1) A 5 inches 7 inches color image requires a resolution of 0.005 inches for each pixel.. If each pixel is coded using 24 bits, determine the size of the file.

2) A source emits 10, 000 words that are made up of 8 symbols, s1, s2, , s8. In those 10, 000 words, the symbols, s1, s2, , s8, appear 5000, 2500, 1250, 625, 500, 75, 25 and 25 times, respectively.

a) Determine the optimal binary representations of the 8 symbols using Huffman code. Draw the code tree and represent the symbols in the tree.

b) Determine the average number of bits used to represent each symbol.

c) How much saving (in %) does the optimal code give, compared to using 3 bits for each symbol?

(Hint: If the answer to Problem # 2b) was x, then this percentage is ((3x) / 3) 100).

3) A (7, 4) cyclic code is designed with a generator polynomial, g(D) = D3 + D + 1.

a) Determine the code word for the message, 1010.

b) Determine the code word for the message, 1100.

c) Determine the error polynomial for the received word, 1110101. Is the received word correct?