Chapter 1 Introduction to Digital Logic

Analog and Digital Signals
Analog Signals
• Continuous
• Infinite range of values
• More exact values, but
more difficult to work with
Digital Signals
• Discrete
• Finite range of values
• Not as exact as analog,
but easier to work with
2
Example:
A digital thermostat in a room displays a temperature of 72.
An analog thermometer measures the room temperature at
72.482. The analog value is continuous and more accurate,
but the digital value is more than adequate for the
application and significantly easier to process electronically.

Example of Analog Signals
• An analog signal can be any time-varying signal.
• Minimum and maximum values can be either positive or negative.
• They can be periodic (repeating) or non-periodic.
• Sine waves and square waves are two common analog signals.
• Note that this square wave is not a digital signal because its minimum value
is negative.
3
0 volts
Sine Wave Square Wave
(not digital)
Random-Periodic

Parts of an Analog Signal
4
Amplitude
(peak-to-peak)
Amplitude
(peak)
Period
(T)
Hz
T
1
F 
Frequency:

Logic Levels
Before examining digital signals, we must define logic levels. A
logic level is a voltage level that represents a defined digital state.
Logic HIGH: The higher of two voltages, typically 5 volts
Logic LOW: The lower of two voltages, typically 0 volts
5
5.0 v
2.0 v
0.8 v
0.0 v Logic Low
Logic High
Invalid
Logic
Level
Logic Level Voltage True/False On/Off 0/1
HIGH 5 volts True On 1
LOW 0 volts False Off 0

Example of Digital Signals
• Digital signal are commonly referred to as square waves or clock signals.
• Their minimum value must be 0 volts, and their maximum value must be 5
volts.
• They can be periodic (repeating) or non-periodic.
• The time the signal is high (tH) can vary anywhere from 1% of the period to
99% of the period.
6
0 volts
5 volts

Parts of a Digital Signal
7
Amplitude
Time
High
(tH)
Time
Low
(tL)
Period (T)
Rising Edge
Falling Edge
Amplitude:
For digital signals, this will ALWAYS be 5
volts.
Period:
The time it takes for a periodic signal to
repeat. (seconds)
Frequency:
A measure of the number of occurrences of
the signal per second. (Hertz, Hz)
Time High (tH):
The time the signal is at 5 v.
Time Low (tL):
The time the signal is at 0 v.
Duty Cycle:
The ratio of tH to the total period (T).
Rising Edge:
A 0-to-1 transition of the signal.
Falling Edge:
A 1-to-0 transition of the signal.
Hz
T
1
F 
Frequency:
%
100


T
t
DutyCycle H

Digital waveform
• Digital waveforms consist of voltage levels that are changing back and
forth between the HIGH and LOW levels or states.
• Figure 1–7(a) shows that a single positive-going pulse is generated
when the voltage (or current) goes from its normally LOW level to its
HIGH level and then back to its LOW level.
• The negative-going pulse in Figure 1–7(b) is generated when the
voltage goes from its normally HIGH level to its LOW level and back
to its HIGH level.
• A digital waveform is made up of a series of pulses.

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 (instantaneously).
• In practice, these transitions never occur instantaneously, although for
most digital work you can assume ideal pulses.

Nonideal Pulse Characteristics

• Figure 1–8 shows a nonideal pulse. In reality, all pulses exhibit some
or all of these characteristics.
• The overshoot and ringing are sometimes produced by stray inductive
and capacitive effects.
• The droop can be caused by stray capacitive and circuit resistance,
forming an RC circuit with a low time constant.
• 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).

• In practice, it is common to measure rise time from 10% of the pulse
amplitude (height from baseline) to 90% of the pulse amplitude and to
measure the fall time from 90% to 10% of the pulse amplitude, as
indicated in Figure 1–8.
• The bottom 10% and the top 10% of the pulse are not included in the
rise and fall times because of the nonlinearities in the waveform in
these areas.
• 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, as indicated in Figure 1–8.

Waveform Characteristics
• Most waveforms encountered in digital systems are composed of
series of pulses, sometimes called pulse trains, and can be classified as
either periodic or nonperiodic.
• 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 nonperiodic 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.

• An example of each type is shown in Figure 1–9.

• The frequency ( f ) of a pulse (digital) waveform is the reciprocal of
the period. The relationship between frequency and period is
expressed as follows:
• 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.

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.
• Notice that, in this case, each change in level of waveform A occurs at
the leading edge of the clock waveform.
• In other cases, level changes occur at the trailing edge of the clock.

• During each bit time of the clock, waveform A is either HIGH or
LOW.
• These HIGHs and LOWs represent a sequence of bits as indicated.
• A group of several bits can contain binary information, such as a
number or a letter.
• The clock waveform itself does not carry information.

Logic Gate
• It is an elementary building block of modern digital electronics.
• Most logic gates have two inputs and one output.
• At any given moment, every terminal is in one of the two binary
conditions, LOW or HIGH represented by different voltage level.
• A switch with an output that will only turn ON when inputs are in
particular position.
• Digital Logic is a representation of signals and a sequence of a digital
circuit through the numbers.

• It is the basis for digital computing and provides a fundamental
understanding on how circuits and hardware communicate within the
computer.
• Digital logic is typically embedded into most electronic devices like
mobile, computer, etc.
• Main components of digital logic consists of five different logic gates
i.e. AND, OR, NOT, NAND and NOR.

Digital Operations
• Arithmetic and Logic Operations
• Counter
• Multiplexer and Demultiplexer
• Encoder and Decoder
• etc…

Integrated Circuit(IC)
• Over the years we have observed how technology has managed to
squeeze itself to a more compact and concise structure.
• For instance, the first computers that were made were the size of a
warehouse of 1000 laptops which we use today.
• How has this been made possible?
• The integrated circuit is the answer to it.
• Three American scientists invented transistors which simplified things
to quite an extent, but it was the development of integrated circuits
that actually changed the face of the electronics technology.

• An integrated circuit (IC) is a miniature ,low cost electronic circuit
consisting of active and passive components fabricated together on a
single crystal of silicon.
• The active components are transistors and diodes and passive
components are resistors and capacitors.
• Digital system uses IC’s for many years because of their small size,
high reliability, low cost and low power consumption.

Advantages of integrated circuits
• 1. Miniaturization and hence increased equipment density.
• 2. Cost reduction due to batch processing.
• 3. Increased system reliability due to the elimination of soldered joints.
• 4. Improved functional performance.
• 5. Increased operating speeds.
• 6. Reduction in power consumption

• IC generally come in 2 types of packages i.e. flat type package and
dual inline package(DIP).
• DIP is most widely used type because of low price and easy to install
on circuit boards.
• The envelope of IC package is made up of plastics or ceramics.
• Most of package have standard size and number of pins range from 8-
64.

Types of Integration/Scale of Integration
• Integrated Circuits can be classified based on its integration scale. An
integration scale denotes the number of components fitted into a
standard Integrated Circuit.
• Small Scale Integration or (SSI) – Contain up to 10 transistors or a few
gates within a single package such as AND, OR, NOT gates.
• Medium Scale Integration or (MSI) – between 10 and 100 transistors
or tens of gates within a single package and perform digital operations
such as adders, decoders, counters, flip-flops and multiplexers.

• Large Scale Integration or (LSI) – between 100 and 1,000 transistors
or hundreds of gates and perform specific digital operations such as
I/O chips, memory, arithmetic and logic units.
• Very-Large Scale Integration or (VLSI) – between 1,000 and 10,000
transistors or thousands of gates and perform computational operations
such as processors, large memory arrays and programmable logic
devices

• Super-Large Scale Integration or (SLSI) – between 10,000 and
100,000 transistors within a single package and perform computational
operations such as microprocessor chips, micro-controllers, basic PICs
and calculators.
• Ultra-Large Scale Integration or (ULSI) – more than 1 million
transistors – the big boys that are used in computers CPUs, GPUs,
video processors, micro-controllers, FPGAs and complex PICs.

Assignment
• Study about Moore’s Law
• Study about IC Fabrication
• Write down the differences between Analog System & Digital System

Chapter 1 Introduction to Digital Logic

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