The word length of characters to be stored in a data processing system is 8 bit (one byte) (i.e., 00000000 is labeled 0 and 1111111 is labeled 255). This data processing system generates characters and stores in to a hard drive (HD). The characters labeled 0 to 31 are the most likely generated characters with probabilities 2/256 each and the characters labeled 32 to 127 are the second most likely generated characters with probabilities 1/256 each, and remaining characters labeled 128 to 255 are used equally with probabilities 1/512 each. The data processing system generates 1024 characters every second, and HD needs to store at least 24 hour of data. (a) If you need to store the data without any processing, what should be the minimum size of the HD? (b) If you need to implement the most efficient lossless compression technique, how much space is it reuired in the HD? (c) If you used Huffman Coding how much space is it required on the HD? (d) Assuming, the read and write process introduces errors on average 1 character per 1000 characters, how many character errors on average can there be in 24 hour recording? (e) In order to correct the errors, you applied (8, 4) extended Hamming code after data compression (compression rate that you found in Part B), what would be the minimum size of the HD? (f) What would be the character error rate after the Hamming code, minimum distance of the extended Hamming code is 4 (d_min = 4)? (g) Please briefly discuss the trade-offs of the systems with "only source coding", "source coding + channel coding", and "no source and channel codings