For this example, we take the message above (ASCII 'N') and modify the message so it becomes an ASCII y and we still ensure that the ICV remains valid using the process described in Chapter 15.
Stating the problem: Given P(x)= 01001110110, derive P'(x)=01111001XXX where XXX is a valid CRC.
First, the delta between the current message, M(x), and the desired message, N(x), is computed by the exclusive OR of the two values.
M(x) = 01001110 N(x) = 01111001 D(x) = 00110111
Now, the CRC is calculated for the delta value:
------------ 1101 |00110111000 1101 1100 1101 010
The remainder of the division is the CRC of the delta. Now the delta and its CRC are exclusive OR'd with P(x):
P(x) 01001110110 D(x) 00110111000 01111001110 CRC(D) 010 P'(x) 01111001100
Now, P'(x) is shown to be a valid message; the remainder of the CRC calculation is 0.
------------ 1101 | 01111001100 1101 1000 1101 1011 1101 1101 1101 0
Because the remainder of the CRC calculation is 0, P'(x) has a valid CRC and the message has been successfully modified.