The document contains homework assignments and lab instructions for an introductory digital circuits course. The homework covers topics like logic gates, binary arithmetic, and circuit design. The labs focus on using equipment like power supplies, multimeters, and oscilloscopes to assemble and test simple circuits using logic gates and adders/subtractors. The overall goal is for students to learn basic digital concepts and gain experience using laboratory test and simulation tools.
1. ECET 105 Week 1 Homework
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1. Does a typical computer have any analog outputs? If so, what are
they?
2. List three advantages of digital signal representation as compared
to their analog representation.
3. Convert 126 x 10+2 to scientific and engineering notations.
4. Make the following conversions:
a. Convert 0.34 seconds to milliseconds.
b. Express 0.0005 x 10-4 farads as picofarads.
5. The frequency of a signal is equal to the reciprocal of the signal’s
period (f = 1/p). For a computer with a 2.4 GHz clock, what is the
clock period? Use engineering notation for your answer.
6. The signal shown below is a sine wave as it might be displayed on
an oscilloscope. If it takes 40 msec. for the waveform to travel
between the points shown by the arrow “B” below, what is the
frequency of the waveform?
7. Power (in watts) is a certain amount of energy (in joules) divided
by a certain length of time (in seconds). The laser with the highest
2. peak power produces energy of 186 joules in 167 femtoseconds. What
is the peak power? Use engineering notation for your answer. (Note:
Use references to determine the value of a femtosecond and the
proper notation for your answer.)
8. Which logic function produces a HIGH output only when all of the
inputs are HIGH?
9. Which logic function produces a HIGH output only when all of the
inputs are LOW?
10. Using the Internet, find the data sheet for the 74LS00 integrated
circuit chip. Answer the following:
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ECET 105 Week 1 iLab Introduction to Laboratory Test
Equipment
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I. OBJECTIVES
1. To learn the function and basic operation of the instruments
comprising a test bench
2. To gain a basic understanding of how to use the power supply,
DMM, oscilloscope, and function generator
3. 3. To take measurements using the power supply, DMM,
oscilloscope, and function generator
4. To determine waveform characteristics of various signals
II. PARTS LIST
Equipment
IBM PC or Compatible with Windows 2000 or Higher
ELVIS II+
Parts
1 - 1.0 kohm Resistor (color bands = brown, black, red, gold)
1 - 4.7 kohm Resistor (color bands = yellow, violet, red, gold)
III. PROCEDURES
A. Introduction to Instruments and Measurements
Before beginning this lab, be sure that you have read the Lab Prepfor
an explanation of how to use the various instruments.
1. Measure DC voltage with the DMM.
a. Attach the power supply +5 V outputs to the DMM inputs.
b. Launch the ELVIS II+ DMM and select DC Voltage.
1. Press Run and record the reading below, including units.
2. Press Stop.
4. DMM measurement ___________________________
2. Measure DC voltage with the oscilloscope.
1. Launch the ELVIS II+
2. Enable Channel 0.
3. Ensure the following settings.
• Probe—10x
• Coupling—DC
• Scale—2 Volts/Div
• Vertical Position—0
• Timebase—50 us/Div
• Trigger Type—Immediate
• Trigger Source—Chan 0 Source
• Horizontal Position—50
• Acquisition Mode—Run Continuously
1. Connect the oscilloscope probe from the oscilloscope to the +5
V output (main probe to +5 V and ground to GND).
2. Press Run and read the voltage on the oscilloscope. Record
your reading with the appropriate unit in engineering notation.
5. Vertical scale _____________ Horizontal scale______________
V = _____________
1. Press Stop.
3. Measure resistance with the DMM.
4. Remove a 1 kohm resistor (color bands are brown, black, red,
gold) from the parts kit. The first three bands indicate the value of the
resistor and the fourth band indicates the accuracy of the resistance. A
gold band indicates that the measured value should be within ±5% of
the specified value.
5. Switch the DMM to ohms (Ω) and measure the resistor value
by clipping the probes to each end of the resistor.
6. Press Start and record the measured value and the calculated
range (1 kohm ±5%) including units.
DMM measurement ____________________________
Theoretical range ______________________________
7. Repeat Step 3 with the 4.7 kohm resistor (color bands are
yellow, violet, red, and gold) including units.
DMM measurement ____________________________
6. ===============================================
ECET 105 Week 2 Homework
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1. What is the duty cycle for a square wave signal that is HIGH for 15
nsec and LOW for 30 nsec?
2. A pulse train is shown on the oscilloscope below. Determine the
period of the pulse.
3. Determine the frequency for a pulse that occurs every 10 ms.
4. What is the base-10 value for the binary number 11012?
5. What are the respective weights of the 1s in Problem 4?
6. How many different values can be represented by 6 bits, 7 bits, 8
bits, and 10 bits?
7. What is the minimum number of bits required to represent each of
the following decimal numbers: 10, 1,000, 100,000, and 1,000,000?
7. Convert the binary value, 1011010100101101,to a hexadecimal
equivalent.
7. 9. Convert the following decimal numbers to 8-bit binary values. For
negative numbers, use the 2’ complement formulation.
10. Express each of the following signed numbers (2s complement
format) in decimal:
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ECET 105 Week 2 iLab Soldering Techniques and the
Electronic Die Kit
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I. OBJECTIVES
1. To learn the basics of soldering.
2. To produce mechanically and electrically sound solder joints.
3. To assemble the Electronic Die Kit.
II. PARTS LIST
Equipment:
Digital Die Kit
Tools:
1 – Soldering Iron
1 – Pair Long-Nose Pliers
1 – Diagonal cutter
1 – Solder and hookup wire
1 – Wire stripper
III. PROCEDURE
8. 1. Preparation
2. Prepare a well-ventilated and clear workspace with ample lighting.
3. Ensure that the workspace includes a mat to work on in order to
prevent the burning of the table or materials during the process.
4. Use a tray, egg crate, or vegetable/fruit tray for all (but especially
the small) parts to avoid losing them. Attach the tray with double-
sided tape to your bench or desktop.
5. Have a waste basket or desktop trash receptacle handy.
6. Ensure that the sponge that accompanies the soldering iron is
sufficiently damp. The level of dampness needed is judged by wetting
the sponge and then squeezing out the excess water until the sponge
can be held in the hand with no noticeable water dripping from it.
CAUTION:
In order to avoid injury to the eyes, goggles or other eye protection
must be worn AT ALL TIMES during the circuit assembly and
soldering process.
A soldering iron at temperature is very hot. It is a fire hazard. It is a
health hazard. Caution must be taken at all times to ensure that
contact with the skin does not occur.
6. Plug in the soldering iron and wait approximately five minutes for
the iron to heat to a proper temperature. The temperature of the iron
may be tested by lightly rubbing the tip of the iron against the moist
sponge. If a majority of water is evaporated, then the iron is ready for
use. The tip should be kept clean and tinned for soldering. The sponge
is used to wipe away excess solder and materials. Tinning means that
there is always a thin layer of solder on the tip.
7. Procure and prepare the dice kit for soldering. Inventory the parts
and materials and ensure that each part fits the circuit board correctly
by checking the parts on the board WITHOUT soldering them to the
board. Put them in the tray until ready to install.
8. Prepare the tools that you will need: soldering iron, rosin core
solder, desolder wick, safety glasses, long-nose pliers, and wire
cutters.
1. Assembling the Electronic Die Kit
9. 2. Start with the seven 220 ohm resistors. Note that the color bands
are red-red-brown-gold.
2. With your long-nose pliers, bend the legs of all seven of the
resistors so that they form 90-degree angles.
3. Insert the 220 ohm resistors into R1, R2, R3, R4, R5, R6, and R7 of
your printed circuit board through the side where you see the labels.
Bend the lead on the side away from the component part, not next to
the resistor body, but on the other side of the pliers. Otherwise, you
may break the connection inside the resistor. Ensure that all
components, with the exception of the IC socket, are not fully inserted
in the board, but have small gaps between them and the circuit board
to avoid excessive heating.
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ECET 105 Week 3 Homework
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1. Determine the output X for the 2-input AND gate with the input
waveforms shown.
2. Determine the output X for the 2-input OR gate with the input
waveforms shown.
10. 3. Determine the output X for the 2-input Exclusive-OR gate with the
input waveforms shown
4. Determine the output X for the 2-input NAND gate with the input
waveforms shown.
5. Is the output from the NAND gate shown in Problem 4 active-
HIGH or active-LOW? Why?
6. Download from a semiconductor manufacturer’s website (such as
ti.com) the data sheet for a DIP packaged quad NOR gate (74x02).
What pins does this chip use for the inputs to the first gate?
7. Draw a logic circuit that performs the following Boolean
expression: Y = A * B.
8. Draw a logic circuit that performs the following Boolean
expression:
9. Which gate is represented by the truth table below?
10. Use a truth table to determine the function of the gate shown
below.
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11. ECET 105 Week 3 iLab Introduction to Digital Logic Gates
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. OBJECTIVES
To understand basic logic functions (AND, OR, and NOT) and their
complement used in Boolean algebra and digital logic design.
To test simple logic small-scale integration (SSI) integrated circuit
(IC) devices.
II. PARTS LIST
Equipment:
IBM PC or Compatible with Windows 2000 or Higher
Parts:
1 – 74LS00 Quad 2-Input NAND Gate IC
1 – 74LS02 Quad 2-Input NOR Gate IC
1 – 74LS04 Hex INVERTER Gate IC
12. 1 – 74LS08 Quad 2-Input AND Gate IC
1 – 74LS32 Quad 2-Input OR Gate IC
1 – 74LS86 Quad 2-Input XOR Gate IC
1 – Set of Four Single-Pole-Double-Throw (SPDT) Switches,
DIP Style
1 – 330 Ω resistor
1 – Light emitting diode (LED), red
III. PROCEDURE
OR Gate Operation
Using the Internet or the campus library, acquire a hard copy of a data
sheet for the 74LS32 quad 2-input OR gate. (HINT: Look at ti.com
for possible help.) One of the OR gates is shown below in Figure 5.1.
Figure 5.1 – 2-Input OR Gate
Fill in the Table 5.1 for ALL possible logic conditions, based on the
information found on the data sheet.
Input (Pin 1) Input (Pin 2) Output (Pin 3)
13. Table 5.1 - 2-Input OR Gate Theoretical Truth Table
Write the Boolean expression below for the relationship between the
device inputs (labeled as A and B) and output (labeled as Y).
OUTPUT Y = ____________________________
Construct the circuit shown in Figure 5.2 (a layout of the breadboard
is shown in Figure 5.3). Be sure that the flat side of the LED (called
the cathode) is connected to ground and that the 74LS32 is connected
to power and ground (Pins 14 and 7, respectively).
Figure 5.2 – OR Gate Test Circuit
Top View
Side View
Figure 5.3 – Breadboard Layout for Figure 5.2
Connect the circuit to verify the logic gate operation recording the
input and output voltages. Fill in Table 5.2below for ALL possible
logic conditions.
Input (Pin 1) Input (Pin 2) Output (Pin 3)
Table 5.2 - 2-Input OR Gate Measured Truth Table
14. Do the results match the manufacturer’s truth table?
__________ (YES or NO)
AND Gate Operation
Acquire a hard copy of a data sheet for the 74LS08 quad 2-input AND
gate.
Figure 5.4 – 2-Input AND Gate
Fill in the truth table below for ALL possible logic conditions based
on the information found on the data sheet.
Input (Pin 1) Input (Pin 2) Output (Pin 3)
Table 5.3 - 2-Input AND Gate Theoretical Truth Table
Write the Boolean expression below for the relationship between the
device inputs (labeled as A and B) and output (labeled as Y).
OUTPUT Y = ____________________________
Construct the circuit shown in Figure 5.5 by replacing the 74LS32
from Figure 5.2 with a 74LS08.
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ECET 105 Week 4 Homework
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1. Draw a logic circuit that performs the following Boolean
expression:
2. Determine the Boolean expression for the circuit shown below.
3. The Boolean expression for an AND gate is . Does the expression
also describe an AND gate? Prove your answer.
4. Write the Boolean expression for the logic circuit shown below.
5. Develop the truth table for the circuit shown in Problem 4.
6. Develop the truth table for the circuit shown below.
7. Develop the Boolean expression for the circuit shown in Problem 6.
16. 8. Draw a logic circuit using only NAND gates to implement the
following Boolean expression: Y =AB + C.
9. Develop a logic circuit, using only NAND gates, to implement a
circuit to meet the requirements of the truth table shown below.
10. Determine the Boolean description for the circuit shown below.
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ECET 105 Week 4 iLab Logic Circuit Design, Simplification,
Simulation, and Verification
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Objectives:
To design a digital logic circuit using a truth table and sum-of-product
(SOP) formulation.
To use the MultiSim program to simplify, simulate, and test the
circuit operation.
17. To build and test the logic circuit to verify that the system performs as
expected.
Results:
Built a circuit board which would turn on the LED light and used
multisim and tools which would simplify to do so. Verified the truth
table to check and see if the vales are accurate.
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ECET 105 Week 5 Homework
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1. Determine the decimal value of each of the following unsigned
binary numbers:
2. Determine the decimal value of each of the following signed binary
numbers displayed in the 2’s complement form:
3. Determine the outputs (Cout, Sout) of a full-adder for each of the
following inputs:
18. 4. The circuit below is an attempt to build a half-adder. Will the Cout
and Sout function properly? Demonstrate your rationale.
5. Determine the outputs for the circuit shown below. Assume that C0
= 0 for all cases.
6. Derive the Boolean equation for A = B, when A and B are 4-bit
numbers.
7. Complete the timing diagram below for a 2-bit adder. (10 points)
8. Answer the following:
What is the frequency of a periodic waveform with a period of 1.0
µsec?
How many bits are required to represent decimal numbers from -256
to +255?
What is the largest positive number that can be represented by 10
signed bits?
19. 9. The full-adder shown below is tested under all input conditions as
shown. Is the circuit operating correctly? If not, what is the most
likely fault?
10. Using a 4-bit adder/subtractor, carry out the binary operations for
9 – 3 and 3 – 9. What can you conclude about the answers and the
carry out bit (C4)?
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ECET 105 Week 5 iLab Designing Adders and Subtractors
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Objectives:
The objectives are to reinforce the concepts of binary
addition/subtraction while using the Quartus II Programmable Logic
Tool as well as getting used to the program. We were also supposed
to build and test a simple adder/subtractor using the eSOC III Board.
Observations/Measurements:
20. Describe any problems you had with this week’s assignment.
1. In the simulation run of the four-bit adder, when we performed the
addition 5 + 3, we did not immediately have an output of 8 on SOUT.
What could be the cause of this?
2. If we changed the count period to 1000 nS for A and B, would this
correct the anomalies in Question 1? Why or why not?
3. How fast can your 4-bit adder/subtractor determine the sum or
difference of two numbers?
4. Use the simulation timing diagram to compare the worst case time
to do an operation with your adder/subtractor with the worst case
using the 74LS283. State which operation takes the longest and list
the time required for both devices.
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ECET 105 Week 6 Homework
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21. 1. When a HIGH is on the output of the decoding circuit below, what
is the binary code appearing on the inputs?
2. Write the Boolean equations for each of the following codes if an
active-LOW decoder output is required. The first decode is shown as
an example.
3. What are the active outputs of a BCD-to-7 segment decoder with an
input of 0100?
4. A 7-segment decoder/driver drives the display below. Using the
waveforms shown, determine the sequence of digits that appear on the
display.
5. Construct a truth table for an active-LOW output BCD (1-of-10)
decoder.
6. Derive the truth table for the Y output in the diagram below.
7. Derive the Boolean equation for the Y output in Problem 6.
8. For the multiplexer shown below, determine the output for the
following input state.
D0 = 0, D1 = 1, D2 = 1, D3 = 0, S0 = 1, S1 = 0.
22. 9. Determine the function of the circuit shown below.
10. Write the Boolean equation for the circuit shown in Problem 9.
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ECET 105 Week 6 iLab Decoders and Multiplexers
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Objectives:
To learn about the operation of a BCD-to-seven-segment decoder
To learn about the operation of a seven-segment display
To learn about the operation of multiplexers
To build and test a multiplexed display circuit using both discrete
components and the eSOC III board
Questions:
Why are the 330 Ω resistors required for the discrete logic circuit, but
not for the MultiSim simulated circuit or the eSOC III circuit?
23. Create a partial truth table showing the requirements for a seven-
segment decoder to output a hexadecimal digit. This requires four
input bits and six output states, A – F. For each output state, show the
segments a-g. The output states for the inputs 0 – 9 are the same as for
the 74LS47 (see focus.ti.com). Use capital letters A, C, E, F and
lower case for b and d.
Why is the seven-segment display driven with an active-LOW signal
using discrete logic and an active-HIGH with the eSOC board?
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ECET 105 Week 7 Homework
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1. Sketch the Q output for the waveforms shown. Assume that Q
starts LOW.
2. Sketch the Q output for the circuit shown below. Assume that Q
starts LOW.
24. 3. Sketch the Q output for the circuit shown below. Assume that Q
starts LOW.
4. Sketch the Q output for the circuit shown below. Assume that Q
starts LOW.
5. Sketch the Q output for the circuit shown below. Assume that Q
starts LOW.
6. Sketch the Q output for the circuit shown below. Assume that Q
starts LOW.
7. Sketch the Q output for the circuit shown below. Assume that Q
starts LOW.
8. Sketch the Q0 and Q1 outputs for the circuit shown below. Assume
that both Q0 and Q1 start LOW.
9. What is the output frequency for Q1 in the circuit shown below?
10. What is the output frequency for Q2 in the circuit shown below?
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ECET 105 Week 7 iLab Add-Subtractor using Flip-Flops
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I. OBJECTIVES
To test the operation of a 74LS74 D flip-flop and compare the
operation with the predicted behavior
To test the operation of a 74LS112 J-K flip-flop and compare the
operation with the predicted behavior
To measure propagation delays of a 74LS112 J-K flip-flop
To build and test an enhanced adder-subtractor
II. PARTS LIST
Equipment:
IBM PC or Compatible with Windows 2000 or Higher
Quartus II Design Software—Version 9.1
Frequency Generator
Oscilloscope
Parts:
26. 2 – 330 Ω resistors, ¼ W 2 – Red LEDs
1 – 74LS74 dual D flip-flop 1 – Green LED
1 – 74LS112 dual J-K flip-flop 1 – SPDT Switch,
DIP configuration
1 – eSOC III FPGA Board
III. PROCEDURE
A. Test the 74LS74 D Flip-Flop
Build the D flip-flop circuit shown in Figure 7.1. The LEDs are wired
as active-LOW since the flip-flop can supply more current in a low
state than in a high state. This means that the green LED is on when is
HIGH and the red LED indicates Q is HIGH. Remember to attach
VCC to pin 14 and ground to pin 7.
Using the circuit, verify that the operation follows the truth table for
this device.
What happens when both and are set low?
Build the J-K flip-flop circuit shown in Figure 7.2. Remember to
attach VCC to pin 16 and ground to pin 8.
Using the circuit, verify that the operation follows the truth table for
this device.
27. Increase the pulse generator output to 1.0 MHz. Set the switches so
that all of the flip-flop inputs are high and remove the LEDs and
resistors. Using the oscilloscope, measure the propagation times for
the Q output from the active clock edge. Record the value below.
Using Quartus II, modify the circuit from Lab 5 as shown in Figure
7.3 by adding three 7474 D-flip-flip chips. Note that a clear function
has been added and that the flip-flop presets are inactive since they
are tied to +5V (labeled VCC).
Perform a simulation to verify the correct operation of the circuit.
Note that in this case, the CLOCK signal is not a periodic signal; the
CLOCK signal is a discrete signal occurring on a switch closure.
Assign pins to the inputs and outputs. Use the DIP switches for your
inputs (0-3 for A, 8-11 for B, 7 for CLEAR, 15 for ADDSUB), one of
the debounced pushbuttons for CLOCK and the red LEDs for outputs
(RD0-4).
Download you program to the eSOC III board and test the operation
of the circuit.
Photograph your final circuit for submission (online) or demonstrate
your circuit to your professor (onsite or blended).
Why is the condition when both and are LOW considered illegal?