IS2120 Homework 2
Due January 23
1. Find the check number (that is, find the value of ?) for the ISBN
(uses a weighted code with base 11):
0-521-63028-?
2. Consider the square code with 25 message bits and 10 check bits.
- a. How many messages can be received? (given any number of errors)
- b. How many of them are valid code words? (that is, with no errors)
- c. How many of them contain a single (and therefore correctable)
error?
- d. Choose one of the other messages (i.e. with two or more errors),
and show how it can be interpreted as more than one possible message
with equal probability.
3. For a block of 35 message bits, compute the efficiencies
for each of the following numbers of message bits. Give four answers:
- a. For a rectangular code
- b. For a triangular code
- c. For a cubic code
- d. For a Hamming code
4. For a triangular code with 6 message bits, and 4 check bits,
what is the probabilitity that a random sequence of 10 bits corresponds
to a valid message?
5. Using the 7 bit Hamming Code, correct the following strings, if
necessary:
- a. 0010000
- b. 0101000
- c. 0010110
- d. 1000001