THE DIGITAL INFORMATION AGE

THE DIGITAL INFORMATION AGE

AN INTRODUCTION TO ELECTRICAL ENGINEERING

SECOND EDITION

(Solutions Manual 100% Original Verified, A+ Grade) 1 / 4

Contents

• Introduction 1

1.1 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Excel Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

• Sensors & Actuators 7

2.1 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Excel Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

• Combinational Logic Circuits 19

3.1 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2 Excel Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

• Sequential Logic Circuits 29

4.1 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.2 Excel Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

• Converting Between Analog & Digital Signals 41

5.1 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 5.2 Excel Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

• Modeling Random Data & Noise 55

6.1 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 6.2 Excel Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

• Detecting Data Signals in Noise 67

7.1 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 7.2 Excel Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

• Designing Signals for Multiple-Access Systems 85

8.1 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 8.2 Excel Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

• Source Coding 109

9.1 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 9.2 Excel Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 10 Channel Coding 131 10.1 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 10.2 Excel Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 11 Data Networks 141 11.1 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 11.2 Excel Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 12 Symbology 151 12.1 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 12.2 Excel Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 2 / 4

Chapter1 Introduction 1.1 Problems Problem 1.1 (Illuminated mouse)You often power your laptop with the battery while you are trav- eling. You need to buy a new mouse, but want to maximize the battery life. Explain why buying the illuminated mouse is not a wise choice.(ans: An illuminated mouse contains an LED light source that requires power, which is supplied by the battery. Hence, battery life will be decreased with an illuminated mouse.) Problem 1.2 (Threshold detection)Digital signals that occur within your computer are designed to

be either 0 V or 5 V. Additive noise produced the following detected values:

−0.1,3.9,0.9,5.1,0.7,4.85

What threshold value would you use to restore the values? Explain why. Restore these detected values to their designed values.(ans: The ideal threshold is mid-way between the two voltage extremes. Hence, with [0,5V], a 2.5V threshold does not favor either 0V or 5V signals. Restored values are

0,5,0,5,0,5

) Problem 1.3 (Error correction)Threshold detection converted signal values 0 V and 5 V into binary logic values 1 and 0. For transmission over a noisy channel, each binary value is transmitted five times.

A threshold detector produces the following binary sequence:

00100 11001 01000 10110 10001

• Assuming at most 2 errors occur per 5-bit code word, estimate the probability of error in the

channel as the number of errors in the sequence divided by the number of data bits transmissions.1© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 3 / 4

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CHAPTER 1.INTRODUCTION

(ans: There are

25 data transmissions and there are 8 errors. This gives Prob[error]= 8 25

= 0.32

)

• What rule

would you apply to try to correct the errors?(ans: Count number of 1’s in each code word, if count≤2then corrected codeword is 00000, otherwise 11111.)

• Write your corrected binary sequence.

(ans:

00000 11111 00000 11111 00000

) Problem 1.4 (Prediction with Moore’s law)Using the current year’s performance as the base, how much more powerful will your computer be in 6 years?

(ans:

P(t1) =P(to)e t 1 −to

1:5

t1=to+ 6gives P(to+ 6) =P(to)e to+6 −to

1:5=P(to)e

6

1:5

P(to+ 6) P(to) =e 4

= 2.7183

4 = 54.6 ) Problem 1.5 (Prediction with Moore’s law)How long will you need to wait for your next computer to be 100 times more powerful than your current computer?

(ans: Inxyears, we have an improvement of one hundred, or

P(to+x) P(to) =e x

1:5= 100

Taking the lo garithm to the basee(natural logarithm) of the left side gives ln ( e x

1:5

) = x 1.5 and equating to the lo garithm of the right side x 1.5 = ln(100)→x= 1.5 ln(100) = 1.5(4.6) = 6.9years )© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

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