Part 1

Digital Concepts

Floyd, Digital Fundamentals, 10th ed

© 2009 Pearson Education
 Syllabus
COURSE OUTCOMES:

Demonstrate knowledge of binary numbers, codes, and arithmetic.

Demonstrate knowledge of Boolean Algebra and its applications.
Demonstrate ability to analyze and design combinational logic circuits.
Demonstrate ability to analyze and design sequential logic circuits.

TOPICS COVERED:

Number systems and codes.

Boolean and switching algebra.
Combinational logic design.
Combinational Building Blocks.
Flip-flops and counters.
Asynchronous and synchronous sequential logic.
Review/Tests.

LABORATORY

Lab familiarization, simple logic gate.

Basic Logic Gates.
Combinational Logic Minimization and Design.
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education
 Digital
Fundamentals
Tenth Edition

Floyd

© 2008 Pearson Education

Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education
 Analog Quantities

Most natural quantities that we see are analog and vary

continuously. Analog systems can generally handle higher
power than digital systems.
Temperature
(°F)

100
95
90
85
80
75
70
Time of day
1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
A .M . P.M .

Digital systems can process, store, and transmit data more

efficiently but can only assign discrete values to each point.
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education
 Analog and Digital Systems

Many systems use a mix of analog and digital electronics to

take advantage of each technology. A typical CD player
accepts digital data from the CD drive and converts it to an
analog signal for amplification.

CD drive

10110011101 Digital-to-analog Linear amplifier

Digital data converter Analog
reproduction
of music audio Speaker
signal
Sound
waves

Floyd, Digital Fundamentals, 10th ed

© 2009 Pearson Education
 Analog and Digital Systems

Digital systems are more immune to noise

Floyd, Digital Fundamentals, 10th ed

© 2009 Pearson Education
 Binary Digits and Logic Levels

Digital electronics uses circuits that have two states, which

are represented by two different voltage levels called HIGH
and LOW. The voltages represent numbers in the binary
system.
VH(max)

In binary, a single number is HIGH

called a bit (for binary digit). A VH(min)

bit can have the value of either Invalid

VL(max)
a 0 or a 1, depending on if the
voltage is HIGH or LOW. LOW
VL(min)

Floyd, Digital Fundamentals, 10th ed

© 2009 Pearson Education
 Digital Waveforms

Digital waveforms change between the LOW and HIGH

levels. A positive going pulse is one that goes from a
normally LOW logic level to a HIGH level and then back
again. Digital waveforms are made up of a series of pulses.

HIGH HIGH
Rising or Falling or Falling or Rising or
leading edge trailing edge leading edge trailing edge

LOW LOW
t0 t1 t0 t1

(a) Positive–going pulse (b) Negative–going pulse

Floyd, Digital Fundamentals, 10th ed

© 2009 Pearson Education
 Pulse Definitions

Actual pulses are not ideal but are described by the rise time,
fall time, amplitude, and other characteristics.
Overshoot
Ringing
Droop
90%
Amplitude tW
50%
Pulse width

10%
Ringing

Base line Undershoot

tr tf
Rise time Fall time

Floyd, Digital Fundamentals, 10th ed

© 2009 Pearson Education
 Periodic Pulse Waveforms

Periodic pulse waveforms are composed of pulses that repeat in

a fixed interval called the period. The frequency is the rate at
which it repeats and is measured in hertz.
1 1
f = T=
T f

The clock is a basic timing signal that is an example of a

periodic wave.
What is the period of a repetitive wave if f = 3.2 GHz?
1 1
T= = = 313 ps
f 3.2 GHz

Floyd, Digital Fundamentals, 10th ed

© 2009 Pearson Education
 Pulse Definitions

In addition to frequency and period, repetitive pulse waveforms

are described by the amplitude (A), pulse width (tW) and duty
cycle. Duty cycle is the ratio of tW to T.
Volts

Pulse
width
Amplitude (A) (tW)

Time
Period, T

Floyd, Digital Fundamentals, 10th ed

© 2009 Pearson Education
 Timing Diagrams

A timing diagram is used to show the relationship between

two or more digital waveforms,
Clock

A diagram like this can be observed

directly on a logic analyzer.

Floyd, Digital Fundamentals, 10th ed

© 2009 Pearson Education
 Serial and Parallel Data

Data can be transmitted by either serial transfer or parallel

transfer.
1 0 1 1 0 0 1 0
t0 t1 t2 t3 t4 t5 t6 t7
Computer Modem

1
Computer Printer
0

0
t0 t1

Floyd, Digital Fundamentals, 10th ed

© 2009 Pearson Education
 Basic Logic Functions

True only if all input conditions

are true.

True only if one or more input

conditions are true.

Indicates the opposite condition.

Floyd, Digital Fundamentals, 10th ed

© 2009 Pearson Education
 Basic System Functions

And, or, and not elements can be combined to form

various logic functions. A few examples are:

The comparison function A

Comparator
A> B

Two
binary A= B Outputs
numbers
B
A< B

Basic arithmetic functions Adder

A
Two Σ Sum
binary
numbers Carry out
Cout
B
Carry in Cin

Floyd, Digital Fundamentals, 10th ed

© 2009 Pearson Education
 Basic System Functions

HIGH
9 Encoder
8
7
6 Binary code
5 for 9 used for

The encoding function

4 storage and/or
3 computation
2
7 8 9 1
4 5 6 0
1 2 3
0 . +/–
Calculator keypad

The decoding function

Decoder

Binary input

7-segment display

Floyd, Digital Fundamentals, 10th ed

© 2009 Pearson Education
 Basic System Functions

The data selection function

Multiplexer Demultiplexer
A D
Data from Data from Data from Data from
A to D B to E C to F A to D
∆t1 ∆t1
∆ t1 ∆ t2 ∆ t3 ∆t 1
B E
∆t2 ∆t2
∆t3 ∆t3
C F

Switching Switching
sequence sequence
control input control input

Floyd, Digital Fundamentals, 10th ed

© 2009 Pearson Education
 Basic System Functions

The counting function

Counter Parallel
output lines Binary Binary Binary Binary Binary
code code code code code
1 2 3 4 5 for 1 for 2 for 3 for 4 for 5
Input pulses Sequence of binary codes that represent
the number of input pulses counted.

…and other functions such as code conversion

and storage.

Floyd, Digital Fundamentals, 10th ed

© 2009 Pearson Education
 Basic System Functions

One type of storage function is the shift register,

that moves and stores data each time it is clocked.
Serial bits
on input line
Initially, the register contains onlyinvalid
0101 0 0 0 0 data or all zeros as shown here.

First bit (1) is shifted serially into the

010 1 0 0 0 register.

Second bit (0) is shifted serially into

01 0 1 0 0 register and first bit is shifted right.

Third bit (1) is shifted into register and

0 1 0 1 0 the first and second bits are shifted right.

Fourth bit (0) is shifted into register and

0 1 0 1 the first, second, and third bits are shifted
right. The register now stores all four bits
and is full.

Floyd, Digital Fundamentals, 10th ed

© 2009 Pearson Education
 Integrated Circuits

DIP (Dual-In-line Pins) chips and

surface mount chips
Pin 1

Dual in-line package Small outline IC (SOIC)

Floyd, Digital Fundamentals, 10th ed

© 2009 Pearson Education
 Integrated Circuits

VCC VCC VCC VCC

14 13 12 11 10 9 8 14 13 12 11 10 9 8 14 13 12 11 10 9 8 14 13 12 11 10 9 8

1 2 3 4 5 6 7
GND
1 2 3 4 5 6 7
GND
1 2 3 4 5 6 7
GND
1 2 3 4 5 6 7
GND
Cutaway view of DIP chip:
'00 ' 02 '04 '08
Plastic
VCC VCC VCC VCC
Chip case
14 13 12 11 10 9 8 14 13 12 11 10 9 8 14 13 12 11 10 9 8 14 13 12 11 10 9 8

1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7
GND GND GND GND
'10 '11 '20 '21

VCC VCC VCC VCC

14 13 12 11 10 9 8 14 13 12 11 10 9 8 14 13 12 11 10 9 8 14 13 12 11 10 9 8 Pins

1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7
GND GND GND GND
'27 '30 '32 '86

Floyd, Digital Fundamentals, 10th ed

© 2009 Pearson Education
 1. Compared to analog systems, digital systems
a. are less prone to noise
b. can represent an infinite number of values
c. can handle much higher power
d. all of the above

Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
© 2008 Pearson Education
 2. The number of values that can be assigned to a bit are
a. one
b. two
c. three
d. ten

Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
© 2008 Pearson Education
 3. The time measurement between the 50% point on the
leading edge of a pulse to the 50% point on the trailing edge
of the pulse is called the
a. rise time
b. fall time
c. period
d. pulse width

Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
© 2008 Pearson Education
 4. The time measurement between the 90% point on the
trailing edge of a pulse to the 10% point on the trailing edge of
the pulse is called the
a. rise time
b. fall time
c. period
d. pulse width

Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
© 2008 Pearson Education
 5. The reciprocal of the frequency of a clock signal is the
a. rise time
b. fall time
c. period
d. pulse width

Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
© 2008 Pearson Education
 6. AND, OR, and NOT gates can be used to form
a. storage devices
b. comparators
c. data selectors
d. all of the above

Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
© 2008 Pearson Education
 7. A shift register is an example of a
a. storage device
b. comparator
c. data selector
d. counter

Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
© 2008 Pearson Education
 8. A device that is used to switch one of several input lines to
a single output line is called a
a. comparator
b. decoder
c. counter
d. multiplexer

Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
© 2008 Pearson Education