Answer:
Explanation:
Given that:
generator polynomial = x⁴ + x + 1
This form can be expressed in binary form as:
[tex]= 1 *x^4 + 0*x^3 +0*x^2 + 1*x^1 + 1*x^0[/tex]
= 1 0 0 1 1
=10011
The given message = 111010
Now, we can see that the length of the polynomial generator = 5
The next thing to do is to add (5-1) = 4 0's to the given message end
i.e. message = 1110100000
The next process is to divide the message with the generator to deduce the remainder which ill be added to the message for us to create a transmitted message
∴
10011║1110100000║111
10011
1 1 100
1 0011
1 1 1 1 0
1 001 1
1 1 0 1 0
1 0 01 1
1 0 010
1 0 01 1
0 010 → Remainder
∴ Transmitted message = 1 1 1 0 1 0 0 0 0 0
0 0 1 0
[tex]1 \ 1 \ 1 \ 0 \ 1 \ 0 \ 0 \ 0 \ 1 \ 0[/tex]
To check and confirm that the message transmitted is correct at the receiver's end, we have to divide the transmitted message with the generator.
So, if the end result of the remainder is 0, then the message is correct, otherwise incorrect.
10011║1110100000║1111
10011
1 1 100
1 0011
1 1 1 1 0
1 001 1
1 1 0 1 0
1 0 01 1
1 0 010
1 0 01 1
00000 → Remainder
Hence, the received message is correct.
