Digital Fundamentals
Thomas L. Floyd
Digital Concepts
Chapter 1
Ch.1 Summary
Analog Quantities
Most natural quantities that we see are analog and
vary continuously. Analog systems can generally
handle higher power than digital systems.
Digital systems can process, store, and transmit data more
efficiently but can only assign discrete values to each point.
Ch.1 Summary
Analog Signals
A waveform that continually varies in a certain manner
is classified as an analog signal.
Examples:
•Sine waves
•Audio waves
•Amplitude modulated (AM) signals
•Frequency modulated (FM) signals
Ch.1 Summary
Digital Signals
A waveform that represents a sequence of discrete
values (1’s and 0’s) is called a digital signal.
Bit streams are found in telecommunications,
computers, and other data system applications.
Ch.1 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 HIGH
(binary 1)
called a bit (for binary digit). VH(min)
A bit can have the value of Unacceptable
VL(max)
either a 0 or a 1, depending
LOW
on if the voltage is HIGH or (binary 0)
VL(min)
LOW.
Ch.1 Summary
Pulse-code Modulation (PCM)
PCM uses a sequence of digital codes to represent
a sampled analog signal.
Sampling produces the
“stair-step” voltage shown.
The higher the sampling
rate, the more accurate
the digitized waveform.
Ch.1 Summary
Analog and Digital Systems
Many systems use a mix of analog and digital circuits to utilize
the advantages of each. A typical CD player accepts digital data
from the CD drive and converts it to an analog signal for
amplification.
Ch.1 Summary
The Comparison Function
And, or, and not elements can be combined to form various
logic functions. The comparison function indicates whether a
binary value is greater than, equal to, or less than, another.
The comparison function is performed by a circuit called
a comparator.
Ch.1 Summary
The Arithmetic Functions
The arithmetic functions include addition, subtraction,
multiplication, and division.
Addition is performed by an adder and subtraction by a
subtracter. Multiplication and division are performed
using circuits that are similar to adders and subtracters.
Ch.1 Summary
The Encoder Function
Code: A set of bits arranged in a unique pattern that
represents specific information.
Encoder: A circuit that converts information into a coded
form.
Ch.1 Summary
The Decoder Function
Decoder: A circuit that converts a binary code into a non-
binary code of some kind.
Example: The decoder below converts a binary coded input
to a form that will light the segments in the 7-segment display
required to display a specific character.
Ch.1 Summary
Basic Logic Functions
Produces a high output
only if all inputs are high.
Produces a high input if one
or more inputs are high.
Changes one logic level to
the other logic level.
Ch.1 Summary
The NOT Operation
Changes one logic level to the other logic level.
The NOT operation is performed by a circuit called
an inverter.
Ch.1 Summary
The AND Operation
Produces a high output only when ALL inputs are
high.
The AND operation is performed by a circuit called
an AND gate.
Ch.1 Summary
The OR Operation
Produces a high output when one or more inputs
are high.
The OR operation is performed by a circuit called
an OR gate.
Ch.1 Summary
Periodic and Nonperiodic Pulse
Waveforms
Ch.1 Summary
Digital Waveforms
Digital waveforms change between the LOW and HIGH
levels.
A positive-going pulse is one that goes from a normally LOW
level to a HIGH level and then back again.
A negative-going pulse is one that goes from a normally HIGH
level to LOW level and then back again.
Ch.1 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 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
Ch.1 Summary
Timing Diagrams
A timing diagram is used to show the relationship
between two or more digital waveforms,
Ch.1 Summary
Series and Parallel Data
Data can be transmitted by either serial transfer or
parallel transfer.
Parallel data transfer
Serial data transfer
Ch.1 Summary
The Counting Function
Counter: A sequential device; a state machine that has a
unique internal sequence of states. Counters are used to count
events or to generate output sequences represented by
changing levels or pulses.
Ch.1 Summary
Pulse Definitions
Actual pulses are not ideal but are described by the rise
time, fall time, amplitude, and other characteristics.
