A bit stream 10011101 is transmitted using the standard CRC method described in thetext. The generator polynomial is x 3 + 1. Show the actual bit string transmitted. Sup-pose that the third bit from the left is inverted during transmission. Show that thiserror is detected at the receiver’s end. Give an example of bit errors in the bit stringtransmitted that will not be detected by the receiver.

The Cyclic Redundancy Check (CRC) is a method used for error detection in digital networks and storage devices. The generator polynomial in this case is x^3 + 1, which corresponds to the binary sequence 1001.

Step 1: Preparation The original bit stream is 10011101. To prepare for the CRC, we append (degree of polynomial) zeros to the end of this bit stream. The degree of our polynomial is 3, so we append three zeros, giving us 10011101000.

Step 2: Division We then perform binary division using our generator polynomial (1001). The result of this division gives us the remainder.

Step 3: Appending the Remainder The remainder from the division is then appended to the original bit stream in place of the appended zeros. This gives us the actual bit string transmitted.

If the third bit from the left is inverted during transmission, the receiver will perform the same division operation. If the remainder is non-zero, this indicates that an error has occurred during transmission.

However, not all errors can be detected. For example, if two bits are inverted such that they cancel each other out during the division operation, the error will not be detected. This is a limitation of the CRC method.