《电子技术（双语）》课件-二进制运算及几种常用的编码

二进制运算及几种常用的编码BinaryArithmeticandSeveralCommonlyUsedEncodings二进制运算及几种常用的编码BinaryArithmeticandSeveralCommonlyUsedEncodings二进制运算及几种常用的编码BinaryArithmeticandSeveralCommonlyUsedEncodingsTeacher:JiaLisi授课教师：贾丽斯计算机依赖数制、码制处理信息

Computersrelyonnumbersystemsandencodingschemestoprocessinformation.Part01教学目标Teachingobjective理解Understand教学目标Teachingobjective二进制加、减、乘、除运算规则。Binaryaddition,subtraction,multiplication,anddivisionrules.熟悉Beproficientin原码、反码、补码、BCD码、格雷码的概念与特点。Theconceptsandcharacteristicsofsignmagnitude,one'scomplement,two’scomplementcode,BCDcode,andGraycode.掌握Master二进制运算操作、编码与二进制的转换技巧。Binaryarithmeticoperations,encoding,andbinaryconversiontechniques.运用Apply分析解决简单实际数字处理问题。Analyzeandsolvesimple,practicaldigitalprocessingproblems.Part02案例导入CaseIntroduction案例导入CaseIntroduction日常计数系统Dailycountingsystem计算机计数系统Computercountingsystem=十进制，规则为逢十进一。Thedecimalsystemfollowstheruleofcarryingovertothenextunitwhenthenumberofunitsreachesten.二进制，是其“通用语言”。Binaryisits"universallanguage".案例导入CaseIntroduction计算机计数系统Computercountingsystem二进制，是其“通用语言”。Binaryisits"universallanguage".计算机计数系统：Computercountingsystem:计算机存储最小单位Thesmallestunitofcomputerstorage:比特（bit），仅两种状态（0和1）。bit,whichhasonlytwostates(0and1).二进制适合硬件实现的原因：状态如同电路的开和关，契合计算机硬件特性。Thereasonwhybinaryissuitableforhardwareimplementation:itsstatesareliketheonandoffstatesofacircuit,whichfitsthecharacteristicsofcomputerhardware.Part03二进制运算Binaryarithmetic二进制运算Binaryarithmetic运算类型

Operationtype核心规则

Corerules功能

Function加法Addition减法

Subtraction乘法

Multiplicatio逢二进一

Carryoverwhenitreachestwo借一当二

Treatingoneinnextunitastwo0乘任何为0，1乘任何为其本身；移位相加。

0multipliedbyanyequals0,and1multipliedbyanyequalsitself;shiftandadd.1+1=10（十进制2）(2indecimal)11×10=110（十进3×2=6）

(3×2=6indecimal)10-1=1（十进制2-1=1）

(2-1=1indecimal)除法

Division类似十进制，乘法逆运算。

Similartodecimal,multiplicationistheinverseoperation.100÷10=10（十进制4÷2=2）

(4÷2=2indecimal)Part04常用编码CommonEncodings常用编码

Commonencodings原码Signmagnitude补码Two'scomplement常用编码CommonEncodings反码One'scomplementBCD码BCDcode格雷码Graycode原码：Signmagnitude:常用编码CommonEncodings最高位符号位（0正、1负），其余位表数值绝对值。Thehighestbitisthesignbit(0forpositive,1fornegative),andtheremainingbitsrepresenttheabsolutevalueofthenumber.例如：Example:+5（00000101）、-5（10000101）反码：Ones'complement:常用编码CommonEncodings正数与原码同；Theones'complementofapositivenumberisthesameasitssignmagnitude;例如：Example:-5反码（11111010）-5inone'scomplement(11111010)负数符号位不变，其余位取反。Theones'complementofanegativenumberisobtainedbyinvertingallthebitsexceptforthesignbit.补码：Two'scomplement:常用编码CommonEncodings正数与原码同；Thetwo'scomplementofapositivenumberisthesameasitssignmagnitude;例如：Example:-5补码（11111011）-5intwo’scomplement(11111011)负数反码最低位加1；Thetwo'scomplementofanegativenumberisobtainedbyadding1totheleastsignificantbitofitsone'scomplement;解决原码符号位运算问题，统一加减法。Itsolvestheproblemofcomplexsignbithandlinginsignmagnitudearithmetic,allowingadditionandsubtractionoperationstobeperformeduniformly.常用编码CommonEncodings二进制是如何进行运算的？Howbinaryoperationsareperformed?有哪些常用编码基于二进制构建？Whatcommonlyusedencodingsarebuiltonbinary?BCD码：BCDcode:常用编码CommonEncodings例如：Example:十进制3（0011）3indecimal(0011)4位二进制表1位十进制（0~9）；Uses4binarybitstorepresentthe10digits0-9inadecimalnumber;8421BCDcodeisthemostcommonlyused(Weights:8,4,2,1).8421BCD码常用（权值8、4、2、1）。格雷码：Graycode:常用编码CommonEncodings相邻代码仅1位不同，减少代码变化错误。Adjacentcodesegmentsdifferbyonlyonebit,reducingerrorscausedbycodechanges.例如：Example:4位格雷码0000与0001、0001与0011相邻仅1位不同。4-bitGraycode0000and0001,0001and0011areadjacentanddifferbyonly1bit.Part05案例分析CommonEncodings二进制加法（3+5）：Binaryaddition(3+5):案例分析CommonEncodings二进制加法（3+5）：Binaryaddition(3+5):原码：00000011Signmagnitude:00000011原码：00000101Signmagnitude:00000101案例分析CommonEncodings二进制加法（3+5）：Binaryaddition(3+5):原码：00000011Signmagnitude:00000011原码：00000101Signmagnitude:0000010100001000案例分析CommonEncodings补码运算（5-3=5+(-3)）：Two'scomplementarithmetic(5-3=5+(-3)):案例分析CommonEncodings原码：00000011Signmagnitude:00000011原码：00000101Signmagnitude:00000101反码：11111100One'scomplement:11111100补码：11111101wo'scomplement:11111101

补码运算（5-3=5+(-3)）：Two'scomplementarithmetic(5-3=5+(-3)):案例分析CommonEncodings补码运算（5-3=5+(-3)）：Two'scomplementarithmetic(5-3=5+(-3)):5补码（00000101）+-3补码（11111101）=000000105intwo'scomplement(00000101)+-3intwo'scomplement(11111101)=00000010案例分析CommonEncodingsPart06教学重点TeachingFocus二进制运算Binaryarithmetic教学重点梳理

Keypointsofteaching加减法进位、借位机制（计算机算术逻辑基础）。Carryandborrowmechanismsinadditionandsubtraction(fundamentalsofcomputerarithmeticlogic).三大应用：整流·限幅·门电路

Threemajorapplications:rectification,amplitudelimitingandgatecircuit原码、反码与补码Signmagnitude、ones'complementandtwo'scomplement定义、转换方法，补码对计算机高效运算的意义。Definition,conversionmethods,andthesignificanceoftwo'scomplementforefficientcomputercomputation.特殊编码SpecialencodingBCD码、格雷码的特性及在数值表示、数据传输的用途。CharacteristicsofBCDandGraycodesandtheirapplicationsinnumericalrepresentationanddatatransmission.应用Applications全加器实现多位二进制加法（数字电路数据算术处理基础）。Afulladderperformsmulti-bitbinaryaddition(fundamentalsofdigitalcircuitdataarithmeticprocessing).Part07未来职业岗位的应用ApplicationofFutureProfessionalPositions计算机编程

Computerprogramming未来职业岗位的应用ApplicationofFutureProfessionalPositions优化算法、提效，底层驱动/高性能算法开发必备Optimizealgorithms,improveefficiency;essentialfordevelopingunderlying/high-performancealgorithms.电子工程Electronicengineering设计数字电路与芯片的基石，保障数据传输/存储/校验准确Thecornerstoneofdigitalcircuitandchipdesign,ensuringaccuratedatatransmission,storage,andverification.二进制运算及几种常用的编