计算机组成远离英文材料.pdf

“计算机组成原理”英文教材 1 1 IN THIS CHAPTER 2-1 Data Types 2-2 Complements 2-3 Fixed-Point Representation 2-4 Floating-Point Representation 2-5 Other Binary Codes 2-6 Error Detection Codes 2-1 Data Types Binary information in digital computers is stored in memory or processor registers.Registers contain either data or control information.Control information is a bit or a group of bits used to specify the sequence of command signals needed for manipulation of the data in other registers.Data are numbers and other binary-coded information that are operated on to achieve required computational results.In this chapter we present the most common types of data found in digital computers and show how the various data types are represented in binary-coded form in computer registers.The data types found in the registers of digital computers may be classified as being one of the following categories:(1)numbers used in arithmeticcomputations,(2)letters of the alphabet used in data processing,and(3)otherdiscrete symbols used for specific purposed.All types of data,except binary numbers,are represented in computer registers in binary-coded form.This is because registers are made up of flip-flops and flip-flops are two-state devices that can store only 1 s and 0 s.The binary number system is the most natural system to use in a digital computer.But sometimes it is convenient to employ different number systems,especially the decimal number system,since it is used by people to perform arithmetic computations.Number Systems A numbersystem of base,or radix,r is a system that uses distinct symbols for r digits.Numbers are representeed by a string of digit symbols.To determine the quantity that the number represents,it is necessary to multiply each digit by an integer power of r and then form the sum of all weighted digits.For example,the decimal number system in everyday use employs the radix 10system.The 10 symbols are 0,1,2,3,4,5,6,7,8,and 9.The string of digits 724.5 is interpreted to represent the quantity.7102+2101+4100+510-1 that is,7 hundreds,plus 2 tens,plus 4 units,plus 5 tenths.Every decimal number can be similarly interpreted to find the quantity it represents.CHAPTER TWO Data Representation(选自 M.M O R R I S M A N O C O M P U T E R S Y S T E M A R C H I T E C T U R E T H I R D E D I T I O N )“计算机组成原理”英文教材 2 2 The binary number system uses the radix 2.The two digit symbols used are 0 and 1.The string of digits 101101 is interpreted to represent the quantity 125+024+123+122+021+120=45 To distinguish between different radix numbers,the digits will be enclosed in parentheses and the radix of the number inserted as a subscript.For example,to show the equality between decimal and binary forty-five we will write(101101)2=(45)10 Besides the decimal and binary number systems,the octal(radix 8)and hexadecimal(radix 16)are important in digital computer work.The eight symbols of the octal system are 0,1,2,3,4,5,6,and 7.The 16 symbols of the hexadecimal system are 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,and F.The last six symbols are,unfortunately,identical to the letters of the alphabet and can cause confusion at times.However,this is the convention that has been adopted.When used to represent hexadecimal digits,the symbols A,B,C,D,E,F correspond to the decimal numbers 10,11,12,13,14,15,respectively.A number in radix r can be converted to the familiar decimal system by forming the sum of the weighted digits.For example,octal 736.4 is converted to decimal as follows:(736.4)8=782+381+680+48-1 =764+38+61+4/8=(478.5)10 The equivalent decimal number of hexadecimal F3 is obtained from the following calculation:(F3)16=F16+3=1516+3=(243)10 Conversion from decimal to its equivalent representation in the radix r system is carried out by separating the number into its integer and fraction parts and converting each part separately.The conversion of a decimal integer into a base r representation is done by successive divisions by r and accumulation of the remainders.The conversion of a decimal fraction to radix r representation is accomplished by successive multiplications by r and accumulation of the integer digits so obtained.Figure 2-1 demonstrates these procedures.The conversion of decimal 41.6875 into binary is done by first separating the number into its integer part 41 and fraction part.6875.The integer part is converted by dividing 41 by r=2 to give an integer quotient of 20 and a remainder of 1.The quotient is again divided by 2 to give a new quotient and remainder.This process is repeated until the integer quotient becomes 0.The coefficients of the binary number are obtained from the remainders with the first remainder giving the low-order bit of the converted binary number.The fraction part is converted by multiplying it by r=2 to give an integer and a fraction.The 2-1“计算机组成原理”英文教材 3 3 new fraction(without the integer)is multiplied again by 2 to give a new integer and a new fraction.This process is repeated until the fraction part becomes zero or until the number of digits obtained gives the required accuracy.The coefficients of the binary fraction are obtained from the integer digits with the first integer computed being the digit to be placed next to the binary point.Finally,the two parts are combined to give the total required conversion.Octal and Hexadecimal Numbers The conversion from and to binary,octal,and hexadecimal representation plays and important part in digital computers.Since 23=8 and 24=16,each octal digit corresponds to three binary digits and each hexadecimal digit corresponds to four binary digits.The conversion from binary to octal is easily accomplished by partitioning the binary number into groups of three bits each.The corresponding octal digit is then assigned to each group of bits and the string of digits so obtained gives the octal equivalent of the binary number.Consider,for example,a 16-bit register.Physically,one may think of the register as composed of 16 binary storage cells,with each cell capable of holding either a 1 or a 0.Suppose that the bit configuration stored in the register is as shown in fig.2-2.Since a binary number consists of a string of 1 s and 0 s,the 16-bit register can be used to store any binary number from 0 to 216-1.For the particular example shown,the binary number stored in the register is the equivalent of decimal 44899.Starting from the low-order bit,we partition the register into groups of three bits each(the sixteenth bit remains in a group by itself).Each group of three bits is assigned its octal equivalent and placed on top of the register.The string of octal digits so obtained represents the octal equivalent of the binary number.Conversion from binary to hexadecimal is similar except that the bits are divided into groups of four.The corresponding hexadecimal digit for each group of four bits is written as shown below the register of Fig.2-2.The string of hexadecimal digits so obtained represents the hexadecimal equivalent of the binary number.The corresponding octal digit for each group of three bits is easily remembered after studying the first eight entries listed in table 2-1.The correspondence between a hexadecimal digit and its equivalent 4-bit code can be found in the first 16 entries of Table 2-2.Table 2-1 lists a few octal numbers and their representation in registers in binary-coded form.The binary code is obtained by the procedure explained above.Each octal digit is assigned a 3-bit code as specified by the entries of the first eight digits in the table.Similarly,Table 2-2 lists a few hexadecimal numbers and their representation in registers in binary-coded form.Here the binary code is obtained by assigning to each hexadecimal digit the 4-bit code listed in the first 16 entries of the table.2-2“计算机组成原理”英文教材 4 4 Comparing the binary-coded octal and hexadecimal numbers with their binary number equivalent we find that the bit combination in all three representations is exactly the same.For example,decimal 99,when converted to binary,becomes 1100011.The binary-coded octal equivalent of decimal 99 is 001 100 011 and the binary-coded hexadecimal of decimal 99 is 0110 0011.If we neglect the leading zeros in these three binary representations,we find that their bit combination is identical.This should be so because of the straightforward conversion that exists between binary numbers and octal or hexadecimal.The point of all this is that a string of 1 s and 0 s stored in a register could represent a binary number,but this same string of bits may be interpreted as holding an octal number in binary-coded form(if we divide the bits in groups of three)or as holding a hexadecimal number in binary-coded form(if we divide the bits in groups of four).The registers in a digital computer contain many bits.Specifying the content of registers by their binary values will require a long string of binary digits.It is more convenient to specify content of registers by their octal or hexadecimal equivalent.The number of digits is reduced by one-third in the octal designation and by one-fourth in the hexadecimal designation.For example,the binary number 1111 1111 1111 has 12 digits.It can be expressed in octals as 7777(four digits)or in hexadecimal as FFF(three digits).Computer manuals invariably choose either the octal or the hexadecimal designation for specifying contents of registers.Decimal representation The binary number system is the most natural system for a computer,but people are accustomed to the decimal system.One way to solve this conflict is to convert all input decimal numbers into binary numbers,let the computer perform all arithmetic operations in binary and then convert the binary results back to decimal for the human user to understand.However,it is also possible for the computer to perform arithmetic operations directly with decimal numbers provided they are placed in registers in a coded form.Decimal numbers enter the computer u sually as binary-coded alphanumeric characters.These codes,introduced later,may contain from six to eight bits for each decimal digit.When decimal numbers are used for internal arithmetic computations,they are 2-1 2-2“计算机组成原理”英文教材 5 5 converted to a binary code with four bits per digit.A binary code is a group of n bits that assume up to 2n distinct combinations of 1 s and 0 s with each combination representing one element of the set that is being coded.For example,a set of four elements can be coded by a 2-bit code with each element assigned one of the following bit combinations;00,01,10,or 11.A set of eight elements requires a 3-bit code,a set of 16 elements requires a 4-bit code,and so on.A binary code will have some unassigned bit combinations if the number of elements in the set is not a multiple power of 2.The 1-decimal digits form such a set.A binary code that distinguishes among 10 elements must contain at least four bits,but six combinations will remain unassigned.Numerous different codes can be obtained b y arranging four bits in 10 distinct combinations.The bit assignment most commonly used for the decimal digits is the straight binary assignment listed in the first 10entries of Table 2-3.This particular code is called binary-coded decimal and is commonly referred to by its abbreviation BCD.Other decimal codes are sometimes used and a few of them are given in Sec.2-5.It is very important to understand the difference between the conversion of decimal numbers into binary and the binary coding of decimal numbers.For example,when converted to a binary number,the decimal number 99 is represented by the string of bits 1100011,but when represented in BCD,it becomes 1001 1001.The only difference between a decimal number represented by the familiar digit symbols 0,1,2,9 and the BCD symbols 0001,0010,1001 is in the symbols used to represent the digits the number itself is exactly the same.A few decimal numbers and their representation in BCD are listed in Table 2-3.2-3 2-4“计算机组成原理”英文教材 6 6 Alphanumeric representation Many applications of digital computers require the handling of data that consist not only of numbers,but also of the letters of the alphabet and certain special characters.An alphanumeric character set is a set of elements that includes the 10 decimal digits,the 26 letters of the alphabet and a number of special characters,such as$,+,and=.Such a set contains between 32 and 64 elements(if only uppercase letters are included)or between 64 and 128(if both uppercase and lowercase letters are included).In the first case,the binary code will require six bits and in the second case,seven bits.The standard alphanumeric binary code is the ASCII(American Standard code for Information Interchange),which uses seven bits to code 128 characters.The binary code for the uppercase letters,the decimal digits,and a few special characters is listed in Table 2-4.Note that the decimal digits in ASCII can be converted to BCD by removing the three high-order bits,011.A complete list of ASCII characters is provided in Table 11-1.Binary codes play an important part in digital computer operations.The codes must be in binary because registers can only hold binary information.One must realize that binary codes merely change the symbols,not the meaning of the discrete elements they represent.The operations specified for digital computers must take into consideration the meaning of the bits stored in registers so that operations are performed on operands of the same type.In inspecting the bits of a computer register at random,one is likely to find that it represents some type of coded information rather than a binary number.Binary codes can be formulated for any set of discrete elements such as the musical notes and chess pieces and their positions on the chessboard.Binary codes are also used to formulate instructions that specify control information for the computer.This chapter is concerned with data representation.Instruction codes are discussed in Chap.5.2-2 Complements Complements are used in digital computers for simplifying the subtraction operation and for logical manipulation.There are two types of complements for each base r system:the r s complement and the(r-1)s complement.When the value of the base r is substituted in the name,the two types are referred to as the 2 s and 1 s complement for binary numbers and the 10 s and 9 s complement for decimal numbers.(r-1)s Complement Given a number N in base r having n digits,the(r-1)s complement of N is defined as(rn-1)-N.For decimal numbers r=10 and r-1=9,so the 9 s complement of N is(10n-1)-N.Now,10n represents a number that consists of a single 1 followed by n 0 s.10n-1 is a number represented by n 9 s.For example,with n=4 we have 104=10000 and 104-1=9999.It follows that the 9 s complement of a decimal number is obtained by subtracting each digit from 9.For example,the 9 s complement of 546700 is 999999-546700=453299 and the 9 s complement of 12389is 99999-12389=87610.For binary numbers,r=2 and r-1=1,so the 1 s complement of N