How do I run error detection on this binary messsage using polynomial/CRC?

Question

"Show the new message to be sent by a sender after performing the CRC calculation >using the generator X3+1 on the message: 101110110:"

I have the following done but I am not sure if it is correct, some help would be appreciated:

I worked out the generator using the following steps:

Step one:
x³+1 . x³ = 1 . there is no x^2 so x^2 = 0 . There is no x^0 so x^0 = 0
x³ + 1 = 1001
generator = 1001

Step two:
I divide the message 101110110 by 1001 I get the remainder of 0101
The new message is 101110101 ??

Is this correct and which part is the CRC?

Answer 1

Note: because the polynomial you are using is of degree 3, the remainder has only 3 bits. So, the message you have to transmit is the original appended by the 3 bit remainder. In this case, the transmitted message is: 101110110101 where the last 3 bits is the remainder you found (correctly!).