Delphi - crc-16

crc over one byte
procedure ByteCrc(data:byte;var crc:word);
VAR i:BYTE;
BEGIN
 FOR i:=0 TO 7 DO
  BEGIN
   IF ((data and $01)XOR(crc AND $0001)<>0) THEN
    BEGIN
     crc:=crc shr 1;
     crc:= crc XOR $A001;
    END
   ELSE crc:=crc shr 1;
   data:=data shr 1; // this line is not ELSE and executed anyway.
  END;
END;

crc over the string
the crc as result is initialized as zero, then each 
byte is processed.

function StringCrc(s:shortstring):word; 
var len,i:integer;
begin
 result:=0;
 len:=length(s);
 for i:=1 to len do bytecrc(ord(s[i]),result);
end;

usage
The data is filled into a shortstring as :

crcstring:shortstring:=chr(data[1])+..+chr(data[N]);

MyCrc:word:=StringCrc(crcstring);

notes

This crc is calculated as X^16+X^15+X^2+1 and can 
protect 2^16 bits or 8192 bytes against single bit 
errors. For longer datablocks, the crc-32 is to be 
used.

This the slow implementation requiring little RAM.
There also exists a fast implementation requiring 
more RAM to hold a table. One byte is processed in
a few assembly instructions.