1. Calculate the even parity of 101011.

2. Consider the bitstring X3 +X2 . After carrying out the operation X4 (X3 +X2 ), what is the resulting bitstring?

3. Consider the generator polynomial X16+1. The maximum length of the remainder has ___ bits.

4. How many registers and XOR gates are required for the polynomial: X5 +X3 +X2 +1?

5. Compute the minimum hamming distance for the following codewords: 00000, 01101, 10110, 11011. Suppose that a string 10001 is received, which codeword is the correct one? 6. A code has the following valid codewords: {111, 100, 001, 010}. How many data bits does it encode?

7. Encode the following message using Hamming (12,8): 1111 0000. Assume even parity.

8. The following bitstring is encoded using Hamming (12,8): 000110100100. Which bit is incorrect? Assume even parity. 9. Calculate the valid codeword for the bitstring 1001 using the following G matrix