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Digital
Fundamentals
Tenth Edition
Floyd
Chapter 1
Digital concepts
Floyd, Digital Fundamentals, 10th ed
2008 Pearson
Education
© 2009 Pearson Education,©Upper
Saddle River,
NJ 07458. All Rights Reserved
Summary
Digital and Analog Quantities
Analog quantity is one having continuous values.
Digital quantity is one having a discrete set of values.
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Digital and Analog Quantities
Most natural quantities that we see are analog and vary
continuously (For example Air Temperature). 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, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Digital and Analog Quantities
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
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 data
Digital-to-analog
converter
Linear amplifier
Analog
reproduction
of music audio
signal
Speaker
Sound
waves
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
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
called a bit (for binary digit). A
bit can have the value of either
a 0 or a 1, depending on if the
voltage is HIGH or LOW.
HIGH
VH(min)
Invalid
VL(max)
LOW
VL(min)
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
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 to its LOW level .
A Negative-going pulse generated when the voltage goes from its
normally HIGH level to its LOW level and back to its HIGH level
HIGH
HIGH
Rising or
leading edge
LOW
Falling or
trailing edge
t0
(a) Positive–going pulse
t1
Falling or
leading edge
LOW
Rising or
trailing edge
t0
t1
(b) Negative–going pulse
Digital waveforms are made up of a series of pulses.
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Pulse Definitions
-Pulse has two edges:
-Leading edge Occurs first at time t0
-Trailing edge Occurs last at time t1
-for a positive-going pulse the leading edge is a rising edge
and Trailing edge is a falling edge
-Pulses ideal when the rising and falling edges are assumed
to change in zero time (in-stantaneously)
HIGH
HIGH
Rising or
leading edge
LOW
Falling or
trailing edge
t0
(a) Positive–going pulse
Floyd, Digital Fundamentals, 10th ed
t1
Falling or
leading edge
LOW
Rising or
trailing edge
t0
t1
(b) Negative–going pulse
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Pulse Definitions
-Rise time (tr) the time required for a pulse to go from its
low level to its high level.
-Fall time (tf) the time required for a pulse to go from its
high level to its low level.
-Amplitude height from baseline.
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
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
Floyd, Digital Fundamentals, 10th ed
Undershoot
tr
tf
Rise time
Fall time
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Periodic Pulse Waveforms
Periodic pulse waveforms are composed of pulses that repeats
in a fixed interval called the period. The frequency is the rate
at which it repeats it self and is measured in hertz.
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Pulse Definitions
In addition to frequency and period, repetitive pulse waveforms
are described by the amplitude (A), pulse width (tW) and duty
cycle.
pulse width (tw) is a measure of the duration of the pulse
Duty cycle is the ratio of pulse width (t)W to period (T).
Volts
Amplitude (A)
Pulse
width
(tW)
Time
Period, T
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Digital Waveform Carries Binary Information
Bit time each bit in a sequence occupies a defined time
interval.
The clock is a basic timing signal that is an example of a
periodic wave.
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Timing Diagrams
A timing diagram is graph of digital waveforms showing the
actual time relationship of two or more waveforms and how
each waveform changes on relation the others.
Clock
A
B
C
A diagram like this can be observed
directly on a logic analyzer.
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Serial and Parallel Data
Data refers to groups of bits, which represented by digital
waveforms must be transferred from one circuit to
another(from memory to CPU), can be transferred by either
serial transfer (sent one bit at a time) or parallel transfer(all
bits in a group are sent at the same time).
1
Computer
Printer
0
1
t0
0
t1
1
t2
1
t3
0
t 4 t5
Computer
0
1
t6
1
0
t7
1
Modem
0
0
1
0
t0
Floyd, Digital Fundamentals, 10th ed
t1
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
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, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
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
numbers
A= B
B
A< B
Basic arithmetic functions
Adder
A
Two
binary
numbers
B
Carry in
Floyd, Digital Fundamentals, 10th ed
Outputs
Σ
Cout
Sum
Carry out
Cin
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Basic System Functions
HIGH
The encoding function
Convert information such as
decimal digit to binary code
7
4
8
1
2
3
0
.
+/–
5
9
6
9
8
7
6
5
4
3
2
1
0
Encoder
Binary code
for 9 used for
storage and/or
computation
Calculator keypad
The decoding function
Decoder
Convert coded information such
as Binary number to decimal form
Binary input
7-segment display
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Basic System Functions
The data selection function
Multiplexer
A
∆t1
B
Demultiplexer
Data from
A to D
Data from
B to E
Data from
C to F
Data from
A to D
∆ t1
∆ t2
∆ t3
∆t 1
D
∆t1
E
∆t2
C
∆t2
∆t3
∆t3
Switching
sequence
control input
Switching
sequence
control input
F
Multiplexer Switches digital data from several input lines onto a single
output line
Demultiplexer Switches digital data from one input line to several
output lines
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Basic System Functions
The counting function
Counter
1
2
3
4
Input pulses
5
Parallel
output lines
Binary
code
for 1
Binary
code
for 2
Binary
code
for 3
Binary
code
for 4
Binary
code
for 5
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, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Integrated Circuits
All the logic elements and functions that have been discussed
are generally available in integrated circuit (IC) form.
integrated circuit (IC) : Is an electronic
circuit that is constructed entirely on a
single small chip of silicon
Chip
Plastic
case
Pins
Fixed-function logic and Programmable logic
are two broad categories of digital ICs
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Fixed-function logic
Fixed-function logic A category of digital integrated circuits
having functions that cannot be altered.
The logic functions are set by the manufacturer and cannot
be altered
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved
Summary
Programmable Logic
Programmable logic devices (PLDs) are an alternative to
fixed function devices. The logic can be programmed for a
specific purpose.
In general, they cost less and use less board space that fixed
function devices.
Floyd, Digital Fundamentals, 10th ed
© 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved