Assume you have ten terminal devices with 9600 bps lines that need to be multiplexed using a synchronous time division mux (TDM). What is the required trunk line capacity for this transmission? Assuming you wish to limit the trunk line utilization to 80%, and assuming that each of the terminals is busy 50% of the time, what line capacity will you need if you chose to use a statistical time division mux?

You are given a compression software that compresses mathematical documents. Assume there are 336 mathematical symbols to be compressed. This software compresses data by categorizing characters into the following 3 categories of frequencies:

Category	Frequency	Number of Bits	Number of Characters
1	0.7	4	16
2	0.25	6	64
3	0.05	8	256

As shown above, 4 bits are used to encode the category 1 characters, 6 bits for category 2, and 8 bits for category 3 characters. In addition, each character is preceded by a 2 bit code that indicates whether the following character is a 4 bit, 6 bit, or 8 bit character. What is the compression ratio of this software for a typical document containing 5000 mathematical symbols