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1、number system 數(shù)字系統(tǒng)numerical nju(:) merikl adj. 數(shù)字的, 用數(shù)表示的numerical value 數(shù)字值decimal desiml adj. 十進(jìn)制,十進(jìn)的,小數(shù)的,以十為基礎(chǔ)的n. 小數(shù)decimal system 十進(jìn)制系統(tǒng)binary bainri adj. 二進(jìn)制的,二進(jìn)位的, 二元的binary system 二進(jìn)制系統(tǒng)octal ktl 八進(jìn)制的octal system 八進(jìn)制系統(tǒng)hexadecimal heksdesIm()l adj. 十六進(jìn)制的n. 十六進(jìn)制 hexadecimal system 十六進(jìn)制系統(tǒng)digit did
2、it n. 阿拉伯?dāng)?shù)字base beis n. 底部, 基礎(chǔ), 根據(jù)地, 基地, 本部, 基數(shù) vt. 以.作基礎(chǔ), 基于.adj.低級(jí)的weight weit n. 權(quán)重,位權(quán),重量,分量power pau n. 數(shù)冪equivalent ikwivlnt adj. 相等的, 相當(dāng)?shù)? 同意義的n. 等價(jià)物, 相等物bit bit n. 位, 比特byte bait n.(二進(jìn)制的)字節(jié),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(guān)conversion of number 數(shù)字轉(zhuǎn)換BCD 二進(jìn)制編碼的十進(jìn)制multiply mltipli v.乘,增加remainder rimeind n. 余數(shù)adj. 剩余的Number System數(shù)字系統(tǒng)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(jì)算機(jī)。它是以O(shè)n或Off的形式(1或0)來(lái)存儲(chǔ)信息,也就是二進(jìn)制(位)的方式。有時(shí)二進(jìn)制數(shù)單獨(dú)使用,有時(shí)它們用來(lái)表示數(shù)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(jìn)制系統(tǒng)PLC中使用各種數(shù)制系統(tǒng)。所有的數(shù)制都有相同的三個(gè)屬性:數(shù)字、基數(shù)和權(quán)。十進(jìn)制系統(tǒng),也就是日常生活中經(jīng)常用的,具有下面屬性:十個(gè)數(shù)字:0,1,2,3,4,5,6,7,8,9基數(shù):10權(quán):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(jìn)制系統(tǒng)可編程序控制器中使用二進(jìn)制。二進(jìn)制系統(tǒng)具有下面的屬性:兩個(gè)數(shù)字:0,1基數(shù):2基數(shù)為2的位權(quán):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(jìn)制系統(tǒng)中的1s和2s排成列,每列對(duì)應(yīng)一個(gè)權(quán)。第一列具有二進(jìn)制權(quán)20。這個(gè)值等于十進(jìn)制的1。這就是最低有效位。二進(jìn)制中每列緊接的下一列的權(quán)是它的兩倍。例如,下一列的權(quán)是21,它相當(dāng)于十進(jìn)制中的2。相鄰著的下
9、一列的十進(jìn)制值是這列的兩倍。一個(gè)數(shù)中最左邊的列意味著具有最高的有效“位”。在這個(gè)例子中,最高的有效權(quán)具有二進(jìn)制位權(quán)27。它的值等于十進(jìn)制數(shù)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(jìn)制到十進(jìn)制的轉(zhuǎn)換下面步驟是用來(lái)說明如何將二進(jìn)制數(shù)轉(zhuǎn)換為十進(jìn)制數(shù)。1)從最低到最高找到有效位1s。2)將所有各列為1的位權(quán)所代表的十進(jìn)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(shù)第四、第五個(gè)數(shù)為1。從右第四位的1相當(dāng)于十進(jìn)制數(shù)8,從右第五位的1相當(dāng)于十進(jìn)制數(shù)16。這個(gè)二進(jìn)制數(shù)相應(yīng)的十進(jìn)制數(shù)是24。PLC中存儲(chǔ)的十進(jìn)制數(shù)是所有的各列為1的位權(quán)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(shù)第四和第六列為1。右面第四位所對(duì)應(yīng)的十進(jìn)制值是8,右面第六位所對(duì)應(yīng)的十進(jìn)制值是32。這個(gè)二進(jìn)制數(shù)相應(yīng)的十進(jìn)制數(shù)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(jié)和字二進(jìn)制最小單位是一位。每八位組成一個(gè)字節(jié)。兩個(gè)字節(jié)或16位組成一個(gè)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(hào)。在二進(jìn)制系統(tǒng)中只有1和0兩個(gè)數(shù)字。二進(jìn)制1表示有信號(hào)或開關(guān)為On.。二進(jìn)制0表示沒有信號(hào)或開關(guān)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(jìn)制編碼的十進(jìn)制(BCD)是每位由四位二進(jìn)制數(shù)表示的十進(jìn)制數(shù)。輸入和輸出設(shè)備上通常使用BCD編碼。撥盤開關(guān)就是利用BCD編碼進(jìn)行輸入的一個(gè)例子。二進(jìn)制數(shù)被分成四位一組,每組表示一個(gè)等值的十進(jìn)制數(shù)。如圖所示的四位撥盤開關(guān),將控制16(44)個(gè)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(jìn)制十六進(jìn)制是PLC使用的另一種系統(tǒng),十六進(jìn)制有下列屬性:十六個(gè)數(shù)字:0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F(xiàn)基數(shù):16基為16的位權(quán):(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(jìn)制中的十個(gè)數(shù)字被用作十六進(jìn)制系統(tǒng)中的前十個(gè)數(shù)字,字母表中的開始六個(gè)字符用作十六進(jìn)制系統(tǒng)中的其余六個(gè)數(shù)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(jìn)制系統(tǒng)在PLC中被采用,是由于它可以把很多的二進(jìn)制位的狀態(tài)表示在很小的空間中,比如表示在計(jì)算機(jī)屏幕或編程器的顯示屏上。每個(gè)十六進(jìn)制數(shù)字可以表示四位二進(jìn)制數(shù)字的準(zhǔn)確值。為了將十進(jìn)制數(shù)轉(zhuǎn)換為十六進(jìn)制數(shù),這個(gè)數(shù)要被基數(shù)16除。
20、例如,轉(zhuǎn)換十進(jìn)制28到十六進(jìn)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(jìn)制數(shù)28被16除,商為1,余數(shù)為12。12相當(dāng)于十六進(jìn)制中的C。十進(jìn)制28對(duì)應(yīng)的十六進(jìn)制數(shù)是1C。要得到十六進(jìn)制數(shù)對(duì)應(yīng)的十進(jìn)制的值,需要將十六進(jìn)制的各位分別乘對(duì)應(yīng)的位權(quán),然后相加。下面的例子把十六進(jìn)制數(shù)2B轉(zhuǎn)換為十進(jìn)制的等價(jià)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(shù)的轉(zhuǎn)換下面的表格顯示了幾個(gè)數(shù)分別以十進(jìn)制、二進(jìn)制、BCD和十六進(jìn)制表示的值。 CMOS( complementary metal-oxide-semiconduct OR Transistor)互補(bǔ)金屬氧化物半導(dǎo)體MOSFET( metallicoxide semiconductor field effect transistor)金屬氧化物半導(dǎo)體場(chǎng)效應(yīng)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(guān)switch 轉(zhuǎn)換,轉(zhuǎn)變transient trnnt current 瞬變電流momentary mumntri瞬間的intrinsic intrinsik 固有的,內(nèi)在的,本質(zhì)的consumption 消費(fèi)(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(chuàng)the second revolutionary in computational machines. The limits of speed and density were conquered解決 by the move發(fā)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(jiǎn)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(zhuǎn)換 from high to low or back. Quiescent 靜態(tài)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(jì)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(jì) 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(duì)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(shí) 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(shù)的 representation of the logical NOR equation.Verify驗(yàn)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(dāng), 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(zhí)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?
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