0000000000010010 000
1111
0000000000001100 000
1111
0000000000000011 000
11 11
0000000000000000 110
The remainder bits, 110, are the check value for this message.
Calculate Check Value Programmatically
In MATLAB®, you can perform this same operation to obtain the check value using bit-wise
operations. First, define variables for the message and polynomial divisor. Use unsigned 32-bit
integers so that extra bits are available for the remainder.
message = 0b1101100111011010u32;
messageLength = 16;
divisor = 0b1111u32;
divisorDegree = 3;
Next, initialize the polynomial divisor. Use dec2bin to display the bits of the result.
divisor = bitshift(divisor,messageLength-divisorDegree-1);
dec2bin(divisor)
ans =
'1111000000000000'
Now, shift the divisor and message so that they have the correct number of bits (16 bits for the
message and 3 bits for the remainder).
divisor = bitshift(divisor,divisorDegree);
remainder = bitshift(message,divisorDegree);
dec2bin(divisor)
ans =
'1111000000000000000'
dec2bin(remainder)
ans =
'1101100111011010000'
Perform the division steps of the CRC using a for loop. The for loop always advances a single bit
each step, so include a check to see if the current digit is a 1. If the current digit is a 1, then the
division step is performed; otherwise, the loop advances a bit and continues.
for k = 1:messageLength
if bitget(remainder,messageLength+divisorDegree)
remainder = bitxor(remainder,divisor);
end
remainder = bitshift(remainder,1);
end
Shift the bits of the remainder to the right to get the check value for the operation.
CRC_check_value = bitshift(remainder,-messageLength);
dec2bin(CRC_check_value)
Perform Cyclic Redundancy Check
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