Chapter 1 HW Solutions X

# Chapter 1 HW Solutions X - CHAPTER 1 INTRODUCTION 1.1...

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1 CHAPTER 1 INTRODUCTION 1.1 EXERCISES Section 1.2: The World of Digital Systems 1.1. What is a digital signal and how does it differ from an analog signal? Give two everyday examples of digital phenomena (e.g., a window can be open or closed) and two everyday examples of analog phenomena. A digital signal at any time takes on one of a finite number of possible values, whereas an analog signal can take on one of infinite possible values. Examples of digital phenomena include a traffic light that is either be red, yellow, or green; a tele- vision that is on channel 1, 2, 3, . .., or 99; a book that is open to page 1, 2, . .., or 200; or a clothes hangar that either has something hanging from it or doesn’t. Examples of analog phenomena include the temperature of a room, the speed of a car, the dis- tance separating two objects, or the volume of a television set (of course, each ana- log phenomena could be digitized into a finite number of possible values, with some accompanying loss of information). 1.2 Suppose an analog audio signal comes in over a wire, and the voltage on the wire can range from 0 Volts (V) to 3 V. You want to convert the analog signal to a digital sig- nal. You decide to encode each sample using two bits, such that 0 V would be encoded as 00 , 1 V as 01 , 2 V as 10 , and 3 V as 11 . You sample the signal every 1 millisecond and detect the following sequence of voltages: 0V 0V 1V 2V 3V 2V 1V. Show the signal converted to digital as a stream of 0 s and 1 s. 00 00 01 10 11 10 01 1.3 Assume that 0 V is encoded as 00 , 1 V as 01 , 2 V as 10 , and 3 V as 11 . You are given a digital encoding of an audio signal as follows: 1111101001010000 . Plot

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2 c 1 Introduction the re-created signal with time on the x-axis and voltage on the y-axis. Assume that each encoding’s corresponding voltage should be output for 1 millisecond. 1.4 Assume that a signal is encoded using 12 bits. Assume that many of the encodings turn out to be either 000000000000 , 000000000001 , or 111111111111 . We thus decide to create compressed encodings by representing 000000000000 as 00 , 000000000001 as 01 , and 111111111111 as 10 . 11 means that an uncompressed encoding follows. Using this encoding scheme, decompress the fol- lowing encoded stream: 00 00 01 10 11 010101010101 00 00 10 10 000000000000 000000000000 000000000001 111111111111 010101010101 000000000000 000000000000 111111111111 111111111111 1.5 Using the same encoding scheme as in Exercise 1.4, compress the following unen- coded stream: 000000000000 000000000001 100000000000 111111111111 00 01 11 100000000000 10 1.6 Encode the following words into bits using the ASCII encoding table in Figure 1.9. a. LET
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Chapter 1 HW Solutions X - CHAPTER 1 INTRODUCTION 1.1...

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