数字逻辑设计及应用教学课件：2-2补码数制.ppt

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1、class-exercises1、1011100010112=8=162、(156)10=()23、convert0.3910toanumberinradix2.Theprecisionmustachieve10%。tenminutesclass-exercises1、1011100010112=56138=B8B162、(156)10=(10011100)23、将0.3910转换为二进制数,要求精度达到10%。0.01102ReviewofthelastlessonPositionalNumberSystemsMSD，LSD

2、，MSB，LSBGeneralPositional-Number-SystemConversionsAdecimalfractionAnumberinBinaryradixBinaryadditionandsubtractionBinarynumberswithcertainwidth;Thenumbersalwaysbesetas0.xxxxxxxx;Wecantakethesenumbersasintegersforoperations!MSB/LSBUnsignednumberOperationsforunsigned

3、numbers0+0=01+0=11+1=10AdditionC:carryS:sumOperationsforunsignednumbersAddition:Overflow?Wrong!Right!0×A=01×A=AMultiplicationShift-add:useaddersandshift-registers;Theproductwidthwillbe2n!OperationsforunsignednumbersNewruledifferfromaddMaybegetnegativenumbersubtracti

4、onShouldusesignednumbertoexpresspositiveandnegativeOperationsforunsignednumbersOncethesignednumbersbeused,subtractioncanbemadebyadd!OperationsforunsignednumbersSubtractionruleisnotnecessary!2.5RepresentationofNegativeNumbers(负数的表示)2.5.1Signed-MagnitudeRepresentation

5、P34[符号–数值表示法（原码）]2.5.2ComplementNumberSystemsP35(补码数制)2.5.3Radix-ComplementRepresentationP36(基数补码表示法)2.5.4Two’s-ComplementRepresentationP37(二进制补码表示法)2.6Two’s-ComplementAdditionandSubtractionP39(二进制补码的加减法)Table2-6P40(十进制数与4位二进制数对照表)2.6.3Overflow(溢出)P412.5.1Signed-Mag

6、nitudeRepresentationanumberconsistsofamagnitudeandasymbolindicatingwhetherthemagnitudeispositiveornegative.MSBastheSignbit(0=plus,1=minus)[最高有效位表示符号位（0=正，1=负）]01111111＝＋12711111111＝－12700101110＝＋4610101110＝－4600000000＝＋010000000＝－02.5.1Signed-MagnitudeRepresentation

7、[符号–数值表示法（原码）]TwopossiblerepresentationsofZero[零有两种表示（+0、–0）]2.Ann-bitsigned-magnitudeintegerrangeis(n位二进制整数表示范围)：–(2n-1–1)~+(2n-1–1)Thesigned-magnitudesystemhasanequalnumberofpositiveandnegativeintegers.P35representtheresultwith8-bitsigned-magnitudeinteger!110-110=

8、?thesigned-magnitudesystemnegatesanumberbychangingitssign.ComplementNumberSystemsitnegatesanumberbytakingitscomplementasdefinedbythesystem