Chapter-1 Introductory Concepts

1-1 Digital and Analog Quantities

1-2 Binary Digits, Logic Levels, and Digital Waveforms
1-3 Basic Logic Functions

Digital Logic Design

CHAPTER OBJECTIVES

 Explain the basic differences between digital and analog quantities

 Show how voltage levels are used to represent digital quantities

 Describe various parameters of a pulse waveform such as rise time, fall time,

pulse width, frequency, period, and duty cycle

 Explain the basic logic functions of NOT, AND, and OR

 Describe several types of logic operations and explain their application in an

example system
1-1 Digital and Analog Quantities
Electronic circuits can be divided into two broad categories, digital and analog. Digital electronics
involves quantities with discrete values, and analog electronics involves quantities with continuous values.

Analog
An analog quantity is one having continuous values.
Most things that can be measured quantitatively occur in nature in analog form.
For example, the air temperature changes over a continuous range of values. Other examples of analog
quantities are time, pressure, distance, and sound.
Digital
A digital quantity is one having a discrete set of values. Digital systems use binary format as 0 and 1.
The Digital Advantage

Digital representation has certain advantages over analog representation in electronics applications.
For one thing, digital data can be processed and transmitted more efficiently and reliably than analog data.
Also, digital data has a great advantage when storage is necessary.
For example, music when converted to digital form can be stored more compactly and reproduced with greater
accuracy and clarity than is possible when it is in analog form.
An Analog System
A public address system, used to amplify sound so that it can be heard by a large audience, is one simple
example of an application of analog electronics. The basic diagram in Figure 1–3 illustrates that sound
waves, which are analog in nature, are picked up by a microphone and converted to a small analog voltage
called the audio signal.
A System Using Digital and Analog Methods

The compact disk (CD) player is an example of a system in which both digital and analog circuits are used.
The simplified block diagram in Figure 1–4 illustrates the basic principle. Music in digital form is stored on
the compact disk.
A laser diode optical system picks up the digital data from the rotating disk and transfers it to the digital-to-
analog converter (DAC). The DAC changes the digital data into an analog signal that is an electrical
reproduction of the original music.
When the music was originally recorded on the CD, a process, essentially the reverse of the one described
here, using an analog-to-digital converter (ADC) was used.
SECTION 1–1 CHECKUP

1. Define analog.

2. Define digital.

3. Explain the difference between a digital quantity and an analog quantity.

4. Give an example of a system that is analog and one that is a combination of both

digital and analog. Name a system that is entirely digital.

1–2 Binary Digits, Logic Levels, and Digital Waveforms
Digital electronics involves circuits and systems in which there are only two possible states.
These states are represented by two different voltage levels: A HIGH and a LOW.

In digital systems such as computers, combinations of the two states (1s and 0s), called codes, are used to
represent numbers, symbols, alphabetic characters, and other types of information.

The two-state number system is called binary, and its two digits are 0 and 1.
A binary digit is called a bit.

Binary Digits
Each of the two digits in the binary system, 1 and 0, is called a bit, which is a contraction of the words
binary digit.

In digital circuits, two different voltage levels are used to represent the two bits.
Generally, 1 is represented by the higher voltage, which we will refer to as a HIGH, and a 0 is
represented by the lower voltage level, which we will refer to as a LOW.

HIGH = 1 and LOW = 0

Another system in which a 1 is represented by a LOW and a 0 is represented by a HIGH is called
negative logic..
Digital Waveforms

Digital waveforms consist of voltage

levels that are changing back and forth
between the HIGH and LOW levels or
states.

The Pulse
As indicated in Figure 1–7, a pulse has two edges: a leading edge that occurs first at time t0 and a trailing
edge that occurs last at time t1 .

For a positive-going pulse, the leading edge is a rising edge, and the trailing edge is a falling edge.
The pulses in Figure 1–7 are ideal because the rising and falling edges are assumed to change in zero time.

A digital waveform is made up of a series of pulses.

Figure 1–8 shows a non-ideal pulse. In reality, all pulses exhibit some or all of these characteristics.

The time required for a pulse to go from its LOW level to its HIGH level is called the rise time (tr ), and
the time required for the transition from the HIGH level to the LOW level is called the fall time (tf ).

The pulse width (tW) is a measure of the duration of the pulse and is often defined as the time interval
between the 50% points on the rising and falling edges,
Waveform Characteristics

A periodic pulse waveform is one that repeats itself at a fixed interval, called a period (T).

The frequency ( f ) is the rate at which it repeats itself and is measured in hertz (Hz).

A non-periodic pulse waveform, of course, does not repeat itself at fixed intervals and may be
composed of pulses of randomly differing pulse widths and/or randomly differing time intervals
between the pulses.
The frequency ( f ) of a pulse (digital) waveform is the reciprocal of the period.
The relationship between frequency and period is

An important characteristic of a periodic digital waveform is its duty cycle,

which is the ratio of the pulse width (tW) to the period (T).
It can be expressed as a percentage.

Example 1.1
A portion of a periodic digital waveform is shown in Figure 1–10. The measurements are in
milliseconds. Determine the following: (a) period (b) frequency (c) duty cycle
Sol:
(a) T = 10ms

Related Problem: A periodic digital waveform has a pulse width of 25 ms and a period of 150 ms.
Determine the frequency and the duty cycle.
The Clock
The Clock In digital systems, all waveforms are synchronized with a basic timing waveform called the
clock. The clock is a periodic waveform in which each interval between pulses (the period) equals the time
for one bit

An example of a clock waveform is shown in Figure 1–11.

Timing Diagrams

A timing diagram is a graph of digital waveforms showing the actual time relationship of two or more
waveforms and how each waveform changes in relation to the others.
Data Transfer
Data refers to groups of bits that convey some type of information.
Binary data, which are represented by digital waveforms, must be transferred from one device to another
within a digital system or from one system to another in order to accomplish a given purpose.

When bits are transferred in serial form from one point to

another, they are sent one bit at a time along a single line,
as illustrated in Figure 1–13(a).

When bits are transferred in parallel form, all the bits in a

group are sent out on separate lines at the same time.
There is one line for each bit, as shown in Figure 1–13(b)
Example 1.2
(a) Determine the total time required to serially transfer the eight bits contained in waveform A of Figure 1–14,
and indicate the sequence of bits. The left-most bit is the first to be transferred. The 1 MHz clock is used as
reference.
(b) What is the total time to transfer the same eight bits in parallel?

Sol:
(a)

Related Problem: If binary data are transferred on a USB at the rate of 480 million bits per second
(480 Mbps),how long will it take to serially transfer 16 bits?
SECTION 1–2 CHECKUP

1. Define binary.

2. What does bit mean?

3. What are the bits in a binary system?

4. Knowing the period of a waveform, how do you find the frequency?

5. Explain what a clock waveform is.

6. What is the purpose of a timing diagram?

7. What is the main advantage of parallel transfer over serial transfer of binary data?
1–3 Basic Logic Functions

In its basic form, logic is the realm of human reasoning that tells you a certain proposition (declarative
statement) is true if certain conditions are true.
Propositions can be classified as true or false.
Many situations and processes that you encounter in your daily life can be expressed in the form of
propositional, or logic, functions.
Since such functions are true/false or yes/no statements, digital circuits with their two-state characteristics
are applicable.
Several propositions, when combined, form propositional, or logic, functions.

For example, the propositional statement “The light is on” will be true if “The bulb is not burned out” is
true and if “The switch is on” is true.

Therefore, this logical statement can be made: The light is on only if the bulb is not burned out and the
switch is on.

In this example the first statement is true only if the last two statements are true.

The first statement (“The light is on”) is then the basic proposition, and the other two statements are the
conditions on which the proposition depends.
The term logic is applied to digital circuits used to implement logic functions. Several kinds of digital logic
circuits are the basic elements that form the building blocks for such complex digital systems as the computer.
Three basic logic functions (NOT, AND, and OR) are indicated by standard distinctive shape symbols in Figure
1–16.

The lines connected to each symbol are the inputs and outputs.

The inputs are on the left of each symbol and the output is on the right.

A circuit that performs a specified logic function (AND, OR) is called a logic gate.

AND and OR gates can have any number of inputs, as indicated by the dashes in the figure.
NOT

 The NOT function changes one logic level to the opposite logic level, as indicated in Figure 1–17.

 When the input is HIGH (1), the output is LOW (0).

 When the input is LOW, the output is HIGH.

 The NOT function is implemented by a logic circuit known as an inverter.

AND

 The AND function produces a HIGH output only when all the inputs are HIGH, as indicated in

Figure 1–18 for the case of two inputs.

 When one input is HIGH and the other input is HIGH, the output is HIGH.

 When any or all inputs are LOW, the output is LOW.

 The AND function is implemented by a logic circuit known as an AND gate.

OR

 The OR function produces a HIGH output when one or more inputs are HIGH, as indicated in
Figure 1–19 for the case of two inputs.

 When one input is HIGH or the other input is HIGH or both inputs are HIGH, the output is
HIGH.

 When both inputs are LOW, the output is LOW.

 The OR function is implemented by a logic circuit known as an OR gate.

SECTION 1–3 CHECKUP

1. When does the NOT function produce a HIGH output?

2. When does the AND function produce a HIGH output?

3. When does the OR function produce a HIGH output?

4. What is an inverter?

5. What is a logic gate?

Summary of Introductory Concepts
1-1 Digital and Analog Quantities

1-2 Binary Digits, Logic Levels, and Digital Waveforms

1-3 Basic Logic Functions

TRUE/FALSE QUIZ

1. An analog quantity is one having continuous values.

2. A digital quantity has no discrete values.

3. There are two digits in the binary system.

4. The term bit is short for binary digit.

5. In positive logic, a LOW level represents a binary 1.

6. A periodic wave repeats itself at a fixed interval.

7. A timing diagram shows the timing relationship of two or more digital waveforms.

8. An AND function is implemented by a logic circuit known as an inverter.

Multiple Choice
Problems