• The CRC frame detects the following errors:
  1. All single -bit errors
  2. Almost all double bit errors
  3. Any odd number of errors.
  4. Any error with larger bursts.

Note: The checksum is often known as Frame Check Sequence (FCS) ---usually 16 bit long.


SHIFT REGISTER

EXCULSIVE OR

CRC POLYNOMIAL FOR X5 + X4 +X3 + X2 + 1

TYPES OF CRC:
1. CRC-12 : X12 + X11 + X2 +X + 1
2. CRC-16 : X16 + X15 + X2 + 1
3. CRC-CCITT : X16 + X15 + X2 + 1
4. CRC32 : X32 + X26 + X23 +X22 +X16 + X12 + X11 +X10 +X8 + X7 + X6 +X5 +X4 +X2+ 1

Cyclic Redundancy Checking

    For Modulo 2 arithmetic

            T = 2 n M + F

•             TR= 2 n M + R
•             Q + R = ( 2 n M ) / P

For Polynomials :

• [ X n M (x) ] / [ P (x) ] = Q (x) + [ R (x) / P (x) ]
• T (x) = X n M (x) + R (x)

Where:
T = ( k+ n) - bit frame to be transmitted, with n < k
M= ( k -bit) message, the first k bits of T
F = ( n - bit) Frame Check Sequence(FCS), the last n bits of T
P = pattern of (n+1) ; this is the predetermined divisor

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