Data Link Layer - 1. Dr. Sanjay P. Ahuja, Ph.D. Fidelity National Financial Distinguished Professor of CIS School of Computing, UNF. Introduction.
Dr. Sanjay P. Ahuja, Ph.D.
Fidelity National Financial Distinguished Professor of CIS
School of Computing, UNF
Original Data Stream: 0110 11111 11111 01101
Data on the line: 0110 11111 0 11111 0 01101
For odd parity: 1 1110001
For even parity: 0 1110001
But some patterns still go undetected.
E.g. if bits 1 and 3 are in error in both
char 1 and char 5. Success rate in detecting
errors is about 75%.
T = (k + n) bit frame to be transmitted, with n<k
M = k-bit message, the first k-bits of T
F = n-bit FCS, the last n-bits of T
P = pattern of (n+1) bits; this is the predetermined divisor
(Note: the FCS or remainder is always 1 bit less than the divisor, P)
Message, M = 1010001101 (10 bits)
Pattern P (divisor) = 110101 (6 bits)
FCS, Remainder (R) = to be calculated (5 bits)
The message is multiplied by 25 (to shift it 5 bits to the left and padded with 0s): 1010001101 00000
This product is now divided by P.
Remainder, R (FCS) = 01110 since remainder has to have 5 bits.
The transmitted message then is 101000110101110. The receiver divides the message it receives by the same divisor, P, and if the remainder is 0, it assumes there were no errors during transmission.
M(x)=1⋅x7 + 1⋅x6 + 1⋅x5 + 0⋅x4 + 0⋅x3+ 0⋅x2 + 1⋅x+ 1 = x7 + x6+x5+x+1