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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1 Introduction
the recreated signal with time on the xaxis and voltage on the yaxis. 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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 Spring '08
 Strickland
 Binary numeral system, Decimal, 1 byte, 3bit, 0 Volts

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