Data Rate Calculations

A bit is either a 0 or a 1, and is abbreviated as "b".
A byte consists of 8 bits, and is abbreviated as "B".
1K = 1000 or 103
1M = 1,000,000 or 106
1G = 1,000,000,000 or 109

The examples below will use power of ten notation.  If you are uncomfortable with that method, just add all on all those zeroes.  Your calculator may overflow, though.

You can easily answer the following question by using common sense, and without having to remember any formulas:  how far will you go if you drive your car at 60 miles/hr for two hours?  The answer is 120 miles, right?  You "solved" this problem intuitively by understanding the units involved.  The "hr" units on the right side of the equation below cancel out, and we are left with miles = miles.
 
                    miles = (miles/hr) x hr

Another way of writing this formula is

                    distance = rate x time
or                       d     =   r    x    t

In data rate calculations, the same method of common sense and understanding units will help you solve problems without having to remember formulas.  In data rate situations, the units become

                    bits = (bits/sec) x sec
or                 bits = rate x time
or                 b    =  r  x  t

Example 1:
How long will it take to transfer a 1.2-MB file using a modem link working at 52,000 bits/sec?

First, convert bytes to bits:
                    1.2 x 106 bytes x 8 (bits/byte) = 9.6 x 106 bits

                    9.6 x 106 bits = 52,000 (bits/sec) x ? sec            or  b = r   x   t
                    9.6 x 106   =   52,000 t
                    184 sec     =   t
                    3.08 min    =   t

Example 2:
How long does it take to back up a 7.8-GB databse using a 1.536-Mb/s connection?

First convert bytes to bits:
                   7.8 x 109 bytes x 8 (bits/byte) = 62.4 x 109 bits = 6.24 x 1010 bits.

                    6.24 x 1010 bits = 1.539 x 106 (bits/sec) x ? sec            or  b = r   x   t
                    (6.24 x 1010 )/(1.539 x 106 ) = t
                    40625 sec   =  t
                    677 min =  t
                    11.3 hr  =  t                (Not the best choice for a daily backup.)

Example 3:
A 108-MB file takes 16.6 seconds to transfer from one locaton to another.  What is the data rate?

First convert bytes to bits
                    108 x 106 bytes x 8 (bits/byte) = 864 x 106 bytes = 8.64 x 108 bits.
                    8.64 x 108 bits = ? bits/sec x 16.6 sec                                 or  b = r   x   t
                     8.64 x 108 /16.6  =  r
                    51.7 x 10  bits/sec =  r            (About the same as an OC-1 connection.)

Expect some very similar questions on this week's homework quiz.