Practice word problems

Problems:
1. you have 300.672 Mbits to send over an OC-3 line. How long will it take ?
2. you want to fax an 8 inch x 11 inch black and white image. You can choose from 300 linear dpi or 2400 linear dpi. You need to be able to transfer the image in less than 10 minutes over a 30,000 bps asynchronous line. Which resolution would you choose and why ?
3. For the same image, what is the minimum capacity SONET/OC level we would need to send the high resolution black and white image in less than one second?
4. What OC level would be needed to send the same high resolution image in less than one second if our fax could send 16 shades of gray?

Answers:
1. Method: figure out the payload for OC-3 from the table on page 153 of the book. Then use the formula: total bits / bitrate = time. 300.672 Mbits / 150.336 Mbps = 2 seconds.
2. Method: Use the same formula: total bits / bitrate = time.
   total bits = 8 inch * 300 dpi * 11 in * 300 dpi * 1 bit per pixel = 7,920,000 bits
   or total bits = 8 inch * 2400 dpi * 11 in * 2400 dpi * 1 bit per pixel = 506,880,000 bits
   

   payload bit rate = 30,000 bps * .8 = 24,000 bps

   time = 7,920,000 bits / 24,000 bps = 330 seconds
   or time = 506,880,000 bits / 24,000 bps = 21,120 seconds
   10 minutes = 600 seconds, so we would choose the lower resolution.

3. Consult the SONET/SDH/OC table in the book. OC-12, 622 Mbps with a payload of 601 Mbps is the minimum we would need.
4. 16 shades of gray requires 4 bits per pixel. So we need 4 times the capacity. 4 times 506.888 Mbits = 2027.552 Mbits. To send that amount in one second requires an OC-48 line with a rate of 2488 Mbps and a payload of 2405 Mbps.