Chapter 6

 

1.      How do we achieve a data rate of 56 kbps in 23 channels using a DS-1 format?

 

One of the 24 voice channels of the DS-1 format is used in digital transmission for synchronization, leaving 23 channels. One bit per each channel's byte is used for control transmission. So, each of the remaining 23 channels gets 7 bits 8,000 times a second (voice sampling rate) for a channel rate of 56 kps (7 * 8,000).

 

3.      Recently, a new scanner was announced that provided 1200 dpi resolution and over 1

billion colors.

 

  1. How much memory in bytes would it take to store a bit map of an 8-by-10 inch

monochrome picture at 1200 dpi with a 10-bit gray scale?

Byte = 8 bit

Several bit = 1 pixel or group of pixel

8 binary = 256

23 channel * 8+1 = 185 bits

8000 * 185 = 1,480,000 or 1.48 mbps

8*10 inch*1200dpi (square)*10 = 1,152,000,000

Answer: 1200 dpi * 1200dpi=1,440,000 pixel (actual dot per square inch)

 

  1. Suppose that the colors are represented  as a combination of three colors- red,

blue, green-each with n bits to represent its intensity. What is the least value of

n that will provide over 1 billion colors?

 

Red=10bits+blue=10bits+green=10 bits=2 to the 30th

 

  1. How long would it take to send a color representation of an 8-by-10 inch picture

at 1200dpi over T-1 line (1.544 Mbps)?

 

8*10*1200*154,400=0.0622 second

 

4.      Phototypesetters often print black or white material at resolution of 2400 dots per

linear inch. Suppose that you want to send a 7-by-11 inch page of material generated by your PC to be printed by such a typesetter.

 

  1. If you store it, uncompressed, as pixels in your PC, how much memory do you

need in bytes.

7*11=77 square inch

2400*2400=1,440,000

bits=443,520,000

byte=55,440,000 (55.4 byte)

 

  1. Suppose you have a modem that transmits at 19,200 bps. How long would it take

you to send the file to he typesetter?

Time=bits/line speed

443,520,000/19,200=23,100 second/3600 (60 min*6- sec)

                               =6.42 hour

 

5.      Assume that you are to design a TDM carrier, say T489, to support 30 voice channels

using 6 bits samples and a structure similar to T-1. Determine the bit rate required. (Look page 103-104 sample)

 

Example: 24*8+1=181

30 voice channel*6 bit+1=181

181*8,000 time per second=1.448 mbps