CRC (Cyclic Redundancy Check)

A cyclic redundancy check (CRC) is an error-detecting code commonly used in digital networks and storage devices to detect accidental changes to raw data. Blocks of data entering these systems get a short check value attached, based on the remainder of a polynomial division of their contents. On retrieval, the calculation is repeated and, in the event the check values do not match, corrective action can be taken against data corruption. CRCs can be used for error correction 

Let's consider following example
11010011101100 is the given data

11010011101100 000 <--- input right padded by 3 bits
1011               <--- divisor (4 bits) = x³+x+1
------------------
01100011101100 000 <--- result
detailed Solution :-
11010011101100 000 <--- input right padded by 3 bits
1011               <--- divisor
01100011101100 000 <--- result
 1011              <--- divisor ...
00111011101100 000
  1011
00010111101100 000
   1011
00000001101100 000
       1011
00000000110100 000
        1011
00000000011000 000
         1011
00000000001110 000
          1011
00000000000101 000 
           101 1
-----------------
00000000000000 100 <---remainder (3 bits)

Click here to get the C program of CRC