(2.2)--第2章 计算机信息表示大学计算机.ppt

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1、0 AND 104lThe phenomenon is abstracted into symbols and combined with symbolsThe phenomenon is abstracted into symbols and combined with symbols1.2 0 1.2 0 and and 1 1lFurther more,the diversity of combination Further more,the diversity of combination is considered to adapt to more semanticsis consi

2、dered to adapt to more semantics1 0 21种11 01 10 00 22种111 110 101 100 011 010 001 000 23种 26种 0 and 1 thinking:Yi Jing-Semantic symbolic expression0 and 1 thinking:Yi Jing-Semantic symbolic expressionWhen there are different combinations,there are more than 64 combinations.Therefore,only Yin and Yan

3、g can express infinite semanticslFrom the perspective of computational science,From the perspective of computational science,Yi JingYi Jing is actually a kind of artificial is actually a kind of artificial coding system,which uses the combination of coding system,which uses the combination of yin an

4、d Yang symbols to express specific yin and Yang symbols to express specific information,which runs through the important information,which runs through the important ideas of binary and coding.ideas of binary and coding.lDiscussion:why do computers use binary?Why not use decimal?1.2 0 1.2 0 and and

5、1 1 0 and 1 thinking:Yi Jing-Semantic symbolic expression0 and 1 thinking:Yi Jing-Semantic symbolic expressionpEasy to implement in the circuitEasy to implement in the circuitpIt is convenient for addition,subtraction and It is convenient for addition,subtraction and counting codingcounting coding(o

6、nly has 4 formulas)(only has 4 formulas)pSuitable for logical operationSuitable for logical operationpPhysically the easiest to implement storagePhysically the easiest to implement storagepStrong anti-interference abilityStrong anti-interference abilitylDiscussion:why do computers use binary?number

7、system in number system in computercomputer052.1 number system in computer2.1 number system in computer1.The concept of number system1.The concept of number systemCarry counting system is a method named by the number of digit Carry counting system is a method named by the number of digit symbols use

8、d to represent numerical values and counting symbols used to represent numerical values and counting according to certain carry rulesaccording to certain carry rules.The number of the number symbols used in the number system is The number of the number symbols used in the number system is called cal

9、led the base of the number systemthe base of the number system,f for example,a decimal or example,a decimal number consists of ten numbers,that is,0,1,2,3,4,5,6,7,number consists of ten numbers,that is,0,1,2,3,4,5,6,7,8,9.The base number of the decimal system is 10,Count to ten 8,9.The base number o

10、f the decimal system is 10,Count to ten to one.to one.T The value of each he value of each bitbit in the number system is called in the number system is called the bitthe bits s valuevalue of the number system of the number system.Decimal representationDecimal representation：lThe use of footmark num

11、bers to represent various carry counting systemsThe use of footmark numbers to represent various carry counting systems (d(dn-1n-1d dn-2n-2dd2 2d d1 1d d0 0.d.d-1-1d d-2-2dd-m-m)r r for example for example：(365.2)(365.2)1010,（11011.01)11011.01)2 2,（3460.32)3460.32)八八,(596.12),(596.12)十六十六lUsing suff

12、ixes to represent various carry counting systemsUsing suffixes to represent various carry counting systems B(binary):B(binary):Binary numberBinary number；O(octal):O(octal):Octal numberOctal number；H(hex):H(hex):Hexadecimal numberHexadecimal number,D(decimal):D(decimal):Decimal numberDecimal number。f

13、or example for example：365.2 365.2 D D,11011.01,11011.01 B B,3460.32,3460.32 O O,596.12,596.12 H HBinary numberBinary numberDecimal numberDecimal numberO Octal number ctal number Hexadecimal numberHexadecimal number000011111022211333100444101555110666111777100081081001911910101012A10111113B11001214C

14、11011315D11101416E11111517F10000162010The relationship between the representations of various number systemsN=aN=an-1n-1r rn-1n-1a an-2n-2r rn-2n-2a a0 0r r0 0a a-1-1r r-1-1a a-m-mr r-m-mThe base number N of R can be expressed as:The R-base number uses R basic symbols(0,1,2,R-1)The R-base number use

15、s R basic symbols(0,1,2,R-1)the basethe base the bitthe bits values value Digital678.34=6102+7101+8100+310-1+410-2 Convert R-base number into decimal system:write R-base number into weight expansion formula,multiply each digit by its own weight,and then accumulate to get the decimal number correspon

16、ding to the R-base number.例例1 1（1101.0111101.011）B B=（）D D （1 1 1 1 0 0 1.1.0 0 1 1 1 1）B B =1 12 23 3+1+12 22 2+0+02 21 1+1+12 20 0+0+02 2-1-1+1+12 2-2-2+1+12 2-3-3 =8+4+0+1+0+0.25+0.1258+4+0+1+0+0.25+0.125 =（13.37513.375）D D8 4 2 1 0.5 0.25 0.125Number system in computer1 1、Convert non decimal to

17、decimalConvert non decimal to decimalN=aN=an-1n-1r rn-1n-1a an-2n-2r rn-2n-2a a0 0r r0 0a a-1-1r r-1-1a a-m-mr r-m-m例例2 2：(5675)(5675)O O=()=()D D。(5675)(5675)O O =5 5 8 83 3+6+68 82 2+7+7 8 81 1+5+5 8 80 0 =2560+384+56+52560+384+56+5 =(3005)(3005)D D例例3 3：(3B)(3B)H H=()=()D D。(3B)(3B)H H=3 =3 16161

18、 1+11+1116160 0 =48+11 48+11=(59)(59)D DNumber system in computer1 1、Convert non decimal to decimalConvert non decimal to decimal（1001.11）B=（）D （2C）H =（）D此页需要启用宏，方可生效9.7544Number system in computer1 1、Convert non decimal to decimalConvert non decimal to decimalpThe method of converting decimal syste

19、m into R-base system:The integral part and the fractional part are converted respectively and then combined.pInteger part:divide r to take the remainder until the quotient is 0.The remainder is arranged from right to left,which is called cardinal division.2 2、Convert decimal to non decimalConvert de

20、cimal to non decimalremainderpThe method of converting decimal system into R-base system:The integral part and the fractional part are converted respectively and then combined.pFractional part:multiply r to get an integer.Integers are arranged from left to right,called Radix multiplication.2 2、Conve

21、rt decimal to non decimalConvert decimal to non decimal例例4 (25.3125)4 (25.3125)D D=（）B B。2 2 25 25 2 2 12 1 12 1 2 2 6 0 6 0 2 2 3 0 3 0 2 2 1 1 1 1 0 1 0 1 (25)(25)D D=(11001)=(11001)B B Note:the remainder taken first is low,and the remainder taken Note:the remainder taken first is low,and the rema

22、inder taken later is high.later is high.2 2、Convert decimal to non decimalConvert decimal to non decimal The conversion of integral part(division base remainder method):The conversion of integral part(division base remainder method):divide by 2 to take the remainder until the quotient is 0,and the d

23、ivide by 2 to take the remainder until the quotient is 0,and the remainder is arranged from right to left.remainder is arranged from right to left.Integral part:25Integral part:25 Divisor dividend remainderDivisor dividend remainder 0.31250.3125 2 2 0.6250 0.6250 0 0 2 2 0.2500 0.2500 1 1 2 2 0.5000

24、 0.5000 0 0 2 2 0.0000 0.0000 1 1 (0.3125)(0.3125)D D=(0.0101)=(0.0101)B B(25.3125)(25.3125)D D=(11001)=(11001)B B+(0.0101)+(0.0101)B B=(=(11001.0101)11001.0101)B BFractional part conversion(multiplication base rounding method):multiply 2 to get an integer,and integers are arranged from left to righ

25、t.Fractional part:0.31252 2、Convert decimal to non decimalConvert decimal to non decimal例例4 (25.3125)4 (25.3125)D D=（）B B。Note:every time the decimal part is converted,the integer part is taken out,and the remaining decimal part is continued to be rounded by R;in addition,when the last decimal part

26、in this question is 0,the conversion is terminated,and when some data are converted,the decimal part may never be 0.At this time,the decimal part after conversion is not accurate,and the number of decimal places reserved depends on the users needs.例例5 (166)D=（）H。Divisor dividend remainderDivisor div

27、idend remainder 16 166 16 10 6 0 10 （A）(166)D=(A6)HNote:in hexadecimal data,the numeral character A represents 10此页需要启用宏，方可生效（11.25）D =（）B（27）D =（）H1011.01 1B2 2、Convert decimal to non decimalConvert decimal to non decimalA After-class tasks fter-class tasks Download Zhidao app,log in,choose univers

28、ity computer course,and study.(the course selection is expected to start on October 9)Download the courseware and review the exercisesOn October 14,online learning,dont go to the classroomOn October 21,the computer class will be held in classroom 255 of Mingde building.YOURLOGO感谢聆听，批评指导THANK YOU TO LISTEN TO CRITICISM GUIDANCE