1. (10 points) Consider a code formed with the code words: 0000, 0011, 1100, 1111, What is the Hamming distance of this code? Can it detect all the single bit errors? Why? Can it correct all the single bit errors?

2. (15 points) A 8-bit message with binary number 10101100 is to be encoded using an even-parity Hamming code. What is the least number of checks bits needed for this code? Then what is the bit pattern after encoding (with the least number of check bits)?

3. (15 points) Suppose that the message is a list of five 4-bit numbers given by 0111 1011 1100 0000 0110, and it is transmitted using 4-bit Internet Checksum. What is the value of the checksum?

4. (15 points) A bit stream 10011101 is transmitted using the standard CRC method. The generator polynomial is x 3 + x 2 + 1. Show the actual bit string transmitted. Suppose the third bit from the left is inverted during transmission. Show that this error is detected at the receiver’s end.

5. (15 points) Repeat the CRC encoding for a bit stream 101001111 with the generator polynomial x 4 + x 2 + x + 1. Show the actual bit string transmitted. Suppose the third bit from the left and the fourth bit from the right are inverted during transmission. Can this error be detected?

6. (15 points) A channel has a transmission rate of 8 kbps and a propagation delay of 20 msec. Consider the Stop-and-Wait protocol. Assume that there is no error and the ACK frame size is the same as the data frame size. For what range of frame sizes do we have an efficiency η of at least 25%? How about the range when the propagation delay is 200msec?

7. (10 points) Frames of 1000 bits are sent over a 100-km long coaxial cable running at a transmission rate of 100 kbps. The ACK frame is of length 400 bits. Assume that the probability of not receiving an ACK is 0.01, and the timeout T is equal to the variable S, which is the total time from a frame is sent until the ACK is received. Assume the propagation speed in coaxial cable is 2 × 108 m/s. What is the efficiency of the Stop-and Wait protocol?

8. (15 points) A 1000-km long data link transmits 64-byte frames using the Go-Back-N protocol. The transmission rate of the link is 1.5 Mbps and the propagation delay is 18 × 10−6 sec/km. How many bits are required to support sequence numbers of frames in order to achieve 100% efficiency (i.e., keep the pipe full)? Assume that there is no error and the ACK frame is of negligible size (its transmission delay is zero).

9. (10 points) Consider a 1000-km long coaxial cable running at a transmission rate of 100 kbps. Here the propagation speed is 2×108 m/s. We use the Go-Back-N protocol for this link with window size W = 10. Assume that there is no error and the ACK frame size is the same as the data frame size. What is the minimum frame size in order to achieve 100% efficiency?

**Subject Computer Science Network Management and Data Communication**