制數字的準確值。為了將十進制數轉換為十六進制數，這個數要被基數16除。

20、例如，轉換十進制28到十六進制：Decimal 28 divided by 16 is 1 with a remainder of 12.12 is equivalent to C in hexadecimal. The hexadecimal equivalent of decimal 28 is 1C. The decimal value of a hexadecimal number is obtained by multiplying the individual hexadecimal digits by the base 16 weight and then adding the

21、results. In the following example the hexadecimal number 2B is converted its decimal equivalent of 43.十進制數28被16除，商為1，余數為12。12相當于十六進制中的C。十進制28對應的十六進制數是1C。要得到十六進制數對應的十進制的值，需要將十六進制的各位分別乘對應的位權，然后相加。下面的例子把十六進制數2B轉換為十進制的等價值43。160 = 1161 = 16B = 11 8.Conversion of NumbersThe following chart shows a few num

22、eric values in decimal, binary, and hexadecimal representation.8 數的轉換下面的表格顯示了幾個數分別以十進制、二進制、BCD和十六進制表示的值。 CMOS( complementary metal-oxide-semiconduct OR Transistor)互補金屬氧化物半導體MOSFET( metallicoxide semiconductor field effect transistor)金屬氧化物半導體場效應晶體管Inverter inv：t 反相器an open-collector inverter 集電極開路反相器

23、Inverter switch 換向開關switch 轉換，轉變transient trnnt current 瞬變電流momentary mumntri瞬間的intrinsic intrinsik 固有的，內在的，本質的consumption 消費(量)；消盡，消耗dissipate dis,peit 消耗Boolean 布爾truth table 真值表gate 邏輯門Pull-up resistor 牽引電阻，上拉電阻Propagation delay 傳輸延遲 Digital circuit elements1.CMOS Element and Watch SwitchingThe c

24、omplementary MOSFET scheme (or CMOS) started 開創the second revolutionary in computational machines. The limits of speed and density were conquered解決 by the move發展 to semiconductors and Very Scale Integration, but the power consumption消耗 and circuit cooling demands of bipolar transistors packed at ext

25、reme非常的 densities were formidable艱難的 problems. The problem is that the transistors were always “ON” (in other words drawing吸取 current and dissipating energy). CMOS circumvents this problem and allow bits to be stored without constant power consumption. A schematic簡圖 of the CMOS inverter反相器 is given

26、in the figure below. As discussed in class the device dissipates energy only when it is switched轉換 from high to low or back. Quiescent 靜態的 operation in either the high or the low state dissipates essentially no power. So cooling the circuit is much easier, and supplying power is much less of a probl

27、em. If you dont believe me, just ask your calculator計算器, digital watch or your laptop便攜電腦.Connect VDD=+5V and ground to the CD4007 pins as depicted描述 below using only one set of transistors. For example, VI=pin 10,VDD=pin 11,GND=pin 9 and VO=pin 12. Connect a 500 resistor between VDD and pin 11 for

28、better performance性能.Slowly ramp the input voltage from zero up to 3.5V. At some point the output should switch from high to low. Note the voltage where the switch occurs.Now connect a 100 resistor in series with pin 9 above the ground point.Try to measure the transient瞬間的 current (momentary瞬間的 volt

29、age across the resistor ) as you slowly ramp the input voltage up and down to make the output switch. If you cant see signal you can cheat by using the Miller effect by adding a medium sized capacitor between output and ground.Try to measure the intrinsic固有的 switching time and estimate估計 the power c

30、onsumption for such an inverter switched at 1MHz compare with a bipolar circuit where the devices are constantly passing current.Estimate the power consumption for switching at 1GHz.2.Gates , Truth Tables, and Pull-up ResistorsOne of the simplest gates is the inverter. The Boolean equation for the i

31、nverter is Y=A-The following is the diagrammatic representation of the inverter.The 7404 chip contain 6 inverters and be schematically represented as followsThe diagram of the chip is drawn as if you are viewing it from above. Note the thick blank line that is used as an orientation定位 mark, located

32、at the left end of the chip. Also note that pins 14 and 7 are connected to an inverter, they are the power supply connections for the chip. Pin 14 must be held at +5V with respect to相對于 pin 7. No pin may be held at a voltage greater than that at pin 14 or less than that at pin 7. So if pin 14 is hel

33、d at +5V then nothing can be greater than +5V and if pin 7 is grounded then you cannot have a voltage to the chip that is less than 0V. This supply pin assignment 用途is common for 7400 series TTL. If you have a question about the wiring of a particular chip, refer to the TTL cookbook詳盡說明書; a copy wil

34、l be kept in the lab. You may also use the websites linked to the course homepage.3. Procedure步驟Wire a 7404 inverter, on the Digit-Designer as followApply a clock signal from the clock on the Digit-designer Box to the input of one of the inverters in the 7404 IC chip. Simultaneously同時 look at the in

35、put and output on the oscilloscope and also the LEDs on the Digit-Designer for a range of clock frequencies from 1kHz to 100kHz.Comment on the input and output of the circuit. Are there any timing problems with this circuit?3) Wire 6 inverters from the 7404 IC chip in series. Connect the Digit-Desig

36、ner clock to the first inverter.Observe the input of the 1st and the output of the last inverter simultaneously on the oscilloscope. Determine the “Propagation delay傳輸延遲” through a signal inverter.4) Wire the following circuit using an open-collector inverter (7404). The 2k”pull-up” resister is nece

37、ssary for speed and noise immunity抗干擾性 when driving a TTL input. The numbers that you see on the diagram are to distinguish the input pins on the 7404 IC chip. So the 1 means that the input A should be connected to pin 1 on the 7404 IC chip and so on. The equation at the bottom right is the algebrai

38、c代數的 representation of the logical NOR equation.Verify驗證 that the circuit performs the logical NOR function.How does the inverter output differ from an inverting Op-amp that you worked with in Lab 6?4.B-2 Translating Boolean Equations Into Electronic CircuitsIn many cases translation of Boolean equa

39、tions into electronic logic can be plished by a straightforward直截了當, one-for-one replacement替代 of a term or group of terms in the equation by a gate. As an illustration例子 ,we will consider the 4-input data selector or “multiplexer”.We have four digital signals that we would like to be able to send o

40、ver a signal wire. We need logic that defines the output Y of a circuit to be the nth input signal Xn, where the number, n, is given. Since n can take on 4 values, it must be a 2-digit binary number, which we will call BA. In other words, BA selects the input Xn, which will appear on the output. The

41、 truth table expressing this circuit is:From this table, a Boolean equation can be written by inspection.From the Boolean equation above , the following schematic that describes the equation can be drawn.In implementing執行 the logic displayed in this diagram, we are slightly hampered妨礙，阻撓 by the fact that a 7400 series 4-input OR gate does not exist. The elegant 極好的solution to this problem involves DeMorgans Theorem德摩根定律 to transform one into the other.Build the above circuit on your digit-Designer and write out the truth table for the circuit. (Isnt this a real pain to build?