When examining X-rays, radiologists often deal with four to six images at a time. For a faithful digital representation of an X-ray photograph, a pixel array of 2048 by 2048 is typically used with a grayscale of intensity for each pixel of 12 bits. As you would hope, radiologists do not look kindly on compression that degrades quality.

a. How many levels of grayscale are represented by 12 bits?

b. How many bits does it take to represent a single X-ray photograph?

c. Suppose five X-rays have to be sent to another site over a T-l line (1.544 Mbps). How long would it take, ignoring overhead?

d. Suppose now that we wish to build a communications system that provides the five X-rays of part (c) upon demand; that is, from the time the X-rays are requested we want them available within 2 seconds. What is the lowest channel rate that can support this demand?

e. The next generation of displays for X-rays is planned for 4096 by 4096 pixels with a 12-bit grayscale. What does the answer to part (d) become when using this resolution?