Download Module 1- Introduction to Digital Concepts

Introduction to Digital Electronics, Module 1: Intro to Digital Concepts
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Module 1- Introduction to Digital Concepts
Introduction:
Any measurement that has a range of values, such as temperature or
pressure, is an analog quantity. A digital value has either an ON state
(higher voltage level) or an OFF state (zero voltage level). Analog
values are contaminated by small variations in voltage levels that
naturally occur in electronic circuits. These small voltage variations,
called noise, do not affect digital systems because they read only an
ON and an OFF state. This section explores how data is sent, received,
and recorded using binary as opposed to analog voltage levels.
Concept 1-1:
Analog quantities use voltage or current levels to represent a
measured quantity that has a range of values. Digital
quantities are sequences of high or low voltage levels that
represent an analog value. Digital signals are affected less by
electrical noise than analog signals.
An analog quantity can be represented by a voltage level, a
temperature, or some graduated value on a scale that can have
multiple levels or values. A digital quantity will always be represented
by a binary sequence of bits, where each bit will only have a high or a
low voltage level. This makes the digital signal easier to distinguish
from a noise voltage that might be present. The actual value must be
converted from binary to decimal before we can understand what the
number represents.
Definition 1.1: Binary
Binary means two levels, high or low. Typically a voltage level below
0.5 volts is considered a low level, or a logical 0. A voltage level from
1.5 volts to 5 volts is considered a high level, or a logical 1.
Definition 1.2: Digital
Digital refers to systems that use binary numbers to represent numeric
values. Each digit in a binary number is weighted according to its
position in the number, allowing combinations of 1’s and 0’s, or binary
digits, to represent larger values. Each digit position in a decimal
number is worth ten times the value of the digit to its right; each digit
in a binary number is worth twice the value of the digit to its right.
Definition 1.3: Bit
Each digit in a binary number is called a bit.
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Concept 1-2:
Analog values can be represented by a series of binary digits,
logic levels, and digital waveforms.
The key to reading a binary value is that it can have only a count of
one before a carry is generated. When the count reaches two, a carry
is generated. By comparison with the more familiar decimal system, a
carry is generated when a count of 10 is reached. Decimal has ten
digits, counting from 0 through 9. Binary has only two counting digits,
0 and 1. One number above a count of 9 in decimal is the number ten.
One number above the count of 1 in binary is the binary number 1 0,
or two. This gives rise to the decimal weighting of 10 for each number
position, and the binary weighting of 2 for each number position.
In decimal, each progressive number position is worth 10 times that of
the previous number; 1, 10, 100, 1000, .... . In binary, each
progressive bit position from Least Significant Bit (LSB), which is the
right most position, to Most Significant Bit (MSB), furthest to the left in
the number, is worth 2 times the previous bit position; 1, 2, 4, 8, 16,
32, 64, ..... . Mathematically, for any based number system, the
position weight, or value, is equal to the base number (10 for decimal,
2 for binary) raised to the power of its position from 0 to n. For
example, the binary number:
1 0 0 1 = 1 * 2^3 + 0 * 2^2 + 0 * 2^1 + 1 * 2^0 = 9.
Digital sequences can be physically realized by bringing out one wire
for each bit, assigning each wire to a bit position, and looking for a
high = 1 or a low = 0 voltage on each wire. This is how a parallel
binary number is sent from one circuit to another.
A single wire can be used to send the same binary data, but one bit
must follow the next until the entire sequence of bits is sent. This is
called serial binary data transmission. When serial data is sent, it
gives rise to a binary waveform, or the electrical sequence of ones and
zeros being sent. Ideally, this sequence should be a perfect square
wave, but it is not. The textbook explains the electrical properties of
this electrical sequence of pulses.
Be sure you understand the concepts of rise time, fall time, pulse
width, period, frequency, duty cycle, ringing, overshoot, noise,
synchronous clocking and asynchronous data.
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Definition 1.4: Bus
In a parallel binary system, each bit has its own wire to send it from
one circuit to another. The individual wires taken together are called a
bus.
Definition 1.5: Parallel data
When each bit of a binary number is brought out electrically on its own
wire, the binary data is parallel data.
Definition 1.6: Serial data
When a binary value is sent from one electronic circuit to another over
a single wire, each bit must be sent in a sequence of serial ones and
zeros until each bit is sent. This sequence of binary changes on a
single wire represents a number of binary bits and is said to be a serial
data stream or simply, “serial data”.
Definition 1.7: Byte
An eight bit binary number is also called a byte.
Definition 1.8: Periodic
A waveform can be either periodic or non-periodic. Periodic means
that the waveform repeats itself every cycle, or every low-to-high-tolow transition.
A clock signal that repeats itself every cycle is an example of a periodic
waveform.
Definition 1.9:
Non-periodic
Non-periodic waveforms go high-to-low-to-high in a non-predictable
sequence, and stay high or low for a non-predictable length of time. A
serial data sequence may generate a non-periodic waveform.
Definition 1.10: Rise time (tr)
In nature, nothing can happen instantaneously. Even though a binary
electrical waveform can go from a low state to a high very rapidly, it
still requires a finite amount of time for this transition to happen. The
time required for a waveform to go from a 10% low to 90% high is
called the rise time.
Definition 1.11: Fall time (tf)
The time required for a waveform to go from 90% high to 10% low.
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Definition 1.12: Pulse width (PWL and PWH)
The time a pulse is either in a low state or in a high state is called the
pulse width. It is measured on the waveform at the 50% level. If a
low pulse is being measured, it is called the “pulse width low” or PWL.
If a high pulse is being measured, it is called the “pulse width high” or
PWH.
SERIAL DATA WAVEFORM
tr
PWH
90%
50%
10%
tf
PWL
tr = rise time or time from 10% to 90% of the waveform.
tf = fall time or time from 90% to 10% of the waveform.
PWH = pulse width high taken at the 50% line on the high pulse
PWL = pulse width low taken at the 50% line on the low pulse
1
0
1
0
0
1
1
The same data used to send out the serial data sequence 1 0 1 0 0 1 1.
Definition 1.13: Period (seconds, s)
Period implies that the waveform is periodic or repeats itself each
cycle, or low to high to low transition. The time required for this
complete cycle is called the period. It is measured from the 50% point
on the first transition to the 50% point on the next.
The period of a waveform is measured in seconds or smaller divisions of seconds
such as milliseconds (ms) - thousands of a second, microseconds (us) – millionths of
a second, or picoseconds (ps) – billionths of a second.
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Definition 1.14: Frequency (Hertz or cycles per second, Hz)
The number of cycles or transitions per second is called the frequency.
Frequency is measured in units call Hertz or Hz. The frequency of a
waveform can be calculated by measuring the period, and then taking
the mathematical inverse.
f = 1/T where T is the period in seconds or fractions of a
second.
Definition 1.15:
Overshoot and ringing
As the voltage of a waveform rises, it tends to overshoot, or rise
above, its normal high level for a very short time, then it will drop
below its norm high level. It will continue to do this for several
transitions, with each one getting closer to its normal high level until it
finally reaches the correct high level. The initial voltage that goes too
high is called the overshoot. The process of going above and below
the final normal high level for a period of time at the beginning of a
low to high transition is called ringing. Its electrical signature is
similar to that of the audio waveform of a bell or chime.
Definition 1.16: Noise
Any electrical disturbance that causes an unwanted change in a
voltage level or a waveform in an electronic circuit is called noise.
Noise can originate from automobile ignitions, lightning, or from within
the circuit itself. When a switch opens or closes, it causes a burst of
electrical noise.
Definition 1.17: Synchronous clocking
Synchronous means periodic, or an event that repeats itself in a nonvarying, uniform way. In digital electronics, a synchronous signal or
periodic clock signal is used to keep data-passing events in step. This
is called synchronous clocking. An example of synchronous clocking is
the keyboard on a typical computer. It sends out a stream of serial
data that represents each key that is pressed, and a synchronous clock
signal that goes high at each time a data bit is ready to be read.
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Definition 1.18: Asynchronous data
If serial data is sent out without an accompanying clock signal to show
where each bit of the serial data is to be read, the data is said to be
asynchronous. Asynchronous data uses clever methods of burying the
clock in the data stream so it does not require a separate clock wire.
This concept will be studied in some depth in the module on data
transmission.
Definition 1.19: Duty cycle
The duty cycle is the percentage of time the waveform is high as
compared to the period of the waveform. It is calculated by dividing
the PWH or pulse width high time by the period of the waveform, and
then multiplying by 100 to get percentage.
Duty Cycle = [(PWH)/(period)] x 100%
Concept 1.3:
There are three basic logic operations and logical functions.
All operations that manipulate binary 1’s and 0’s and use them to
control computers and electronic equipment reduce down to three
simple operations: AND, OR and INVERT. A logic gate is a device
that will input two or more binary bits at a time, and either AND them,
OR them, or INVERT them to accomplish higher mathematics and
control functions. We will start by learning what the AND, OR and
INVERT functions do, and how the accompanying gates work. The
expanded NAND, NOR and XOR gates combine traditional AND, OR
and INVERT functions for additional capabilities.
Introduction to Digital Electronics, Module 1: Intro to Digital Concepts
An INVERTER is the simplest of all gates. It outputs the opposite
binary level that it inputs. A logical "1" becomes a logical "0", and a
logical "0" becomes a logical "1". It does nothing else to the data.
An AND gate has two or more input lines for parallel binary bits, and
one output bit. The rule is that if all inputs are a high, or a logical "1",
then the output is a high, or a logical "1". The output is a logical "0"
for any other binary combination of ones and zeros on the input lines.
An OR gate has two or more input lines for parallel binary bits, and
one output bit. The rule is that if any of the inputs are a high or a
logical "1", then the output is a high or a logical "1". The only time
that the output is a low or a logical "0" is when all inputs are low or at
logical "0".
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A NAND gate is produced by inverting the output of an AND gate, or
by inverting all of the inputs to an OR gate. The rule simply becomes
the inverse of the AND gate, or if all inputs to the NAND gate are high,
or at a logical "1", then the output is low, or at a logical "0". The
output is high or at logical "1" for all other input combinations.
A NOR gate is produced by inverting the output of an OR gate, or
inverting all of the inputs to an AND gate. The output becomes the
inverse of the OR gate, and the rule is the inverse of the OR gate as
well. If any of the inputs to the NOR gate are at a high or a logical "1",
then the output becomes a low or a logical "0". The output will only be
at a high or logical "1" state if all inputs to the NOR gate are at low, or
logical "0" states.
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The last gate considered here is the EXCLUSIVE OR, or XOR gate. The
XOR gate has the rule that if all of the inputs are the same, either at a
high, or logical "1", or all low, or at a logical "0", then the output is at
a low or logical "0". If any of the inputs differ from any of the other
inputs, the output becomes a high, or a logical "1". The XOR is often
called the "binary comparator gate".
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Concept 1-4:
Complex digital logic circuits are integrated into single device
packages.
Modern technology has developed ways of putting millions of gates on
a single piece of silicone less than 1 mm square. These small “chips”
of silicone are packaged in plastic cases with small electrical
connections going from the silicone to the leads on the case. The
cases come in a variety of sizes, shapes and pin configurations. One
of the most common is to have a case with two rows of parallel pins
running down the sides. This is called a dual inline parallel package
(DIP). For this course we will use mostly DIP type integrated circuits
(IC's).
Concept 1.5:
Familiarize yourself with laboratory testing and
troubleshooting equipment.
You should understand how to adjust and use the following
equipment:
1.
digital voltmeter - to measure resistance, continuity, voltage,
and current.
2. oscilloscope - to observe voltage waveforms.
3. frequency counter - to measure oscillator clock frequencies.
4. logic probe - to observe the logical state of a binary signal
("1" or "0"), or to inject a test pulse into a logic circuit.
5. laboratory power supply - to generate the regulated +5 volts
power and to set up the current limiting feature of the power supply
to protect your circuit under test.
6. function generator - to generate a 5 Vp square wave function that
can drive a logic circuit being tested.