Homework #5 Solutions
cs349 -- Networks

Questions 8 and 15 from Chapter 2

8) Assume that a SONET reciver resynchronizes its clock whenever
   a 1 bit appears; otherwise, the receiver samples the signal in
   the middle of what it believes is the bit's timeslot.

   a) What relative accuracy is required to receive 48 zero bytes
      in a row?

   We need to drift less than 1/2 of a bit-width per
   384 bits (48 bytes), which is an accuracy of about one
   part in 768, or 0.13%


15) Suppose we want to transmit the message 11001001 and protect
    it from errors using the CRC polynomial x^3 + 1

    a)  Use polynomial long division to determine the message
        that should be transmitted.

	1001 ) 11001001000
               1001
               ----
                1011
                1001
                ----
                  1000
                  1001
                  ----
                     1100
                     1001
                     ----
                      1010
                      1001
                      ----
                        11

	The remainder is 11, so we have to subtract 11 from
	the message, which is the same as XORing, so the
	signal that goes out is

	11001001011   (the last three bits are the CRC)

    b) Suppose the leftmost bit gets inverted in transit.  What
       is the result of the receiver's CRC calculation?

	The received signal is 01001001011 which we divide by 1001


	1001 ) 01001001011
                1001
                ----
                      1011
                      1001
                      ----
                        10  Since the remainder is non-zero,
			    we know that something went wrong!