Question

Assume a 10-bit data sequence, D = 1100101001 and generator polynomial, P(X) = X^4 + X^3 + X + 1.

a. Calculate FCS and indicate the transmitted bit sequence.

b. In the class, we learned that a bit error in the data portion can be detected at the receiver. Can the receiver detect a bit error if it happens in the FCS field? Show an example by assuming that the last two bits in the FCS field are in error.

Answer 1

a) FCS(Frame Check Sequence) : refers to the extra bits and characters intentionally added to data packets for error detection and control.

Here data D=1100101001 and generator polynomial, P(X) = X^4 + X^3 + X + 1

that implies the predetermined divisor P will be of 5 bits(degree of polynomial +1= 4+1) lets take value of P =11010

now divide the value of data sequence with P and append the remainder to data sequence that will give data to be transmitted.

b) Data word to be sent - 100100
   Key - 1101

Sender Side:

Therefore, the remainder is 001 and hence the 
code word sent is 100100001.

Receiver Side
Let there be an error in transmission media
Code word received at the receiver side - 100000001

Since the remainder is not all zeroes, the error is detected at the receiver side.