2.8*
Computer-Related Applications:
Time
2.8
OBJECTIVES
1. Convert from one time unit to another
2. Find the distance electricity travels in various
time spans
This section focuses on computer-related applications of arithmetic. It is designed to help
you work with units of time. The vocabulary and concepts of this section will reappear in
later sections that focus on memory size and computer speed. First, we will lay the foundation for discussing computer speed.
Units Analysis
When converting units, it is important, and helpful, to carry out all unit
arithmetic.
Example
1
Convert 1 years into minutes.
2
To accomplish this, we must recall that there are 365
days
h
min
, 24
, and 60
.
yr
day
h
This will allow us to set up the following expression.
1
min
1
days
h
yr 365
24
60
2
yr
day
h
Before we even try working with the numbers, check the units to make certain
that our result will be in “min(utes).”
Because the years, days, and hours all cancel, we are left with only minutes.
We’ll go ahead with the computation.
3
days
h
min
yr 365
24
60
788,400 min
2
yr
day
h
1
There are 788,400 minutes in 1 years.
2
Our first example further illustrates the idea introduced in the Units Analysis box above.
© 2001 McGraw-Hill Companies
Example 1
Converting Time Units
Elizabeth was born September 15, 1980, at 4:00 P.M. E.D.T. How many minutes will she
have lived as of September 15, 2005, at 4:00 P.M. E.D.T.?
There are several approaches we could take to solving this problem. We will begin by
finding the number of minutes in a 365-day year. As always, take great care to do the
*The authors have classified this as an optional section. They have found the material to be motivational and
interesting to many students. But, information in this section is not requisite for subsequent chapters. It is
covered in summary exercises and indicated as optional but it does not appear in the chapter test.
201
CHAPTER 2
MULTIPLYING AND DIVIDING FRACTIONS
units arithmetic.
365 days/yr 24 h/day 60 min/h 525,600 min/yr
Now, we account for all 25 years from 1980 to 2005.
25 yr 525,600 min/yr 13,140,000 min
Although this answer may be “close enough” for some purposes it does not completely
answer the question. Why not? Elizabeth has also lived through several February twentyninths. How many? There have been six of them; 1984, 1988, 1992, 1996, 2000, and 2004.
(Why didn’t we count 1980?)
6 days 24 h/day 60 min/h 8640 min
Elizabeth will have lived for 8640 min 13,140,000 min 13,148,640 min
CHECK YOURSELF 1
Consuelo was born October 7, 1972, at 1:00 A.M. C.S.T. How many seconds will she
have been alive on October 7, 2004, at 1:00 A.M. C.S.T?
What has made the computer such a valuable tool? The computer really does nothing that
we couldn’t do before it existed. It just does it incredibly faster. A set of books that might
have taken 50 accountants 2 months to audit can be checked by one person with a computer
in a matter of minutes.
The development of ever-faster computers has forced us to look at time in smaller increments. The two boxes introduce two terms that are commonly used when a second is too
large a chunk of time for a particular application.
Definitions: Millisecond (ms)
There are 1000 milliseconds in 1 second. This also means that 1 millisecond
1
equals
second.
1000
These two statements lead us to two different conversion units, which we
will use later.
1000
ms
s
and
1
s
1000 ms
© 2001 McGraw-Hill Companies
202
COMPUTER-RELATED APPLICATIONS: TIME
SECTION 2.8
203
Definitions: Microsecond (ms)
Similarly, there are 1,000,000 microseconds in 1 second. This also means that
1
1 microsecond equals
second. The abbreviation for microsecond uses
1,000,000
the Greek letter mu, m.
The conversion units become:
1,000,000
ms
s
and
1
s
1,000,000 ms
Example 2
Converting Units of Time
(a) How many milliseconds are in 3 minutes?
s
ms
1000
180,000 ms
min
s
(b) How many microseconds are in an hour?
3 min 60
min
s
ms
60
1,000,000
3,600,000,000 ms
h
min
s
There are 3 billion, 600 million microseconds in an hour. In the course of a dull lecture
(in some nonmath class, no doubt) you can almost see them go by!
1 h 60
CHECK YOURSELF 2
(a) How many milliseconds are there in 2 hours?
(b) How many microseconds are there in 20 minutes?
Computers operate through a set of instructions called a program. The speed at which the
instructions are performed determines the speed of the computer.
Example 3
Finding Computer Speed
© 2001 McGraw-Hill Companies
If a computer can execute 25 instructions per millisecond, how many instructions can it
execute in 3 minutes?
s
inst
ms
25
1000
60
3 min 4,500,000 instructions
ms
s
min
CHECK YOURSELF 3
If a computer can execute 12 instructions per microsecond, how many instructions
can it execute in 2 minutes?
An interesting way to compare these various units of time requires use of the distance
formula.
CHAPTER 2
MULTIPLYING AND DIVIDING FRACTIONS
Rules and Properties:
The Distance Formula
drt
(Distance Rate Time)
Electricity, the key to computer speed, travels at the speed of light, 186,000 miles per sec3
ond (mi/s). That means that, in 1 second, light travels nearly the distance from Earth to
4
its moon.
Example 4
Finding Distance Traveled
(a) How far does electricity travel in 1 millisecond?
1 ms 186,000
mi
1
s
186 mi
s
1000 ms
In 1 millisecond, electricity travels approximately the distance from Dallas, Texas, to
Oklahoma City, Oklahoma.
(b) How far does electricity travel in 1 microsecond?
mi
1
s
1 ms 186,000
s
1,000,000 ms
186
mi
1000
© 2001 McGraw-Hill Companies
204
COMPUTER-RELATED APPLICATIONS: TIME
SECTION 2.8
205
We know that this is less than a mile, but by how much? We will use the fact that there
are 5280 feet in each mile to help us see how far that is.
186
ft
982,080
ft
mi 5280
1000
mi
1000
Rounding the numerator to 1,000,000, we get 1000 feet.
In 1 microsecond, electricity travels about three football fields.
10
20
30
40
50
40
30
20
10
10
20
30
40
50
40
30
20
10
10
20
30
40
50
40
30
20
10
10
20
30
40
50
40
30
20
10
10
20
30
40
50
40
30
20
10
10
20
30
40
50
40
30
20
10
CHECK YOURSELF 4
Sound travels just over 1000 feet per second. How far does sound travel in
1 millisecond?
As small as the time measures millisecond and microsecond may seem, they are not small
enough to be reasonable measures of some computer events. As a result two other measures
were developed.
Definitions: Nanosecond (ns)
There are 1 billion nanoseconds in a second. That leads to the following
conversion units.
1,000,000,000 ns/s
1
s/ns
1,000,000,000
and
Definitions: Picosecond (ps)
There are 1 trillion picoseconds in a second! Again, we have two related
conversion units.
© 2001 McGraw-Hill Companies
1,000,000,000,000 ps/s
and
1
s/ps
1,000,000,000,000
Example 5
Finding Distance Traveled
How far does electricity travel in 1 nanosecond?
186,000
mi
1
s
ft
98,208
5280
ft 1 ft
s
1,000,000,000 ns
mi 100,000
CHAPTER 2
MULTIPLYING AND DIVIDING FRACTIONS
In 1 nanosecond, electricity travels only 1 foot! This is shorter than the distance from a keyboard to the actual computer. Nanoseconds are used to measure how long it takes a signal
to get from the keyboard to the computer and back.
1
Can you even imagine the distance electricity travels in 1 picosecond? It travels about
1000
of a foot. Picoseconds are used when measuring how long it takes a signal to move on a
computer chip.
5062AN
35F2992
SFG15291
C158
5957AN
35F2092
SFG15361
C127
5912AN
35F2992
SFG10641
C068
CHECK YOURSELF 5
How far does electricity travel in 300 picoseconds? Round off your answer to the
nearest inch.
CHECK YOURSELF ANSWERS
1. 1,009,843,200 s
2. (a) 7,200,000 ms; (b) 1,200,000,000 ms
3. 1,440,000,000 instructions
4. 1 ft
5. 4 in.
© 2001 McGraw-Hill Companies
206
Name
2.8
Exercises
Section
Date
In exercises 1 to 10, complete each statement.
1. 3000 ms _________ s
2. 10 s _________ ms
3. 1 ms _________ ns
4. 5,000,000 ps _________ ms
5. 150,000 ms _________ ms
6. 35 ns _________ ps
ANSWERS
1.
2.
3.
4.
5.
6.
7.
7. 2 ms _________ ns
8. 10 min _________ ms
9. 5,000,000 ns _________ ms
10. 15 ms _________ ps
8.
9.
10.
In exercises 11 to 18, determine how far electricity travels in the given time. Express your
answer in miles.
11.
12.
11. 5 ms
12. 10 ms
13. 2 min
14. 20 ms
13.
15. 250 ms
16. 1 min
17. 10 ms
18. 30 ms
14.
15.
In exercises 19 to 26, determine how far sound travels in the given time. Express your
answer in feet.
16.
17.
19. 30 min
20. 10 s
21. 30 s
22. 10 min
18.
23. 2 min
24. 75 s
25. 720 ms
26. 1 hr
19.
20.
27. Lauren was born on April 28, 1983. How many minutes had she been alive on
April 28, 1999? (Don’t forget leap years.)
21.
© 2001 McGraw-Hill Companies
22.
23.
24.
25.
26.
27.
207
ANSWERS
28.
28. A computer can execute 36 instructions per microsecond. How many instructions can
it execute in 4 minutes?
29.
29. A computer program has 2,412,340,000 instructions. If it can execute 48 instructions
per microsecond, how many seconds will it take to execute the program?
30.
30. Light travels at a speed of 186,000 mi/s and sound travels at a speed of 1000 ft/s.
(a) What is the speed of sound in miles/hour?
1
(b) How long will it take for an observer to see a flash of lightning if it occurs mile
2
away?
(c) How long will it take for an observer to hear the sound of the crack of lightning?
Answers
3. 1000
5. 150
7. 2,000,000
9. 5
11. 930 mi
1860
13. 22,320,000 mi
15. 46,500 mi
17.
mi
19. 1,800,000 ft
1000
21. 30,000 ft
23. 120,000 ft
25. 720 ft
27. 8,415,360 min
1
29. 50 s
4
© 2001 McGraw-Hill Companies
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