# Check code

## Composition

Anycodewithacheckcodeiscomposedoftwoparts:thebodycodeandthecheckcode(suchastheorganizationcode).Thebodycodeisthenumberthatrepresentsthecodeobject.Theverificationcodeisanumberattachedtothebodycodetoverifytheaccuracyofthebodycodeduringtheinputprocess.Eachbodycodecanonlyhaveonecheckcode,andthecheckcodeisobtainedthroughaprescribedmathematicalrelationship.

## Checksumalgorithm

Differentchecksumalgorithmsareoftendifferent.Commoncheckcodealgorithmsinclude:codedistance,paritycheck,Hammingcheck,cyclicredundancycheck,etc.

## Algorithmexample

### IDcardcheckcode

AccordingtothenationalstandardGB11643-1999ofthePeople’sRepublicofChina,thecalculationmethodfortheverificationcodeofthecitizen’sidentitynumberofthePeople’sRepublicofChinaistheISO7064:1983.MOD11-2verificationcodecalculationmethod.

Assuminga17-digitnumberis

 17-digitnumber 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 Weightingfactor 7 9 10 5 8 4 2 1 6 3 7 9 10 5 8 4 2

368

Calculatethesumoftheproductofthe17-digitnumberandthecorrespondingweightingfactorS:1×7+2×9+3×10+4×5+5×8+6×4+7×2+8×1+9×6+0×3+1×7+2×9+3×10+4×5+5×8+6×4+7×2=368;CalculatetheremainderTofS÷11:368mod11=5;CalculatetheremainderRof(12-T)÷11,ifR=10,thecheckcodeisaletter"X";ifR≠10,thecheckcodeisthenumber"R":(12-5)mod11=7.The17-digitcheckcodeis7,whichisaggregatedinto123456789012345677.

TheformulaoftheweightingfactorisWi=2^(n-1)(mod11),wherenisthenumbersequencestartingfrom1fromrighttoleft.

Sequence

ai12345678901234567?

Wi79105842163791058421

### OrganizationCheckCode

Thenationalorganizationcodeconsistsofeightdigits(oruppercaseLatinletters)bodycodeandonedigit(OruppercaseLatinletters)checkcode.Thecheckcodeiscalculatedaccordingtothefollowingformula:

 8 C9=11-MOD(∑Ci×Wi,11) i=1

MOD-representingtheremainderfunction;i-representingthepositionnumberofthecodecharacterfromlefttoright;

Ci-representingthevalueofthecodecharacteratthei-thposition,listedinthefollowing"codecharacterset"Characters;

C9-indicatingcheckcode;

Wi-indicatingtheweightingfactoratthei-thposition,thevalues​​areasfollows:

weightingfactor

p>
 i 1 2 3 4 5 6 7 8 Wi 3 7 9 10 5 8 4 2

WhentheMODfunctionvalueWhenitis1(ieC9=10),thecheckcodeshouldberepresentedbythecapitalLatinletter“X”;whentheMODfunctionvalueis0(ieC9=11),thecheckcodeisstillrepresentedby“0”;whenthevalueofC9Whenitis1to9,thecheckcodeisdirectlyrepresentedbythevalueofC9.

## See

• Checkcodesystem

• Redundancycheck

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