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 10^{3}

1M = 1,000,000 or 10^{6}

1G = 1,000,000,000 or 10^{9}^{}

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 10^{6} bytes x 8 (bits/byte) = 9.6 x 10^{6} bits

9.6 x 10^{6} bits = 52,000 (bits/sec) x ? sec
or b = r x t

9.6 x 10^{6 } = 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 10^{9} bytes x 8 (bits/byte) = 62.4 x 10^{9} bits
= 6.24 x 10^{10} bits.

6.24 x 10^{10} bits = 1.539 x 10^{6} (bits/sec) x ? sec
or b = r x t

(6.24 x 10^{10} )/(1.539 x 10^{6} ) = 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 10^{6} bytes x 8 (bits/byte) = 864 x 10^{6} bytes
= 8.64 x 10^{8} bits.

8.64 x 10^{8} bits = ? bits/sec x 16.6 sec
or b = r x t

8.64 x 10^{8} /16.6 = r

51.7 x 10^{6 } bits/sec = r
(About the same as an OC-1 connection.)

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

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