Suppose in a class of 100 students, there is a homework due every week. The professor wants to encourage students to hand in their homework early so, for each homework, he gives extra credit to the first 25 students who turn their homework in. The professor wants to have a record of which students get the extra credit for each week. So, for each week, he stores the list of 25 students who will get extra credit for that week.(a) The professor decides to store the results of each week by saving a list of PIDs of the students who got the extra credit. i. How many bits are required to store each result (each list consists of 25 PIDs and one PID is a string with 9 characters and each character can be stored as an 8-bit ASCII code.)? ii. If 1 KB is 8,192 bits, how many weeks of this data can the professor store? iii. Come up with a more efficient way to store PIDs using the fact that the first character is either A or U and the following 8 characters are digits (0,1,...,9).) Show that storing PIDs this way, the professor can almost triple the number of weeks he can store on 1 KB. (b) Devise an encoding scheme that can fit 100 weeks of data into 1 KB. (Describe the scheme and also how many bits you need for each week of data.)