《计算机专业英语》电子教案PPT第3章.ppt
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1、Computer English Chapter 3 Number Systems and Boolean Algebra1Chapter 3 Number Systems and Boolean AlgebraKey points:useful terms and definitions of Number system and Boolean AlgbraDifficult points:Conversion of the Number Systems and Boolean Algbra2 计算机专业英语Chapter 3 Number Systems and Boolean Algeb
2、raRequirements:1.Concepts of Number System and their conversion 2.Boolean Algebra 3.Moores Law 4.科技英语中数学公式的读法 3 计算机专业英语Chapter 3 Number Systems and Boolean AlgebraNew Words&Expressions:hexadecimal adj.十六进制的;n.十六进制 radix n.根,基数octal adj.八进制的;n.八进制 alphabet n.字母表fractional adj.分数的,小数的 whole number n.整
3、数remainder n.余数 significant figure n.有效数字quotient n.商 algorithm n.算法complement n.补码,余角 carry n.进位 3.1 Number Systems Abbreviations:Binary-coded hexadecimal(BCH)二进制编码的十六进制4 计算机专业英语Chapter 3 Number Systems and Boolean AlgebraThe use of the microprocessor requires a working knowledge of binary,decimal,
4、and hexadecimal numbering systems.This section provides a background for those who are unfamiliar with number systems.Conversions between decimal and binary,decimal and hexadecimal,and binary and hexadecimal are described.3.1 Number Systems 使用微处理器需要掌握二进制、十进制和十六进制数制系统的基本知识,本节为那些不熟悉数制系统的读者提供这方面的背景知识。说
5、明了十进制与二进制之间、十进制与十六进制之间,及二进制与十六进制之间的转换。5 计算机专业英语Chapter 3 Number Systems and Boolean AlgebraBefore numbers are converted from one number base to another,the digits of a number system must be understood.Early in our education,we learned that a decimal,or base 10,number was constructed with 10 digits:0
6、 through 9.The first digit in any numbering system is always a zero.For example,a base 8(octal)number contains 8 digits:0 through 7;a base 2(binary)number contains 2 digits:0 and 1.3.1.1 Digits 将数从种数制向另一种数制转换之前,必须了解数的计数系统。在早期教育中,我们已学习了十进制数,或以10为基的数,它由10个数字组成:0到9。任何计数制的第一个数字总是零,这种规则适用于任何其他数制。例如,以8为基的
7、数(八进制)包含8个数字:0到7,而以2为基的数(二进制)包含2个数字:0和 l。6 计算机专业英语Chapter 3 Number Systems and Boolean AlgebraIf the base of a number exceeds 10,the additional digits use the letters of the alphabet,beginning with an A,For example,a base 12 number contains 12 digits:0 through 9,followed by A for 10 and B for 11,Not
8、e that a base 10 number does not contain a 10 digit,just as a base 8 number does not contain an 8 digit.The most common numbering systems used with computers are decimal,binary,and hexadecimal(base 16).(Many years ago octal numbers were popular.)Each system is described and used in this section of t
9、he chapter.3.1.1 Digits 如果基数大于10,其余数字用从A开始的字母表示,例如,以12为基的数包含12个数字,0到9,之后用A代表10,B代表11。注意,以10为基的数不包含数字10,如同以8为基的数不包括数字8一样。计算机中最通用的计数制是十进制、二进制、八进制和十六进制(基为16)。每种计数制都将在本节中进行说明和应用。7 计算机专业英语Chapter 3 Number Systems and Boolean AlgebraOnce the digits of a number system are understood,larger numbers are cons
10、tructed by using positional notation.In grade school,we learned that the position to the left of the units position was the tens position,the position to the left of the tens position was the hundreds position,and so forth.(An example is the decimal number 132:This number has 1 hundred,3 tens,and 2
11、units.)What probably was not learned was the exponential value of each position:The units position has a weight of 100 or 1;the tens position has weight of 101,or 10;and the hundreds position has a weight of 102,or 100.3.1.2 Positional Notation 一旦我们理解了计数制的数字后,就可用位计数法构造更大的数值。在小学时我们都学过个位的左边一位是十位,十位左边一
12、位是百位,以此类推(例如十进制数132,这个数字有个百,三个十和两个一)。或许我们没有学过每个位的指数值:个位的权为l00,即1;十位的权为101或10;而百位的权为102或l00。8 计算机专业英语Chapter 3 Number Systems and Boolean AlgebraThe exponential powers of the positions are critical for understanding numbers in other numbering systems.The position to the left of the radix(number base)
13、point,called a decimal point only in the decimal system,is always the units position in any number system.For example,the position to the left of the binary point is always 20 or 1;the position to the left of the octal point is 80 or 1.In any case,any number raised to its zero power is always 1,or t
14、he units position.3.1.2 Positional Notation 位的指数幂在理解其他计数制中的数时是个关键。基数小数点,在十进制中称为十进制小数点,其左边的位在任何数制中都是个位。例如,二进制小数点左边的位是20或1。而八进制小数点左边的位是80或1。在任何情况下,任何数的零次幂总是1,或1个单位。9 计算机专业英语Chapter 3 Number Systems and Boolean AlgebraThe position to the left of the units position is always the number base raised to th
15、e first power;in a decimal system,this is l01,or l0.In a binary system,it is 21,or 2;and in an octal system it is 81,or 8.Therefore,an 11 decimal has a different value from an 11 binary.The 1l decimal is composed of 1 ten plus 1 unit and has a value of 11 units;while the binary number 11 is composed
16、 of 1 two plus 1 unit,for a value of 3 decimal units.The 11 octal has a value of 9 units.3.1.2 Positional Notation 个位左边的位总是基数的1次幂,在十进制系统中是101,或10;在二进制中是21,或2;而在八进制中是81,或8。因此,十进制的11与二进制的11具有不同的数值。十进制11表示个10加上一个1,其值为11;二进制11表示个2加上个1,其值为3;八进制11的值为9。10 计算机专业英语Chapter 3 Number Systems and Boolean Algebra
17、In the decimal system,positions to the right of the decimal point have negative powers.The first digit to the right of the decimal point has a value of 10-1,or 0.1.In the binary system,the first digit to the right of the binary point has a value of 2-1,or 0.5.In general,the principles that apply to
18、decimal numbers also apply to numbers in any other number system.3.1.2 Positional Notation 在十进制系统中,对于十进制小数点右边的位,它的幂为负数。十进制小数点右边第一位数的值为10-1,或0.1。在二进制中,二进制小数点右边第位数的值为2-1或0.5。一般来说,十进制使用的计数法可以用于任何其他数制。11 计算机专业英语Chapter 3 Number Systems and Boolean AlgebraExample 3-1 shows a 110.101 in binary(often writt
19、en as 110.1012).It also shows the power and weight or value of each digit position.To convert a binary number to decimal,add the weights of each digit to form its decimal equivalent.The 110.1012 is equivalent to a 6.625 in decimal(4+2+0.5+0.125).Notice that this is the sum of 22(or 4)plus 21(or 2),b
20、ut 20(or 1)is not added because there are no digits under this position.The fraction part is composed of 2-1(0.5)plus 2-3(or.125),but there is no digit under the 2-2(or.25).3.1.2 Positional Notation 例3-1给出了一个二进制数110.101(通常写成110.1012),也给出了这个数每个位的幂、权和值。为了把二进制数转换为十进制,将每位数字的权相加,就得到了它的等效十进制值。二进制110.101等于
21、十进制的6.625(4+2+0.5+0.125)。注意,这个和的整数部分是由22(4)加21(2)构成,之所以没有用20(1)是因为这个位的数为零。小数部分由2-1(0.5),加2-3(0.125)构成,但是没有用2-2(0.25)。12 计算机专业英语Chapter 3 Number Systems and Boolean AlgebraThe prior examples have shown that to convert from any number base to decimal,determine the weights or values of each position of
22、 the number,and then sum the weights to form the decimal equivalent.Suppose that a 125.78 octal is converted to decimal.To accomplish this conversion,first write down the weights of each position of the number.This appears in Example 3-2.The value of 125.78 is 85.875 decimal,or 164 plus 2 8 plus 5 1
23、 plus 7.125.3.1.3 Conversion to Decimal 前面的例子说明了将任何其他基数的数转换为十进制数时,十进制数的值取决于该数每个位上的权或值,它们的和就是等效的十进制数值。假定要将125.78(八进制)转换为十进制。为了完成这个转换,首先写出该数每一位数的权,如例3-2所示,125.78的值是十进制的85.875,即1 64+2 8+5 1+7 0.125。13 计算机专业英语Chapter 3 Number Systems and Boolean AlgebraNotice that the weight of the position to the left
24、of the units position is 8.This is 8 times 1.Then notice that the weight of the next position is 64,or 8 times 8.If another position existed,it would be 64 times 8,or 51 2.To find the weight of the next higher-order position,multiply the weight of the current position by the number base(or 8,in this
25、 example).To calculate the weights of position to the right of the radix point,divide by the number base.In the octal system,the position immediately to the fight of the octal point is 1/8,or.125.The next position is.125/8,or.015625,which can also be written as 1/64.3.1.3 Conversion to Decimal 注意,该数
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