请教检查码的算法! (200分)

向各位高手请教检查码的算法!
N个数,最后一位为检查码,
如123456789X,求计算X的
各种详细算法!
最好有几种!谢谢!

奇偶校验，CRC等很多，看看书，很多的，有算法说明，不难！

查错用CRC,XOR
纠错用RS,BCH

XOR 最简单， 给你贴一段crc32吧
(*
CRC32 Calc Class
(C) 1996 Glen Why
*)
unit CRC32CALC;
interface
uses
SysUtils, Classes;
type
ECRC32CalcError = class( Exception );
TGetDataEvent = procedure( pData ointer;
Var cbData :Integer ) of object;
TCRC32Calc = class( TComponent )
private
FBufferSize : Integer;
FBuffer ointer;
FOnGetData :TGetDataEvent;
FBusy :Boolean;
procedure SetBufferSize( Value :Integer );
procedure SetOnGetData( Value :TGetDataEvent );
function GetBufferAllocated :Boolean;
property BufferAllocated :Boolean
read GetBufferAllocated;
protected
procedure ValidateIdleState;
procedure AllocateBuffer;
procedure GetData( pData ointer;
var cbData :Integer );
virtual;
function IsValidBufferSize( Value :Integer ):Boolean;
virtual;
property Buffer ointer
read FBuffer;
public
constructor Create( anOwner :TComponent );
override;
destructor Destroy;
override;
function CalcFile( Stream :TFileStream ):Longint;
function CalcMem( pData ointer;
cbData :Integer ) :Longint;
function CalcGen :Longint;
property Busy :Boolean
read FBusy;
published
property BufferSize :Integer
read FBufferSize write SetBufferSize;
property OnGetData :TGetDataEvent
read FOnGetData write SetOnGetData;
end;

procedure Register;

implementation
uses
FileMapping;
procedure Register;
begin
RegisterComponents( 'more...', [ TCRC32Calc ] );
end;

function CRC32R( CRC :Longint;
const Data;
cbData :Longint ) :Longint;
assembler;
asm
or edx, edx
je @@exi
jecxz @@exi
push ebx
@@upd:
movzx ebx, al
xor bl, [ edx ]
shr eax, 8
and eax, 00FFFFFFh
xor eax, cs:[ ebx + OFFSET @@C32TT ]
inc edx
loop @@upd
pop ebx
@@exi:
ret
@@C32TT:
DD 000000000h, 077073096h, 0ee0e612ch, 0990951bah
DD 0076dc419h, 0706af48fh, 0e963a535h, 09e6495a3h
DD 00edb8832h, 079dcb8a4h, 0e0d5e91eh, 097d2d988h
DD 009b64c2bh, 07eb17cbdh, 0e7b82d07h, 090bf1d91h
DD 01db71064h, 06ab020f2h, 0f3b97148h, 084be41deh
DD 01adad47dh, 06ddde4ebh, 0f4d4b551h, 083d385c7h
DD 0136c9856h, 0646ba8c0h, 0fd62f97ah, 08a65c9ech
DD 014015c4fh, 063066cd9h, 0fa0f3d63h, 08d080df5h
DD 03b6e20c8h, 04c69105eh, 0d56041e4h, 0a2677172h
DD 03c03e4d1h, 04b04d447h, 0d20d85fdh, 0a50ab56bh
DD 035b5a8fah, 042b2986ch, 0dbbbc9d6h, 0acbcf940h
DD 032d86ce3h, 045df5c75h, 0dcd60dcfh, 0abd13d59h
DD 026d930ach, 051de003ah, 0c8d75180h, 0bfd06116h
DD 021b4f4b5h, 056b3c423h, 0cfba9599h, 0b8bda50fh
DD 02802b89eh, 05f058808h, 0c60cd9b2h, 0b10be924h
DD 02f6f7c87h, 058684c11h, 0c1611dabh, 0b6662d3dh
DD 076dc4190h, 001db7106h, 098d220bch, 0efd5102ah
DD 071b18589h, 006b6b51fh, 09fbfe4a5h, 0e8b8d433h
DD 07807c9a2h, 00f00f934h, 09609a88eh, 0e10e9818h
DD 07f6a0dbbh, 0086d3d2dh, 091646c97h, 0e6635c01h
DD 06b6b51f4h, 01c6c6162h, 0856530d8h, 0f262004eh
DD 06c0695edh, 01b01a57bh, 08208f4c1h, 0f50fc457h
DD 065b0d9c6h, 012b7e950h, 08bbeb8eah, 0fcb9887ch
DD 062dd1ddfh, 015da2d49h, 08cd37cf3h, 0fbd44c65h
DD 04db26158h, 03ab551ceh, 0a3bc0074h, 0d4bb30e2h
DD 04adfa541h, 03dd895d7h, 0a4d1c46dh, 0d3d6f4fbh
DD 04369e96ah, 0346ed9fch, 0ad678846h, 0da60b8d0h
DD 044042d73h, 033031de5h, 0aa0a4c5fh, 0dd0d7cc9h
DD 05005713ch, 0270241aah, 0be0b1010h, 0c90c2086h
DD 05768b525h, 0206f85b3h, 0b966d409h, 0ce61e49fh
DD 05edef90eh, 029d9c998h, 0b0d09822h, 0c7d7a8b4h
DD 059b33d17h, 02eb40d81h, 0b7bd5c3bh, 0c0ba6cadh
DD 0edb88320h, 09abfb3b6h, 003b6e20ch, 074b1d29ah
DD 0ead54739h, 09dd277afh, 004db2615h, 073dc1683h
DD 0e3630b12h, 094643b84h, 00d6d6a3eh, 07a6a5aa8h
DD 0e40ecf0bh, 09309ff9dh, 00a00ae27h, 07d079eb1h
DD 0f00f9344h, 08708a3d2h, 01e01f268h, 06906c2feh
DD 0f762575dh, 0806567cbh, 0196c3671h, 06e6b06e7h
DD 0fed41b76h, 089d32be0h, 010da7a5ah, 067dd4acch
DD 0f9b9df6fh, 08ebeeff9h, 017b7be43h, 060b08ed5h
DD 0d6d6a3e8h, 0a1d1937eh, 038d8c2c4h, 04fdff252h
DD 0d1bb67f1h, 0a6bc5767h, 03fb506ddh, 048b2364bh
DD 0d80d2bdah, 0af0a1b4ch, 036034af6h, 041047a60h
DD 0df60efc3h, 0a867df55h, 0316e8eefh, 04669be79h
DD 0cb61b38ch, 0bc66831ah, 0256fd2a0h, 05268e236h
DD 0cc0c7795h, 0bb0b4703h, 0220216b9h, 05505262fh
DD 0c5ba3bbeh, 0b2bd0b28h, 02bb45a92h, 05cb36a04h
DD 0c2d7ffa7h, 0b5d0cf31h, 02cd99e8bh, 05bdeae1dh
DD 09b64c2b0h, 0ec63f226h, 0756aa39ch, 0026d930ah
DD 09c0906a9h, 0eb0e363fh, 072076785h, 005005713h
DD 095bf4a82h, 0e2b87a14h, 07bb12baeh, 00cb61b38h
DD 092d28e9bh, 0e5d5be0dh, 07cdcefb7h, 00bdbdf21h
DD 086d3d2d4h, 0f1d4e242h, 068ddb3f8h, 01fda836eh
DD 081be16cdh, 0f6b9265bh, 06fb077e1h, 018b74777h
DD 088085ae6h, 0ff0f6a70h, 066063bcah, 011010b5ch
DD 08f659effh, 0f862ae69h, 0616bffd3h, 0166ccf45h
DD 0a00ae278h, 0d70dd2eeh, 04e048354h, 03903b3c2h
DD 0a7672661h, 0d06016f7h, 04969474dh, 03e6e77dbh
DD 0aed16a4ah, 0d9d65adch, 040df0b66h, 037d83bf0h
DD 0a9bcae53h, 0debb9ec5h, 047b2cf7fh, 030b5ffe9h
DD 0bdbdf21ch, 0cabac28ah, 053b39330h, 024b4a3a6h
DD 0bad03605h, 0cdd70693h, 054de5729h, 023d967bfh
DD 0b3667a2eh, 0c4614ab8h, 05d681b02h, 02a6f2b94h
DD 0b40bbe37h, 0c30c8ea1h, 05a05df1bh, 02d02ef8dh
end;

{ TCRC32Calc }
const
MIN_BUFFER_SIZE = $1000;
MAX_BUFFER_SIZE = $100000;
DEF_BUFFER_SIZE = MIN_BUFFER_SIZE;

procedure TCRC32Calc.SetBufferSize( Value :Integer );
begin
ValidateIdleState;
if ( FBufferSize <> Value ) and IsValidBufferSize( Value ) then
begin
if FBuffer <> nil then
begin
FreeMem( FBuffer );
FBuffer := nil;
FBufferSize := 0;
if Value <> 0 then
GetMem( FBuffer, Value );
end;
FBufferSize := Value;
end;
end;

procedure TCRC32Calc.SetOnGetData( Value :TGetDataEvent );
begin
ValidateIdleState;
FOnGetData := Value;
end;

procedure TCRC32Calc.ValidateIdleState;
begin
if busy then
raise ECRC32CalcError.Create( 'CRC Calc is Busy' );
end;

constructor TCRC32Calc.Create( anOwner :TComponent );
begin
inherited Create( anOwner );
FBufferSize := DEF_BUFFER_SIZE;
end;

destructor TCRC32Calc.Destroy;
begin
if FBuffer <> nil then
FreeMem( FBuffer );
inherited Destroy;
end;

function TCRC32Calc.GetBufferAllocated :Boolean;
begin
result := assigned( Fbuffer );
end;

procedure TCRC32Calc.AllocateBuffer;
begin
if not BufferAllocated then
GetMem( FBuffer, FBufferSize );
end;

procedure TCRC32Calc.GetData( pData ointer;
var cbData :Integer );
begin
if assigned( FOnGetData ) then
FOnGetData( pData, cbData ) else
cbData := 0;
end;

function TCRC32Calc.IsValidBufferSize( Value :Integer ):Boolean;
begin
result := ( Value >= MIN_BUFFER_SIZE ) and ( Value <= MAX_BUFFER_SIZE );
end;

function TCRC32Calc.CalcFile( Stream :TFileStream ):Longint;
begin
ValidateIdleState;
FBusy := true;
try
with TFileMapping.Create( Stream )do
try
result := not CRC32R( $FFFFFFFF, Memory^, Stream.Size );
finally
free;
end;
finally
FBusy := false;
end;
end;

function TCRC32Calc.CalcMem( pData ointer;
cbData :Integer ) :Longint;
begin
ValidateIdleState;
FBusy := true;
try
result := not CRC32R( $FFFFFFFF, pData^, cbData );
finally
FBusy := false;
end;
end;

function TCRC32Calc.CalcGen :Longint;
var C :Integer;
begin
ValidateIdleState;
FBusy := true;
try
AllocateBuffer;
result := $FFFFFFFF;
repeat
C := FBufferSize;
GetData( FBuffer, C );
result := CRC32R( result, FBuffer^, C );
until ( C = 0 );
result := not result;
finally
FBusy := false;
end;
end;
end.

可以到网上去下载

给你一段身份证15位升18位的程序,最后一位为检查码,
function usercard(ID: string):string;
const
W:array [1..18] of integer = (7,9,10,5,8,4,2,1,6,3,7,9,10,5,8,4,2,1);
A:array [0..10] of char = ('1','0','x','9','8','7','6','5','4','3','2');
var
i, j, S: integer;
NewID: string;
begin

if Length(ID) <> 15 then
result:= ''
else
begin
NewID:= ID;
Insert('19', NewID, 7);
S:= 0;
try
for i:=1 to 17do
begin
j:= StrToInt(NewID) * W;
S:= S + j;
end;
except
result:= '';
exit;
end;
S:= S mod 11;
Result:= NewID + A;
end;
end;

sqlman,
你还有问题吗？可以结束了吧！
关于CRC，和海明码《计算机组成原理》书上有，

对清华的那一本!

多人接受答案了。