1. (10 points) Consider an image of 1024×768 pixels with 3 bytes/pixel. Assuming that the image is uncompressed. How long does it take to transmit (or push out) the image over a 56-kbps (56000 bits/sec) modem channel? Over a 1-Mbps cable connection? Over a 10-Mbps Ethernet? Over a 100-Mbps Ethernet? 2. (10 points) Suppose that two hosts, A and B, are separated by 20 kilometers and are connected by a direct link. At what bandwidth would propagation delay (at a speed of 2 × 108 m/s) equal transmission delay for 100-byte packets? What about 512-byte packets? 3. (4 points) Suppose that a system has an n-layer protocol hierarchy. Applications generate messages of length M bytes. At each of the layers, an h-byte header is added. Assuming that there is no packet segmentation/fragmentation and aggregation, what fraction of the network bandwidth is filled with headers? 4. (15 points) Compare the delay in sending an x-bit message over a k-link path in a circuit-switched network and in a lightly loaded (no queueing delay) packet-switched network. The circuit setup time is s sec, the propagation delay is d sec per link, the 1 packet size is p bits, and the data rate is b bps per link. Under what conditions does the packet-switched network have a lower delay (lower end-to-end latency)? Assume that x/p is a positive number and there is no header added to each packet. 5. (15 points) Consider sending a large file of f bits from Host A to Host B. There are two links (and one switch) between A and B. Host A divides the file into packets of d bits each and adds 100 bits of header to each packet, forming packets of p = 100+d bits overall. Each link has a transmission rate of b bps. Find the value of d that minimizes the delay of moving the file from Host A to Host B (end-to-end delay). Disregard queueing delay and propagation delay here. 6. (5 points) In a constellation diagram, all the points lie on a circle centered on the origin. What kind of modulation is being used? 7. (5 points) Television channels are 6 MHz wide. How many bits/sec can be sent if eight-level digital signals are used? Assume a noiseless channel. 8. (10 points) Consider a 40-MHz channel with target data rate of 400 Mbps. What should be the minimum signal-to-noise ratio (in dB) that the channel needs to have in order to achieve the target data rate? At least how many signal levels are required? 9. (10 points) How much bandwidth is there in 0.2 microns of spectrum at a wavelength of 2 micron? Note that 1 micron is 10−6 meters, and the fundamental relation between the frequency f, the wavelength _, and the speed of light c (in a vacuum) is given by _f = c, where c = 3 × 108 meters/sec. Hint: Deal with the lowest and highest frequencies of the bandwidth corresponding to the wavelength range of 0.2 microns.