LGW2ECh3Solutions

# LGW2ECh3Solutions - Communication Networks(2nd Edition...

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Communication Networks (2 nd Edition) Chapter 3 Solutions Solutions to Chapter 3 1. Suppose the size of an uncompressed text file is 1 megabyte. Solutions follow questions: a. How long does it take to download the file over a 32 kilobit/second modem? T 32k = 8 (1024) (1024) / 32000 = 262.144 seconds b. How long does it take to take to download the file over a 1 megabit/second modem? T 1M = 8 (1024) (1024) bits / 1x10 6 bits/sec = 8.38 seconds c. Suppose data compression is applied to the text file. How much do the transmission times in parts (a) and (b) change? If we assume a maximum compression ratio of 1:6, then we have the following times for the 32 kilobit and 1 megabit lines respectively: T 32k = 8 (1024) (1024) / (32000 x 6) = 43.69 sec T 1M = 8 (1024) (1024) / (1x10 6 x 6) = 1.4 sec 2. A scanner has a resolution of 600 x 600 pixels/square inch. How many bits are produced by an 8-inch x 10-inch image if scanning uses 8 bits/pixel? 24 bits/pixel? Solution: The number of pixels is 600x600x8x10 = 28.8x10 6 pixels per picture. With 8 bits/pixel representation, we have: 28.8x10 6 x 8 = 230.4 Mbits per picture. With 24 bits/pixel representation, we have: 28.8x10 6 x 24 = 691.2 Mbits per picture. 3. Suppose a computer monitor has a screen resolution of 1200 x 800 pixels. How many bits are required if each pixel uses 256 colors? 65,536 colors? Solution: The number of pixels is 1200 x 800 = 960000 pixels per screen. With 256 colors, we have: 9.6x10 5 x log 2 256 = 9.6x10 5 x 8 = 7.68 x 10 6 bits per screen. With 65536 colors, we have: 9.6x10 5 x log 2 65536 = 9.6x10 5 x 16 = 15.36 x 10 6 bits per screen. 4. Explain the difference between facsimile, GIF, and JPEG coding. Give an example of an image that is appropriate to each of these three methods. Solution: Facsimile scans a black-and-white image into rows of black and white dots, which are then compressed. The scanning process introduces distortion in the sense that the scanned image is not the same as the original image. GIF takes image data, in binary form, and applies a lossless data compression scheme. JPEG involves scanning an image and applying a lossy compression scheme that is designed so that the distortion is not visible. Leon-Garcia/Widjaja 1

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Communication Networks (2 nd Edition) Chapter 3 Solutions 5. A digital transmission system has a bit rate of 45 megabits/second. How many PCM voice calls can be carried by the system? Solution: PCM channels = (45x10 6 bits/sec) / (64x10 3 bits/sec channel) = 703 channels. 6. Suppose a storage device has a capacity of 1 gigabyte. How many 1-minute songs can the device hold using conventional CD format? using MP3 coding? Solution: A stereo CD signal has a bit rate of 1.4 megabits per second, or 84 megabits per minute, which is approximately 10 megabytes per minute. Therefore a 1 gigabyte storage will hold 1 gigabyte/10 megabyte = 100 songs. An MP3 signal has a lower bit rate than a CD signal by about a factor of 14, so 1 gigabyte storage will hold about 1400 songs.
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