1.1.7 – Logic Data Sheets
Logic Data Sheets:
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Use the Google Classroom and previous documents/work to learn more about Logic Data
Sheets.
1.1.8 & 1.1.9 – Soldering & De-soldering & Board Game Counter
Soldering & De-soldering:
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Use the Google Classroom for the presentation on 1.1.8, the images there are crucial for
soldering knowledge.
Board Game Counter:
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Use the Google Classroom for the presentation on 1.1.9, the images there are crucial for
soldering and Board Game Counter knowledge.
1.2.0 – Circuit Design Process & Troubleshooting
Circuit Design Process:
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Word Problem – Identify and define the requirement specifications. What are the inputs?
What are the outputs? Sometimes it is helpful to create a table that defines what it means
for a specification to be “high” or “low.”
Identify Circuit Types Required – What ICs are required and available for the design?
Will any part of the circuit require an analog design? Is there combination logic required?
Is there sequential logic required? Is a clock signal needed? Do I have the necessary
datasheets? Pin diagrams?
Create a Truth Table for Combination Logic Section.
Hand Calculations and Sketches of Initial Circuit.
Simulation.
Breadboard and Test (Implementation).
Circuit Design – Best Practices:

Prototype and test the circuit incrementally. Don’t design and build the entire circuit to
find it does not work properly. It is easier to troubleshoot the circuit in sections rather
than attempt to try and trouble the entire completed circuit.
Combinational Logic – Design Process(es):
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Word Problem → Create Truth-Table → Write Logic Expression → Boolean
Simplification (if applicable) → AOI Logic Implementation.
Word Problem → Create Truth-Table → K-Mapping → AOI Logic Implementation →
NAND Only Logic Implementation OR NOR Only Logic Implementation.
Troubleshooting:
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Troubleshooting is the process you must undertake to isolate the source of a problem in a
circuit and then fix it.
This process is sometimes referred to as debugging. However, debugging typically
applies to isolating a problem with software, whereas troubleshooting is typically
associated with fixing hardware problems.
Sources of Problems:
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Design Error: With this the circuit works perfectly as designed, but the design is incorrect
and does not meet design specifications.
Build Error: With this error the circuit was designed properly, but was either built
incorrectly or has a bad component.
Design & Build Error: With this error both the circuit design and build were done
incorrectly.
If you follow the design process to simulate and verify your design prior to building it,
the third error type will not occur.
Regardless of the error type, design or build, the process of identifying the error and
fixing it is the same: Divide and Conquer.
Divide and Conquer:
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In order to successfully troubleshoot a problem, you must be able to ask the right
questions; the answers to these questions will guide you to the solution.
Test → Working? → Yes? You’re done; if not, continue → Re-create a fault → Divide
and Conquer → Correct the problem → Test again (repeat if needed).
Common Errors:
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Are all ICs connected to Vcc (5V) and GND (Ground)?
Are you using the correct IC?
Are any ICs upside down in relation to how you thought you wired it?
Is the IC good? (All pins in the breadboard; does it produce the correct logic?)
If using a PCB, are all solder connections done properly?
Sometimes what works in simulation does not always work when prototyped:
- Bounce in switches/buttons.
- Software timed clocks.
1.2.2 – Analog & Digital Signals
Analog and Digital Signals:
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Analog Signals are continuous, have an infinite range of values, and have far more exact
values; they, however, are more difficult to work with.
Digital Signals are discrete, they have a finite range of values (2) and are not as exact as
analog; however, they are far easier to work with.
Examples of Analog Signals:
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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.
Waves with a negative value cannot be digital signals.
Analog waves have an amplitude (peak to peak), another amplitude (peak (positive to
zero)), a period (the time it takes to go from zero (middle) back to zero (middle) again),
and a frequency which can be found using the formula f = 1/T.
Logic Levels:
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Before understanding digital signals you must understand 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.
Logic Level
High
Low
Voltage
5 Volts
0 Volts
True/False
True
False
On/Off
On
Off
0/1
1
0
Examples of Digital Signals:
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Digital signals 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.
Digital signals have parts as well, they have amplitude (this will always be 5 volts for
digital signals), periods (the time it takes for a periodic signal to repeat (measured in
seconds)), frequency (a measure of the number of cycles of the signal per second
(measured in hertz)), time high (the time (in seconds) the signal is low or 0 volts), a duty
cycle (the ratio of tH to the period (T) expressed as a percentage) a rising edge (a 0-to-1
transition of the signal) and a falling edge (a 1-to-0 transition of the signal).
Oscilloscope:
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The oscilloscope is a piece of electronic test equipment that is used to capture and
measure time-varying signals, both analog and digital.
Can be found on the workbench (physical), part of a simulation tool (virtual), or as part of
a virtual instrumentation package on your computer (software).
See PowerPoint for images of the Virtual Oscilloscope and its labels.
1.2.3 – Binary Number System
Decimal to Binary Conversion:
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Successive division the method of decimal to binary conversion wherein you divide the
decimal number by two (2); the remainder of this is the Least Significant Bit (LSB) of
the binary number. If the quotient is zero, the conversion is complete, otherwise repeat
the steps above using the quotient as the decimal number. The new remainder is the next
most significant bit of the binary number.
Binary to Decimal Conversion:
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Weighted multiplication is how we convert binary numbers into decimal numbers; this is
done by multiplying each bit of the binary number by its corresponding bit-weighting
factor (i.e. Bit-0→20=1; Bit-1→21=2; Bit-2→22=4; etc.).
Sum up all the products in the step above to get the decimal number.
1.2.4 – Sequential Logic
Sequential Logic:
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Use the Google Classroom for the presentation on 1.2.4, the images there are crucial for
Sequential Logic knowledge.
1.2.5 – The 555 Timer
The 555 Timer:
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The 555 Timer is an 8-pin IC that is capable of producing accurate time delays and/or
oscillators.
In the time delay mode, the delay is controlled by one external resistor and capacitor.
In the oscillator mode, the frequency of oscillation and duty cycle are both controlled
with two external resistors and one capacitor.
Capacitor:
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A capacitor is an electrical component that can temporarily store a charge (voltage). The
rate that the capacitor charges/discharges is a function of the capacitor’s value and its
resistance.
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To understand how the capacitor is used in the 555 Timer oscillator circuit, you must first
understand the basic charge and discharge cycles of the capacitor.
Capacitor Charge Cycle:
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Capacitor is initially discharged.
Switch is moved to position A.
Capacitor will charge to +12V.
Capacitor will charge through the resistor.
Equation: VC = (VFinal – VInitial) * (1 – e-t/RC ) + VInitial
VC is the voltage across the capacitor; VFinal is the voltage across the capacitor that is
fully charged, and VInitial is any initial voltage across the capacitor as it begins to charge.
Capacitor Discharge Cycle:
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Capacitor is initially charged.
Switch is moved to position B.
Capacitor will discharge to +0V.
Capacitor will discharge through the resistor.
Equation: VC = (VInitial – VFinal) * (e-t/RC )
VC is the voltage across the capacitor; VFinal is the voltage across the capacitor that is
fully discharged, and VInitial is any initial voltage across the capacitor as it begins to
discharge.
Wrapping Up 1.2.5:

For the remaining information on 1.2.5 you will need to view the PowerPoint on the
Google Classroom for the necessary images to understand schematics, block diagrams,
and other aspects of the 555 Timer.
1.2.6 & 1.2.7 – Understanding Analog & Digital Design
Understanding Analog & Digital Design:
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For both 1.2.6 and 1.2.7 you will need to view the PowerPoint on the Google Classroom
for the necessary images and text to understand these concepts; there are many images
associated with the text that must be observed at the same time to fully grasp this topic.
2.1.0 – Combinational Logic Design
Combinational Logic Design:
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Design Process V1: Word Problem → Create Truth-Table → Write Logic Expression →
Boolean Simplification (if applicable) → AOI Implementation.
Design Process V2: Word Problem → Create Truth-Table → K-Mapping → AOI Logic
Implementation → NAND Only Logic Implementation OR NOR Only Logic
Implementation.
Design Process V3: Word Problem → Create Truth Table → K-Mapping & Write Logic
Expression → Programmable Logic / AOI Implementation → NAND Only Logic
Implementation OR NOR Only Logic Implementation.
2.1.1 – AOI Design: Truth Tables to Logic Expressions
Constructing a Truth Table:
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A truth table shows how a logic design’s output respond to all combinations of possible
inputs.
A logic design with N inputs with have 2N input combinations.
The inputs are listed in binary order (i.e., counting in order) in the columns to the left.
The output(s) are listed in the column(s) to the right. Note, some logic circuits can have
more than one output.
View the PowerPoint on Google Classroom for diagrams of Truth Tables and how to
make one.
Truth Table to Logic Expression:
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Write the Minterm adjacent to every row in the truth table that contains a one in the
output column.
Write the Sum of Products (SOP) logic expression by summing together all the
Minterms.
Logic Expression to Truth Table:
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For each term in the logic expression, place a one in the output column for the input
condition that matches the term.
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Some terms may match more than one input condition.
Design Specifications of Truth Table:
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Identify the number of input variables.
Assign variable names and establish the assignment condition for each variable (i.e., what
does a 0 or a 1 mean for the input?)
Create a truth table.
2.1.2 – AOI Design: Logic Analysis
Circuit to Truth Table to Logic Expression:
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Add test-points at the output of every gate.
Add a column to the truth table for every test-point.
Working from the inputs to the output, complete the truth table for each test-point,
ultimately ending at the circuit’s output.
From the completed truth table, identify the Minterms from the truth table anywhere the
output is one.
Using the extracted Minterms, write the Sum of Products logic expression.
View the PowerPoint in Google Classroom to see images of how this works.
Circuit to Logic Expression to Truth Table:
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Working from the inputs to the output, write the cumulating logic expression at the
output of each gate concluding with the expression for the circuit’s output.
Using the circuit’s output logic expression derive the circuit’s truth table.
View the PowerPoint in Google Classroom to see images of how this works.
2.1.3 – AOI Logic Implementation
Designing (AOI) Sum of Product (SOP) Logic Circuits:
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Implement each Minterm in the logic expression with an AND gate with the same
number of inputs as there are variables in the Minterm. (i.e., AB = 2 input gate, ABC = 3
input gate, ABCD = 4 input gate, etc).
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OR together the outputs of the AND gates to produce the logic expression.
If necessary, gates can be cascaded to create gates with more inputs.
Designing (AOI) Product of Sum (POS) Logic Circuits:
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Implement each Maxterm in the logic expression with an OR gate with the same number
of inputs as there are variables in the Maxterm. (i.e. A+B = 2 input gate, A+B+C = 3
input gate, A+B+C+D = 4 input gate, etc.).
AND together the outputs of the OR gates to produce the logic expression.
If necessary, gates can be cascaded to create gates with more inputs.
2.1.4 Circuit Simplification: Boolean Algebra
What is Boolean Algebra?:
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Boolean algebra is a mathematical technique that provides the ability to algebraically
simplify logic expressions. These simplified expressions will result in a logic circuit that
is equivalent to the original circuit, yet requires fewer gates.
For the rest of Boolean Algebra please read the PowerPoint on the Google Classroom for
images in relation to the process’ required to complete the simplification.
2.1.5 Circuit Simplification: DeMorgan’s Theorems
DeMorgan’s Theorems:
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For the entirety of Circuit Simplification using DeMorgan’s theorems please view the
PowerPoint in the Google Classroom, these images will assist you in proper
simplification using DeMorgan’s theorems.