Problem 1. Assume that each word of your machine has 32 bits. Assume that you can multiply two n-word numbers in time 2n 2 with a standard algorithm. Assume that you can multiply two n-word numbers in time 10n lg 3 with a ""fancy"" algorithm. For each part briefly justify and show your work. (a) Approximately how large does n have to be for the fancy algorithm to be better? (b) Approximately how many bits is that? (c) Approximately how many decimal digits is that?

Consider a slotted aloha system, where the time slot equals the fixed duration of each packet. assume that there are 4 stations a,b,c,d sharing the medium. (a) stations a,b,c,d receive one packet each from higher layers at times 1.3, 1.5, 2.6,5.7 respectively. show which transmissions take place when, according to the slottedaloha protocol; describe all transmissions until all four packets have been successful.when needed, each station has access to the following sequence of random number, provided by a random number generator and drawn uniformly between 0 and 1: (1) station a draws numbers: 0.31, 0.27, 0.78, 0.9, 0.9, 0.11, 0. (2) station b draws numbers: 0.45, 0.28, 0.11, 0.83, 0.37, 0.22, 0. (3)station c draws numbers: 0.1, 0.2, 0.3, 0.4, 0. (4) station d draws numbers: 0.36, 0.77, 0.9, 0.1, 0.1, 0.1, 0.1, 0. (b) in slotted aloha, a station transmits in each time slot with a given probability. what probabilities would you assign to each of the four stations so as to: (i) maximize the efficiency of the protocol? (ii) maximize fairness among the four stations? (c) will the efficiency increase or decrease if we modify slotted aloha as follows: (i) get rid of slots and allow stations to transmit immediately? (ii) implement carrier sensing? (iii) implement collision detection? (iv) implement collision avoidance?

In this lab, you complete a python program that calculates an employee's annual bonus. input is an employee's first name, last name, salary, and numeric performance rating. if the rating is 1, 2, or 3, the bonus rate used is .25, .15, or .1 respectively. if the rating is 4 or higher, the rate is 0. the employee bonus is calculated by multiplying the bonus rate by the annual salary.

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