电气专业毕业设计中英文对照翻译Word文档格式.docx

1、3.2 Digital Number SystemsThe most common number system used today is the decimal system,in which 10 digits are used for counting. The number of digits in the system is called its base （or radix）.The decimal system，therefore，has a base of 10.Numbering systems have a place value，which refers to the p

2、lacement of a digit with respect to others in the counting process. The largest digit that can be used in a specific place or location is determined by the base of the system. In the decimal system the first position to the left of the decimal point is called the units place. Any digit from 0 to 9 c

3、an be used in this place.When number values greater than 9 are used,they must be expressed with two or more places.The next position to the left of the units place in a decimal system is the tens place.The number 99 is the largest digital value that can be expressed by two places in the decimal syst

4、em.Each place added to the left extends the number system by a power of 10.Any number can be expressed as a sum of weighted place values.The decimal number 2583,for example, is expressed as （21000）+（5100）+（810）+（31）.The decimal number system is commonly used in our daily lives. Electronically, howev

5、er, it is rather difficult to use. Each digit of a base 10 system would require a specific value associated with it, so it would not be practical.3.2.1 Binary Number SystemElectronic digital systems are ordinarily the binary type，which has 2 as its base. Only the numbers 0 or 1 are used in the binar

6、y system.Electronically,the value of 0 can be associated with a low-voltage value or no voltage. The number 1 can then be associated with a voltage value larger than 0. Binary systems that use these voltage values are said to have positive logic. Negative logic,by comparison,has a voltage assigned t

7、o 0 and no voltage value assigned to 1 .Positive logic is used in this chapter.The two operational states of a binary system,1 and 0,are natural circuit conditions. When a circuit is turned off or has no voltage applied，it is in the off, or 0,state. An electrical circuit that has voltage applied is

8、in the on，or 1,state. By using transistor or ICs，it is electronically possible to change states in less than a microsecond. Electronic devices make it possible to manipulate millions of 0s and is in a second and thus to process information quickly.The basic principles of numbering used in decimal nu

9、mbers apply in general to binary numbers.The base of the binary system is 2,meaning that only the digits 0 and 1 are used to express place value. The first place to the left of the binary point,or starting point，represents the units，or is,location. Places to the left of the binary point are the powe

10、rs of 2.Some of the place values in base 2 are 2=1,2=2,2=4,2=8,2=16,25=32,and 26=64.When bases other than 10 are used,the numbers should have a subscript to identify the base used.The number 100is an example.The number 100（read“one,zero,zero, base 2”）is equivalent to 4 in base 10,or 410.Starting wit

11、h the first digit to the left of the binary point,this number has value （020）+（021）+（122）.In this method of conversion a binary number to an equivalent decimal number，write down the binary number first. Starting at the binary point，indicate the decimal equivalent for each binary place location where

12、 a 1 is indicated. For each 0 in the binary number leave a blank space or indicate a 0 Add the place values and then record the decimal equivalent.The conversion of a decimal number to a binary equivalent is achieved by repetitive steps of division by the number 2.When the quotient is even with no r

13、emainder,a 0 is recorded.When the quotient has a remainder. as 1 is recorded.The division process continues until the quotient is 0.The binary equivalent consists of the remainder values in the order last to first.3.2.2 Binary-coded Decimal （BCD） Number SystemWhen large numbers are indicated by bina

14、ry numbers，they are difficult to use. For this reason，the Binary-Coded Decimal（BCD） method of counting was devised. In this system four binary digits are used to represent each decimal digit.To illustrate this procedure，the number 105，is converted to a BCD number.In binary numbers，10510=10001012.To

15、apply the BCD conversion process，the base 10 number is first divided into digits according to place values.The number 10510 gives the digits 1-0-5.Converting each digit to binary gives 0001-0000-0101BCD.Decimal numbers up to 99910 may be displayed by this process with only 12 binary numbers. The hyp

16、hen between each group of digits is important when displaying BCD numbers.The largest digit to be displayed by any group of BCD numbers is 9.Six digits of a number-coding group are not used at all in this system.Because of this, the octal （base 8） and the hexadecimal （base 16） systems were devised.

17、Digital circuits process numbers in binary form but usually display them in BCD,octal,or hexadecimal form.3.2.3 Octal Number SystemThe octal （base 8） number system is used to process large numbers by digital circuits.The octal system of numbers uses the same basic principles as the decimal and binar

18、y systems.The octal number system has a base of 8. The largest number used in a base 8 system is 7. The place values starting at the left of the octal point are the powers of eight: 80=1,81=8,82=64,83=512,84=4096,and so on. The process of converting an octal number to a decimal number is the same as

19、 that used in the binary-to-decimal conversion process. In this method,however,the powers of 8 are used instead of the powers of 2. The number for changing 3828 to an equivalent decimal is 25810.Converting an octal number to an equivalent binary number is similar to the BCD conversion process. The o

20、ctal number is first divided into digits according to place value. Each octal digit is then converted into an equivalent binary number using only three digits.Converting a decimal number to an octal number is a process of repetitive division by the number 8.After the quotient has been determined，the

21、 remainder is brought down as the place value.When the quotient is even with no remainder，a 0 is transferred to the place position.The number for converting 409810 to base 8 is 100028.Converting a binary number to an octal number is an important conversion process of digital circuits. Binary numbers

22、 are first processed at a very high speed. An output circuit then accepts this signal and converts it to an octal signal displayed on a readout device.Assume that the number 1101001002 is to he changed to an equivalent octal number. The digits must first be divided into groups of three，starting at t

23、he octal point.Each binary group is then converted into an equivalent octal number.These numbers are then combined，while remaining in their same respective places，to represent the equivalent octal number.3.2.4 Hexadecimal Number SystemThe hexadecimal number system is used in digital systems to proce

24、ss large number values.The base of this system is 16，which means that the largest number used in a place is 15.Digits used by this system are the numbers 0-9 and the letters A-F. The letters A-P are used to denote the digits 10-15，respectively. The place values to the left of the hexadecimal point a

25、re the powers of 16:160=1，161=16，162=256, l63=4096，164=65536， and so on.The process of changing a hexadecimal number to a decimal number is similar to that outlined for other conversions. Initially，a hexadecimal number is recorded in proper digital order.The place values，or powers of the base，are th

26、en positioned under the respective digits in step 2.In step 3，the value of each digit is recorded. The values in steps 2 and 3 are then multiplied together and added. The sum gives the decimal equivalent value of a hexadecimal number.The process of changing a hexadecimal number to a binary equivalen

27、t is a simple grouping operation. Initially，the hexadecimal number is separated into digits. Each digit is then converted to a binary number using four digits per group. The binary group is combined to form the equivalent binary number.The conversion of a decimal number to a hexadecimal number is ac

28、hieved by repetitive division，as with other number systems. In this procedure the division is by 16 and remainders can be as large as 15.Converting a binary number to a hexadecimal equivalent is the reverse of the hexadecimal to binary process. Initially，the binary number is divided in groups of fou

29、r digits，starting at the hexadecimal point. Each number group is then converted to a hexadecimal value and combined to form the hexadecimal equivalent number.3.3 Binary Logic CircuitsIn digital circuit-design applications binary signals are far superior to those of the octal，decimal，or hexadecimal systems. Binary signals can be processed very easily through electronic circuitry，since they can be represented by two stable states of operation. These states can be easily defined as on or off, 1 or 0，up or down，voltage or no volta