FINAL EXAMINATION SAMPLE QUESTIONS
ECOR 1032 CIRCUITS & MECHATRONICS
SECTION A, B, AND C
Date and Time: December 12, 2025 at 9:00am
Duration: 180 minutes
Department Name & Course #: Electronics ECOR 1032
Course Instructor(s): MacEachern & Tait
# of Students: TBD
AUTHORIZED MEMORANDA:
• NON-GRAPHING AND NON-PROGRAMMABLE CALCULATORS
• CLOSED BOOK, CLOSED NOTES
• ONE DOUBLE-SIDED “CHEAT” SHEET (8.5” x 11”)
• SCANTRON SHEET
INSTRUCTIONS AND INFORMATION:
• ATTEMPT ALL QUESTIONS.
• ALL QUESTIONS ARE EQUAL VALUED.
• THIS EXAM HAS 171 QUESTIONS.
• FILL IN AND SUBMIT THE PROVIDED SCANTRON SHEET FOR MARKING.
• THE EXAMINATION MAY NOT BE TAKEN FROM THE EXAM LOCATION.
• INTERPRETATION OF THE QUESTIONS IS THE STUDENT’S RESPONSIBILITY.
• EACH QUESTION HAS ONLY ONE CORRECT ANSWER. IF THERE IS AMBIGUITY
PICK THE BEST ANSWER.
ECOR 1032
FINAL EXAM - MASTER MERGE
1. Determine the Boolean logic expression for the circuit
shown below.
6. Which method is most commonly used for controlling the speed of a standard DC motor in microcontroller applications?
a) Adjusting the physical load torque.
b) Reversing the supply polarity.
c) Using Pulse Width Modulation (PWM) to adjust
the average voltage.
d) Changing the magnetic field material.
A
B
Y
C
a) Y = A · B · C
b) Y = (A + B) · C
c) Y = (A + B) · C
d) Y = A · B + C
7. What is the defining characteristic that distinguishes
a servo motor from a standard continuous-rotation
DC motor?
a) It operates only at very high speeds.
b) It requires an AC power supply.
c) It incorporates internal feedback (potentiometer/encoder) for precise position control.
d) It cannot produce torque at zero speed.
2. An ideal Analog-to-Digital Converter (ADC) with
a resolution of N bits produces how many distinct
quantization levels?
a) 2N −1
b) 2N
c) 2N − 1
d) N 2
3. For an N -bit ADC operating over an input range of
0 to VFS , the theoretical quantization step size (∆) is
calculated as:
VFS
a)
N −1
VFS
b) N
2
2N
c)
VFS
VFS
d) N
2 −1
8. A resistor R is connected in series with a capacitor C
and driven by a sinusoidal source. The magnitude of
the total impedance |Z| is:
p
a) qR2 + (ωC)2
1 2
b) R2 + ωC
1
c) R + ωC
d) √ 2 1
2
R +(ωC)
9. A resistor and an inductor are connected in parallel.
Their equivalent impedance Zeq is:
a) R + jωL
−1
1
b) R1 + jωL
4. An ideal op-amp is configured as a voltage follower
(buffer). If the input voltage is Vin = 5 V, what is the
output voltage?
a) 0 V
b) 2.5 V
c) 5 V
d) -5 V
2025
R
c) jωL
p
d)
R2 + (ωL)2
10. A Norton equivalent circuit for a linear network consists of:
a) A current source in series with a resistor.
b) A current source in parallel with a resistor.
c) A voltage source in series with a resistor.
d) A voltage source in parallel with a resistor.
5. A sensor outputs a maximum signal of 10 mV. Your
ADC has a full-scale range of 2 V. What amplifier gain
is required to map the sensor range to the full ADC 11. Decreasing the quantization step size in an analog to
range?
digital converter will improve:
a) 50
b) 200
c) 20
d) 100
1. The maximum allowable input frequency.
2. The resolution.
3. The processing speed.
4. None of the other answers are correct.
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ECOR 1032
12. Which of the following best describes the process of 18. What is an ideal operational amplifier (Op-Amp)?
quantization in ADC?
1. An amplifier with infinite open-loop gain, infi1. Conversion of a continuous signal to a discretenite input resistance, and zero output resistance.
time signal.
2. An amplifier with finite gain and resistance val2. Conversion of a discrete-time signal to a discrete
ues.
amplitude signal.
3. An amplifier that only works with digital sig3. Conversion of a binary word to an analog signal.
nals.
4. Conversion of a discrete signal to a continuous4. An amplifier that requires no external power
time signal.
supply.
13. Which of the following actions can help avoid alias19. What is the voltage gain (Av ) of an ideal voltage foling in ADC?
lower (unity gain buffer)?
1. Decrease the sampling rate.
1. 0 V/V
2. Increase the resolution of the ADC.
2. 1 V/V
3. Use a sampling frequency at least twice as high
3. Infinity
as the maximum frequency in the signal.
4. -1 V/V
4. Use a sampling frequency equal to the maximum frequency in the signal.
20. Which property of an analog signal (continuoustime and continuous-amplitude) fundamentally chal14. What is the minimum sampling frequency required
lenges direct computer processing without converto accurately sample a 500 kHz analog signal?
sion?
1. 500 kHz
2. 1 MHz
a) Its discrete time steps, leading to synchroniza3. 250 kHz
tion issues.
4. 750 kHz
b) Its continuous amplitude, requiring infinite storage precision.
15. For a range of 0-5V, and a 10-bit resolution, what is
c) Its bandwidth-limited spectrum, restricting frethe binary value for a voltage of 3.65V?
quency content.
1. 1011101011
d) Its vulnerability to noise, amplifying transmis2. 1101101011
sion errors.
3. 0111010110
4. 1011011011
21. Continuous-time and discrete-amplitude signals are
exemplified by which practical signal type?
16. What happens to the logical operation of an OR gate
a) A sampled audio file on disk.
when both the inputs and the output are inverted?
b) A pulse width modulated output from a GPIO
1. It becomes an AND gate.
with continuous time variation.
2. It remains an OR gate.
c) An ideal impulse train modulating amplitude.
3. It becomes a NOR gate.
d) A binary bitstream from an encoder.
4. It becomes a NAND gate.
22. The digitization pipeline via pulse-coded modulation (PCM) involves three stages. Which stage in1. The process of increasing the amplitude of an
herently discards information by rounding to finite
electrical signal.
levels, transitioning from infinite to finite amplitude
2. The process of converting a digital signal to an
precision?
analog signal.
a) Sampling, which discretizes time.
3. The process of filtering out unwanted noise from
b) Quantization, which maps to discrete codes.
a signal.
c) Encoding, which serializes bits.
4. The process of converting a low-frequency sigd) Reconstruction, which interpolates samples.
nal to a high-frequency signal.
17. What is signal amplification?
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ECOR 1032
b) The 14-bit system has ≈ 12 dB higher SQNR.
c) The 14-bit system has ≈ 40 dB higher SQNR.
d) Both systems have the same SQNR if the sampling rate is identical.
23. Quantization error is modeled as additive noise
bounded by half the least significant bit (LSB). For
high-fidelity systems, this error’s power spectral density is white, assuming uniform distribution. What
does this imply for SNR scaling?
29. You are designing a transmission link with a hard
limit of 1.2 Mbps (1,200,000 bits/sec). Constraint 1:
The input signal bandwidth is 24 kHz. To prevent
aliasing with a safety margin, the sampling rate is
set to exactly 2.5 times the bandwidth. Constraint 2:
You must maximize the audio quality (highest possi24. A digital audio system operates at a sampling rate
ble N ) without exceeding the link speed. What is the
of fs = 48 kHz. According to the Nyquist theorem,
theoretical maximum SNR (dB) achievable?
what is the absolute maximum analog frequency that
a) ≈ 98 dB (N = 16)
can be represented without aliasing?
b) ≈ 110 dB (N = 18)
a) 12 kHz
c) ≈ 122 dB (N = 20)
b) 24 kHz
d) ≈ 146 dB (N = 24)
c) 48 kHz
30. A microcontroller ADC has a fixed input range of 0–
d) 96 kHz
4 V. Constraint 1: The quantization error magnitude
25. Using the standard ”Rule of 6 dB,” what is the apmust be strictly less than 0.2 mV (Errormax < 0.2 mV).
proximate theoretical Signal-to-Noise Ratio (SNR) for
Recall that Errormax = ∆/2. Constraint 2: The sama 10-bit ADC?
pling rate is 44.1 kHz. Determine the minimum bit
depth N and the data rate.
a) ≈ 48 dB
b) ≈ 62 dB
a) 529.2 kbps (N = 12)
c) ≈ 84 dB
b) 573.3 kbps (N = 13)
d) ≈ 96 dB
c) 617.4 kbps (N = 14)
a) SNR improves linearly with N .
b) SNR doubles with each additional bit.
c) SNR increases by 6 dB per bit.
d) SNR is independent of sampling rate.
d) 661.5 kbps (N = 15)
26. A 12-bit ADC operates on a 0 to 4.096 V range.
What is the maximum theoretical quantization error 31. A client demands a high-fidelity system with a the(rounding error) for an input signal?
oretical Signal-to-Noise Ratio (SNR) of at least 96 dB.
Constraint 1: Find the lowest integer bit depth N that
a) ±0.5 mV
satisfies the SNR requirement (SN R = 6.02N + 1.76).
b) ±1.0 mV
Constraint 2: The sampling rate is 48 kHz. What is
c) ±2.0 mV
the resulting data rate?
d) ±5.0 mV
a) 672 kbps
b) 720 kbps
c) 768 kbps
d) 1.152 Mbps
27. In a linear PCM system, if you increase the resolution by 1 bit, by what factor does the Quantization
Noise Power (Pq ) decrease (assuming constant fullscale range)?
32. Digital signals achieve noise immunity primarily
through what mechanism that analog signals lack?
a) It decreases by a factor of 2.
b) It decreases by a factor of 4.
c) It decreases by a factor of 6.
d) It decreases by a factor of 12.
28. Comparing a 12-bit system to a 14-bit system,
which statement is true regarding the Signal-toQuantization-Noise Ratio (SQNR)? (In class we called
the SQNR the “SNR” for simplicity.)
a) The 14-bit system has ≈ 6 dB higher SQNR.
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a) Continuous amplitude variation allowing selfcorrection.
b) Threshold-based decision making that regenerates clean levels post-noise.
c) Infinite state representation mitigating additive
distortions.
d) Frequency-domain filtering inherent to discrete
sampling.
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ECOR 1032
33. In binary representation, the MSB and LSB positions 38. A 3-bit ADC operates with a reference range of 0 to
7 V. Determine the quantization step size (Q) and the
determine the weighting of bits in positional notadigital output code for an input voltage VA = 4.2 V.
tion. For a 16-bit word, how does the LSB contribute
to the total value relative to the MSB?
a) Q = 0.875 V, Code = 1002
b)
Q = 1 V, Code = 1002
a) Equal weight, as all bits are binary.
15
15
c) Q = 0.875 V, Code = 1012
b) 1/2 of the MSB’s 2 weight.
d) Q = 0.875 V, Code = 0112
c) Inverse scaling, with LSB as 20 and MSB as 2−15 .
d) Dynamic, based on the signal’s bandwidth.
39. A 3-bit ADC has an input range of 0 to 10 V. Which
analog voltage range corresponds to the output code
34. The formula for bits required to encode an integer M
1102 (decimal 6)?
is n = ⌈log (M +1)⌉. This arises because binary states
2
range from 0 to 2n −1. Why does the +1 term appear?
a) [7.5 V, 8.75 V)
b) [6.25 V, 7.5 V]
c) [8.75 V, 10 V]
d) [5 V, 6.25 V)
a) To account for the zero state in the count.
b) To include the MSB carry-over in the ceiling
function.
c) To shift the range for signed representations.
40. A 10-bit ADC has a full-scale range of 0 to 5 V. Calcud) To compensate for quantization steps in ADC
late the binary output code for an input of 3.65 V.
mapping.
a) 10111010112
b)
10111011012
35. Increasing bit depth enhances amplitude resolution,
c) 10111110112
while higher sampling rate improves temporal fid)
10111001112
delity. In ADC design, what trade-off does this impose on system resources?
a) Bandwidth expansion at the cost of power efficiency.
b) Data rate as fs ×n bits/sample, straining storage
and processing.
√
c) Noise floor reduction proportional to 2n .
d) Dynamic range compression for low-SNR inputs.
41. A 10-bit ADC operates with a bipolar input range of
−5 V to +5 V. Determine the binary output code for
an input of 3.65 V.
a) 11011101012
b) 11011101112
c) 10111101012
d) 11011011012
42. A 12-bit ADC is configured for a bipolar range of −10
V to +10 V. Calculate the voltage resolution (LSB size)
36. In the practice problem for a 12-bit bipolar ADC (-10V
of this system.
to +10V), the output for 2.5V is 1010000000002 . This
corresponds to decimal 2560. What fraction of the full
a) 4.88 mV
range does this represent?
b) 9.77 mV
c) 2.44 mV
a) 1/8, due to quadrant folding.
d) 19.53 mV
b) 2560/4096 = 5/8, reflecting the normalized position from Vmin .
43. Using the same 12-bit ADC system as the previous
c) 2.5/20 = 1/8, but scaled by 212 .
question (Range ±10 V), determine the binary output
d) Exactly 1/4, as MSB indicates sign bit.
code for an input signal of +2.5 V.
a) 1010000000002
b) 1000000000002
c) 1010000000012
d) 1100000000002
37. Determine the minimum number of bits required to
represent the decimal integer 2710 in unsigned binary,
and provide that binary sequence.
a) 5 bits, 110112
b) 4 bits, 11012
c) 6 bits, 0110112
d) 5 bits, 101112
44. A digital system requires a Signal-to-Noise Ratio
(SNR) of at least 80 dB. What is the minimum integer bit depth (N ) required to meet this specification?
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ECOR 1032
a) The weight of the object.
b) The stiffness of a virtual spring pulling the object toward the target.
c) The friction of the floor.
d) The maximum speed of the motor.
a) 13 bits
b) 12 bits
c) 14 bits
d) 11 bits
45. Calculate the minimum bit depth required to achieve
an SNR of at least 70 dB.
51. Proportional control requires the ability to output
partial power (e.g., 20%, 50%, 80%), not just ON/OFF.
a) 12 bits
What hardware component allows a digital chip to do
b) 11 bits
this?
c) 13 bits
d) 10 bits
a) A mechanical relay.
b) A Circuit Breaker.
c) A PWM (Pulse Width Modulation) driver.
d) A simple switch.
46. Calculate the theoretical maximum SNR for a 16-bit
ADC, assuming quantization noise is the only error
source.
a) 98.08 dB
b) 96.32 dB
c) 94.56 dB
d) 100 dB
52. We derived that the steady-state error (the permanent
droop) is ess = mg
Kp .
If you double the Proportional Gain (Kp ), what happens to the error?
47. An EEG signal contains frequencies up to fmax = 100
Hz. If the signal is sampled at fs = 512 Hz, calculate
the oversampling ratio relative to the Nyquist rate.
a) 2.56
b) 5.12
c) 1.28
d) 4.096
a) The error doubles.
b) The error stays the same.
c) The error is cut in half.
d) The error becomes zero.
53. Since increasing Kp reduces the error, why don’t we
just set Kp = 1, 000, 000 to make it perfect?
a) It costs too much money for high gain.
b) The system would react too violently, causing
dangerous oscillation (ringing).
c) The computer cannot calculate numbers that
large.
d) The error would technically increase.
48. A high-precision 24-bit ADC is used for EEG measurements with a full-scale range (Vpp ) of 500 µV. Calculate the voltage magnitude of the Least Significant
Bit (∆).
a) ∼30 nV
b) ∼60 nV
c) ∼15 nV
d) ∼120 nV
54. How does the I-term fix the ”Drone Droop” (Steady
State Error) that the P-term couldn’t fix?
49. Because a Hysteresis controller is always slightly
overshooting (to turn off) and undershooting (to turn
on), what happens to the temperature graph?
a) It changes the physics of the drone.
b) As long as a small error exists, the I-term grows
larger and larger until it provides enough power
to lift the drone.
c) It simply multiplies the P-term by 2.
d) It resets the controller every few seconds.
a) The temperature oscillates forever (a permanent
ripple).
b) The temperature eventually stabilizes at a perfect flat line.
55. A drone is flying upward very fast. It is getting closer
c) The system eventually overheats and fails.
to the target, so the Error is *decreasing* rapidly.
d) The sensor stops reading data.
Does the **Derivative Output** add power (speed
up) or subtract power (slow down)?
50. Proportional control is calculated as Output = Kp ×
Error. In mechanical terms, what does the Gain (Kp )
a) It adds power to get there faster.
represent?
b) It does nothing.
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ECOR 1032
c) It subtracts power (opposes the motion) to pre- 61. For a given P-only control system, the steady-state error is inversely proportional to the gain (ess ∝ 1/Kp ).
vent overshooting.
If Kp is doubled, how does the steady-state error
d) It shuts down the system.
change?
56. In the world of PID control, which time-frame does
a) It doubles.
each term focus on?
b) It remains constant.
a) P = Past, I = Present, D = Future.
c) It is halved.
b) P = Present, I = Past, D = Future.
d) It becomes zero.
c) P = Future, I = Present, D = Past.
62. In practice, what prevents us from setting the Propord) They all look at the Present.
tional Gain (Kp ) to infinity to eliminate error?
57. An open-loop heating system operates at a fixed 50%
a) High cost of implementation.
duty cycle, maintaining a room at 22◦ C. If the exterb) System instability (overshoot, ringing, or oscilnal temperature suddenly drops, how will the system
lation).
respond?
c) Limitations in processor speed.
d) It would increase the steady-state error.
a) The system will automatically increase power to
maintain 22◦ C.
b) The room temperature will drop, as the system 63. Which PID term allows the controller to ”remember”
past errors and eliminate steady-state offset?
cannot detect or compensate for the disturbance.
c) The system will oscillate around the setpoint.
a) Proportional
d) The system will shut down to prevent damage.
b) Integral
c) Derivative
58. A ”Bang-Bang” controller switches fully ON or OFF
d) Feed-forward
based on a threshold. In a system with low inertia
(fast response), what is the primary disadvantage of 64. An integral controller (Ki = 2) is operating on a systhis control scheme?
tem with a constant error of 3 units. Calculate the rate
of change of the controller output.
a) Large steady-state error.
b) Excessive ”Chatter” (high-frequency switching)
which damages hardware.
c) Computational complexity.
d) Inability to reach the setpoint.
a) 0 units/sec
b) 2 units/sec
c) 3 units/sec
d) 6 units/sec
59. Mechanically, a Proportional Controller (u = Kp e) is 65. Which PID term acts as a ”virtual brake” or damper,
analogous to which physical component connecting
reacting to how quickly the error is changing?
the actual position to the target?
a) Proportional
a) A mass / weight.
b) Integral
b) A spring.
c) Derivative
c) A friction damper.
d) Gain Scheduling
d) A lever.
66. As a system rapidly approaches its setpoint, the error
60. Which hardware component is typically used by digmagnitude decreases. How does the Derivative term
ital microcontrollers to emulate an analog proporaffect the total controller output?
tional output (e.g., 50% power)?
a) It adds to the output to accelerate the system.
a) A mechanical Relay.
b) It subtracts from the output to prevent overb) A PWM (Pulse Width Modulation) driver.
shoot.
c) A Circuit Breaker.
c) It has no effect until the error reaches zero.
d) An Op-Amp Comparator.
d) It resets the Integral term.
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ECOR 1032
67. A discrete derivative controller with Kd = 5 samples
the error at 1-second intervals. At t = 1, e = 10. At
t = 2, e = 6. Calculate the derivative output component.
a) −20
b) +20
c) −4
d) +80
68. Which set of time-domain descriptions best matches
the P, I, and D terms respectively?
a) Overdamped (Too slow).
b) Aggressive Tuning (Gain too high, insufficient
D-term).
c) Steady State Error.
d) Perfect Tuning.
72. In a graph showing the internal efforts of a PI controller for a hovering drone, you see the P-term drop
to zero while the I-term slowly rises to a steady high
value. What is happening?
a) The system is crashing.
b) The Integral is taking over the load (gravity) as
the error reaches zero.
c) The Derivative is braking.
d) The Hysteresis is kicking in.
a) Past, Present, Future.
b) Present, Past, Future.
c) Future, Present, Past.
d) Present, Future, Past.
69. You see a graph like in Fig. 1 where the temperature
rises to a high limit, turns off, drops to a low limit,
and turns back on. It repeats this ”sawtooth” wave
forever. What control strategy is this?
73. You are tuning a robot arm. It moves to the target
fast but keeps vibrating (jittering) when it arrives.
Which term should you likely increase to stop the jitter/vibration?
a) Increase P (Push harder).
b) Increase I (Accumulate more).
c) Increase D (Apply more braking/damping).
d) Remove the motor.
74. You are designing a robot to stay 50cm from a wall.
What is your Reference r(t)?
a) The voltage of the battery.
b) The actual distance measured by the sonar.
c) The number ”50”.
d) The speed of the wheels.
Figure 1
a) PID Control.
b) Hysteresis (Bang-Bang with Deadband).
c) Proportional Control.
d) Derivative Control.
75. In the same robot, the sonar measures 40cm. What is
the Error e(t)?
a) 50 − 40 = +10 (Too close, steer away).
b) 40 − 50 = −10 (Too far, steer in).
c) 40 cm.
d) 50 cm.
70. You see a system response that rises quickly but stops
short of the target (e.g., stops at 0.8 when the target is 76. In the feedback loop, what is the specific job of the
1.0). It is perfectly stable but has a permanent gap.
Sensor?
What is the likely cause?
a) To make decisions.
a) P-Only Control (Gain too low).
b) To convert a physical quantity (Heat, Distance)
b) Integral Gain is too high.
into a signal (Voltage, Data).
c) Derivative Gain is too high.
c) To set the target reference.
d) The sensor is broken.
d) To power the heater.
71. You see a system that shoots way past the target, 77. A PID controller calculates that it needs to apply 150
Volts to the motor to correct a large error. The battery
swings back down, shoots up again, and rings like
is only 12 Volts. What happens?
a bell before settling. What does this indicate?
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ECOR 1032
a) The battery generates 150 Volts magically.
b) The controller applies 12 Volts (Saturation) and
the system responds slower than calculated.
c) The controller crashes.
d) The error becomes zero instantly.
What is the boolean expression for the final output?
a) Y = A · B
b) Y = A + B
c) Y = A · B
d) Y = A · B
78. A drone is hovering perfectly using a PI controller. 83. Consider a circuit with inputs A, B, and C.
Suddenly, a heavy weight is added to it. What hap• Gate 1 (OR): Inputs are A and B.
pens immediately, and what happens eventually?
• Gate 2 (AND): Inputs are the output of Gate 1
a) It falls and never recovers.
and input C.
b) It falls slightly (error created), P and I kick in, I
grows until it provides the extra lift, and it returns to the setpoint.
c) It shoots upwards.
d) The D-term handles the weight.
• Gate 3 (NOT): Input is the output of Gate 2.
Which equation matches this circuit?
a) Y = (A + B) · C
b) Y = (A + B) · C
c) Y = A + B · C
d) Y = A + (B · C)
79. A car dashboard light (L) should turn ON (L = 1) if
the Door is Open. The door sensor, however, is ”Active Low” (it outputs logic 0 when the door is open,
and logic 1 when closed). How do you express the 84. I am a 2-input logic gate. My output is High (1) only
when my inputs are equal (both 0 or both 1). Which
logic for the light L in terms of the sensor D?
gate am I?
a) L = D
a) XOR
b) L = D
b)
XNOR
c) L = D · 1
c) NAND
d) L = D + 0
d) AND
80. A fire suppression system is triggered (Y = 1) if neither Smoke Sensor A (A) nor Smoke Sensor B (B) de- 85. I am a 2-input logic gate. If you connect my inputs
together (Input A = Input B), I act exactly like a NOT
tects clean air. (Assume sensors output 1 for clean air,
gate. If you leave my inputs separate, I output Low
0 for smoke).
(0) only when both inputs are High.
Logic: Trigger if NOT (A is clean) AND NOT (B is clean).
a) OR
a) Y = A · B
b) AND
b) Y = A + B
c) NAND
c) Y = A · B
d) XOR
d) Y = A + B
86. In a 3-input truth table (Inputs A, B, C), Row 5 repre81. A conveyor belt selector (Y ) must activate if a packsents the input state A = 1, B = 0, C = 1. What is the
age is detected by Sensor A (A = 1) OR Sensor B
corresponding minterm (SOP term)?
(B = 1), but NOT if both sensors detect it simultaa) A + B + C
neously (which indicates a jam).
b) A · B · C
a) Y = A + B
c) A · B · C
b) Y = A · B
d) A · B · C
c) Y = A ⊕ B (XOR)
d) Y = A ⊙ B (XNOR)
87. The Boolean expression AB + A simplifies to which
of the following?
82. A logic circuit has two inputs, A and B.
1. B
• Level 1: A NOT gate inverts input A.
2. AB + A
3. A + B
• Level 2: An AND gate takes the output of Level
4. B + A
1 and input B.
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ECOR 1032
88. Look at the answer to the previous question (Y =
d) The hardwired circuit allows for easier firmware
AB + AB). If you implement this logic, you will noupdates.
tice the output Y does not actually depend on input
93. You are designing a ”Smart Home” lighting conA. What is the simplified logic?
troller. The user wants to change the logic (e.g., turn
a) Y = A
lights on at 6 PM instead of 5 PM) via an app. Which
b) Y = B
implementation is best?
c) Y = B
a) Hardwired Logic Gates (requires soldering to
d) Y = 1
change).
b) Software/Microcontroller (requires code up89. Analyze the truth table below. Determine the cordate).
rect logic equation in Product of Sums (POS) form.
A B Y
c) Pneumatic Logic.
a) Y = A + B
0 0 1
d)
Relay Ladder Logic.
b) Y = A + B
0
1
1
1
0
1
1
1
0
c) Y = A · B
d) Y = A · B
94. In the ”Lab Cart” buzzer example, we could read sensors with a microcontroller but use a physical NOT
gate on the Brake sensor before it reaches the pin.
90. Determine the Boolean expression that strictly
Why?
matches the logic function defined in the
a) To make the circuit look more complex.
A B C Y
b) To invert the ”Active Low” brake signal to ”Ac0 0 0 0
tive High” so the software code is cleaner.
0 0 1 0
c)
Because
microcontrollers cannot read ”Low”
0 1 0 1
signals.
0 1 1 0
following truth table.
1 0 0 0
d) To increase the voltage to 12V.
1
1
1
0
1
1
1
0
1
0
0
0
95. Evaluate the expression Y = A + B · C. Which operation happens first?
a) OR (A + B) happens first.
b) AND (B · C) happens first.
c) They are evaluated left to right.
d) It depends on the voltage.
a) Y = A · B · C
b) Y = A · B · C
c) Y = A · B · C
d) Y = A + B + C
91. You replace a Python script running on a Raspberry
96. Which expression is equivalent to A · (B + C)?
Pi (loop speed ≈ 50µs) with a hardwired 7400-series
a) A · B + C
NAND gate circuit (propagation delay ≈ 10ns). Apb)
A+B·A+C
proximately how much faster is the reaction time of
c) A · B + A · C
the hardware circuit?
d) A + (B · C)
a) 5× faster
b) 100× faster
97. When converting a continuous analog signal (like a
c) 5, 000× faster
sine wave) into a 1-bit digital signal, what process is
d) They are effectively the same speed for human
used?
perception.
a) Amplification.
92. You are designing the emergency E-Stop for a robotic
arm. Why might you choose a hardwired logic gate
circuit over a microcontroller?
b) Thresholding.
c) Frequency modulation.
d) Filtering.
98. If a float sensor is configured such that the switch
a) The microcontroller is more expensive.
closes when the tank is full, what logic level does the
b) The hardwired circuit consumes more power.
GPIO pin read when the water is above the threshc) The hardwired circuit cannot ”crash” or freeze
old?
due to software bugs.
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ECOR 1032
a) LOW (0).
b) HIGH (1).
c) Floating (Undefined).
d) Negative (-1).
b) Ultra-low latency (processing speed).
c) Ability to run an Operating System.
d) Centralized control of all decisions.
105. What is the typical execution time for a hardware
99. In Python code for an embedded system, which conlogic gate (like a 7404 IC)?
struct is used to continually monitor the state of a sena) 5 to 20 nanoseconds (ns).
sor?
b) 40 to 200 microseconds (µs).
a) A try...except block only.
c) 10 milliseconds (ms).
b) A while True: loop.
d) 0.1 seconds.
c) A single if statement without a loop.
106. A Raspberry Pi running a Python loop typically has
d) A time.sleep() command.
a latency in which range?
100. If a requirement changes so that an LED must turn
a) 1 to 5 ns.
ON when the tank is empty (Sensor LOW), but the
b) 40 to 200 µs.
hardware provides a HIGH signal when full, what
c) 1 to 2 seconds.
logic operator is required?
d) 5 to 10 minutes.
a) AND
107. Why is hardware logic often preferred for safetyb) OR
critical shut-off systems (e.g., an industrial pump)?
c) NOT (Inversion)
d) BUFFER
a) Hardware logic is inherently more reliable and
101. In Python, how is the logical inversion of a sensor
state expressed?
a) sensor state * -1
b) invert(sensor state)
c) not (sensor state == GPIO.HIGH)
d) sensor state == GPIO.NULL
does not ”crash” like software.
b) Hardware logic is cheaper to modify after installation.
c) Hardware logic allows for complex data logging.
d) Hardware logic consumes more power, ensuring signal strength.
102. Why might one implement logic inversion in hard- 108. In a multi-channel system where two sensors conware (using a NOT gate) rather than software?
trol two independent LEDs, how does the software
handle the logic?
a) To save power on the LED.
b) Because the sensor cannot output LOW.
a) By using a single if statement for both.
c) To satisfy a fixed software requirement (e.g.,
b) By using parallel, independent if blocks in the
locked code expecting HIGH for ON).
loop.
d) To increase the voltage level of the signal.
c) By physically wiring the sensors together.
d) By using a logical AND operator.
103. What electronic component is commercially available to provide multiple hardware inverters in a sin- 109. The ”Logical AND” function (Tank 1 AND Tank 2
gle package?
must be full) effectively performs which mathematical operation on the binary inputs?
a) The Hex Inverter (e.g., 7404 IC).
b) The Quad Operational Amplifier.
a) Addition (0 + 1 = 1).
c) The 555 Timer.
b) Multiplication (0 × 1 = 0).
d) The Full Bridge Rectifier.
c) Subtraction.
d) Division.
104. Which of the following is a primary advantage of
using hardware logic (gates) over a processor (soft- 110. Which operator would you use to implement a
ware)?
safety check where a machine starts only if Sensor A
is HIGH and Sensor B is HIGH?
a) Ease of changing logic functionality later.
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ECOR 1032
a) XOR.
b) NAND.
c) XNOR.
d) Buffer.
a) Logical OR.
b) Logical NOT.
c) Logical AND.
d) Logical XOR.
111. What is the main trade-off when using a processor 118. Which of the following is listed as a sensor com(software) instead of hardware gates?
monly used in Mechanical Engineering to measure
force and torque?
a) Software is faster but harder to debug.
b) Software is more flexible but has higher latency
and power consumption.
c) Software uses fewer GPIO pins.
d) Hardware requires an Operating System.
A. RTDs
B. Strain gauge load cells
C. Potentiometers
D. Accelerometers
112. Which gate outputs HIGH (1) only if all its inputs 119. According to the standard measurement chain,
are HIGH (1)?
which step immediately follows the Transducer?
a) OR Gate.
A. Signal Conditioning
b) NAND Gate.
B. Physical Quantity
c) AND Gate.
C. Digital System
d) XOR Gate.
D. Electrical Signal
113. Which gate outputs HIGH (1) if any of its inputs are 120. If sensor 1’s average measurement is close to the true
HIGH (1)?
value (25◦ C), while sensor 2’s average measurement
is far from 25◦ C but has small variation around its
a) OR Gate.
own average, sensor 1 is described as accurate, and
b) AND Gate.
sensor 2 is described as having what characteristic?
c) NOR Gate.
d) XNOR Gate.
A. High sensitivity
114. The NAND Gate is equivalent to which combination of operations?
a) OR followed by NOT.
b) AND followed by NOT.
c) NOT followed by OR.
d) Exclusive OR.
B. Low drift
C. Precision
D. Zero offset
121. Standards that are the most accurate and reliable,
used to define the fundamental units of measurement
(like the kilogram, meter, and second), are known as:
A. Secondary standards
B. Working standards
C. Calibration standards
D. Primary standards
115. How is the NOR Gate output defined?
a) It is HIGH only when all inputs are HIGH.
b) It is the inverse of the OR gate (HIGH only when
all inputs are LOW).
c) It checks for equality between inputs.
122. An ideal electronic sensor should provide zero outd) It is HIGH if any input is HIGH.
put with zero input. This characteristic is known as:
116. The XOR (Exclusive OR) gate outputs HIGH (1)
when:
a) The inputs are identical.
b) The inputs are different.
c) Both inputs are HIGH.
d) Both inputs are LOW.
A. Low hysteresis
B. Zero offset
C. High linearity
D. Low drift
123. What static characteristic defines the maximum and
minimum values of the physical variable that can be
measured?
117. Which gate acts as an ”Equality Detector” (outputs
A. Hysteresis
HIGH when inputs are the same)?
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ECOR 1032
A. The time constant in a first-order system.
B. Backlash caused by looseness in a mechanical
joint.
C. Non-linearities resulting from loading effects in
a potentiometer.
D. The offset voltage at 0◦ C in an RTD circuit.
B. Full-scale (FS)
C. Output range
D. Input range
124. A zero-order sensor, which exhibits no delays and
only changes the amplitude of the input signal, is
characterized by what mathematical relationship between input x(t) and output y(t)?
130. (Figure Analysis) Refer to the ”First-Order Sensor
Equivalent Circuit”. Which component in this equivA. y(t) = R · C · x(t)
alent circuit represents the thermal capacitance (C) of
B. y(t) = k · x(t)
the alcohol in the thermometer?
C. y(t) = k
·
dx(t)/dt
R
D. y(t) = x(t)dt
A. The thermal resistance (R)
125. What type of displacement sensor relies on the motion of a magnetic core to change the mutual inductance between primary and secondary coils?
B. The voltage supply
C. The Capacitor (C)
D. The input fluid temperature (θF )
A. Potentiometer
131. For an LVDT (Linear Variable Differential TransB. Piezoresistive sensor
former), the direction of displacement (x) from the
C. Capacitive sensor
central position (x = 0) is determined by which charD. Linear Variable Differential Transformer (LVDT)
acteristic of the output voltage (VOU T )?
126. When classifying sensors by the physical measurement variable used, displacement measurement using a movable contact on a resistor relates to which
variable?
A. The amplitude of VOU T
B. The frequency of VOU T
C. The mutual inductance (k1 + k2 )
D. The phase (ϕ) of VOU T
132. For a voltage divider used to convert resistance
change (RS = R0 (1 + x)) to a voltage output (Vout ),
where RL = R0 k, maximum voltage sensitivity to
changes in the measurand (i.e., maximum dV /dx)
occurs when the load resistor RL is approximately
equal to:
127. A strain gauge measures changes in which physical
quantity?
A. k = 0
A. Inductance
B. Capacitance
C. Resistance
D. Voltage
1. Temperature
2. Pressure
3. Electrical resistance
4. Capacitance
B. k approaches infinity
C. k = 1
D. k = 1 + x
128. The most common implementation of a Resistive
Temperature Device (RTD) mentioned, which provides an almost linear response, is a:
A. 10kΩ Thermistor
B. 100Ω Platinum resistor (Pt100)
C. Semiconductor gauge
D. Bourdon tube
129. The definition of hysteresis refers to the difference
between two output values corresponding to the
same input based on the trajectory followed by the
sensor. An example given for this effect is:
133. When using strain gauges, what specific measure is
commonly employed to compensate for pronounced
temperature effects, particularly in semiconductor
gauges?
A. Using a Wheatstone bridge with only active
gauges.
B. Placing ”dummy” gauges subject to temperature changes but no mechanical stress.
C. Filtering the output signal in the frequency domain.
D. Maximizing the gauge factor to minimize temperature dependence.
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ECOR 1032
134. In the process description of a piezoresistive pres- 139. (Calculation) A Negative Temperature Coefficient
(NTC) thermistor has characteristics Ro = 10kΩ at
sure sensor, the physical quantity Pressure is first conTo = 25◦ C and β = 3950K. If the measured resistance
verted into what intermediate variable inside the diis RS = 3587Ω, what is the calculated temperature T
aphragm material?
in Kelvin (K)?
A. Voltage Output
A. 298.00K
B. Strain
B. 322.98K
C. Resistance Change
C. 300.96K
D. Digital Representation
D. 373.15K
135. (Figure Analysis) Refer to the ”RTD Voltage Divider
S
Circuit”. Using the formula Vout = VCC RSR+R
, the fi- 140. What is the fundamental difference between the
L
resistance-temperature response of a Negative Temnal simplified expression for Vout in terms of VCC and
perature Coefficient (NTC) thermistor and a typical
k (where RL = R0 k) shows that which specific resisPlatinum RTD (Pt100)?
tance value cancels out?
A. RL
B. RS
C. R (resistivity)
D. R0 (resistance at reference temperature)
136. (Calculation) An RTD temperature measurement
system uses a first-order linear model where R0 =
100Ω and α = 0.0038. If a measurement results in a
sensor resistance RS = 119.4Ω, what is the calculated
temperature rise ∆T ?
A. 47.37◦ C
B. 50.00◦ C
C. 51.05◦ C
D. 56.00◦ C
137. (Calculation) A thermistor measurement uses a
voltage supply VS = 5.000V and a load resistor
RL = 10000Ω. If the measured output voltage Vo is
1.320V, what is the sensor resistance RS ? (Based on
the source material derivation).
A. 1000 Ω
B. 2785 Ω
C. 3587 Ω
D. 10000 Ω
A. The RTD uses inductance while the thermistor
uses capacitance.
B. The RTD response is modeled by a secondorder differential equation, while the thermistor
is zero-order.
C. The RTD response is nearly linear with temperature, while the thermistor response is strongly
non-linear (exponential).
D. The RTD provides high sensitivity over a narrow
range, while the thermistor provides low sensitivity over a wide range.
141. (Figure Analysis) Refer to the ”NTC Thermistor
Voltage Output Curve” (described in comments). By
observing the curves for varying RL , which conclusion about linearity is supported?
A. The output voltage is perfectly linear across the
entire temperature range displayed.
B. The slope (sensitivity) changes noticeably across
the temperature range, indicating a non-linear
response.
C. Maximum sensitivity occurs only when RL is
equal to Ro at the reference temperature.
D. The circuit provides zero offset at 0◦ C regardless
of RL .
138. If an RTD divider circuit provides a sensitivity of 142. What type of sensor involves the use of a cantilever
4mV/◦ C around 50◦ C, what magnitude of error in
beam with strain gauges, where a seismic mass atthe voltage measurement would cause a 1◦ C error in
tached to the end causes bending, enabling the meathe temperature measurement?
surement of acceleration?
A. 1.0 × 10−3 V
B. 2.721V
C. 1.320V
D. 4.0 × 10−3 V
A. LVDT
B. Piezoresistive pressure sensor
C. Spring-mass-damper accelerometer
D. Bourdon tube
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ECOR 1032
D. +20 dB
143. Which element is not listed in the sources as a potential factor limiting the accuracy of a temperature
measurement derived from a resistive sensor circuit? 149. In the full signal conditioning chain described, what
stage immediately follows the initial Sensor/Voltage
A. The resolution of the measurement system.
Divider?
B. Noise and interference in the signal.
A. ADC
C. The stability of the supply voltage VS .
B. Buffer
D. The frequency response of the signal conditionC. Amplifier
ing circuit.
D. LPF Stage
144. What are the three primary signal integrity prob150. What configuration allows for high gain but sacrilems addressed by signal conditioning?
fices high input impedance (i.e., does not inherently
A. Phase Shift, Non-linearity, and Drift
provide impedance matching at the input)?
B. Amplitude Mismatch, Impedance Mismatch,
A. Buffer
and Noise & Frequency Mismatch
B. Non-Inverting Amplifier
C. High Current Draw, Low Voltage Swing, and
C.
Active LPF
Thermal Runaway
D. Inverting Amplifier
D. Common-Mode Rejection, Offset Voltage, and
Slew Rate
151. A system uses a 12-bit ADC with a VRange of 5V.
What is the quantization step size (Q), which repre145. What operational amplifier configuration is primarsents the smallest detectable change?
ily used to solve the ”Impedance Mismatch” problem
by providing a gain of 1, high input impedance, and
A. 4.88 mV
low output impedance?
B. 2.44 mV
A. Inverting Amplifier
B. Non-Inverting Amplifier
C. Voltage Follower (Buffer)
D. Active Low-Pass Filter
C. 1.22 mV
D. 0.61 mV
B. Use a voltage follower to buffer the noise source.
C. Remove unwanted high-frequency noise before
the signal reaches the ADC using a Low-Pass Filter (LPF).
D. Increase the ADC’s dynamic range.
A. 3.0V
B. 2.8V
C. 2.5V
D. 2.0V
152. A thermistor circuit has an open-circuit voltage
(Vsource ) of 3.0V and an output impedance (Zout ) of
146. What is the goal when addressing ”Noise & Fre10 kΩ. If it is connected directly to an ADC with an
quency Mismatch”?
input impedance (Zin ) of 50 kΩ, what is the voltage
measured by the ADC (Vload )?
A. Increase the sensor’s sensitivity.
147. Sensors like RTDs and Thermistors typically produce what kind of signal output?
a) Large, full-range voltage swings
b) High current changes
c) Small voltage changes in a voltage divider
d) Digital pulses
153. In a non-inverting amplifier configuration, if the desired gain (G) is 25, and the design selects Rg =
10 kΩ, what value is required for the feedback resistor
(Rf )?
A. 24 kΩ
B. 230 kΩ
C. 240 kΩ
D. 250 kΩ
148. Approximately how much SNR improvement does
a gain of 10 provide?
154. A Pt100 sensor system has a sensitivity (Ssensor )
of 4 mV/◦ C. The desired temperature resolution is
A. +1.76 dB
0.05◦ C. If the ADC resolution (Q) is 4.88 mV, what is
B. +6 dB
the minimum gain (Gmin ) required?
C. +10 dB
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ECOR 1032
C. To prevent the high impedance of the thermistor
divider from being loaded by the input resistor
(Rg ) of the amplifier.
D. To provide initial low-pass filtering.
A. 12.2
B. 16.3
C. 24.4
D. 48.8
155. If an active Low-Pass Filter (LPF) is designed using 160. The Nyquist theorem is recalled in relation to which
R = 10 kΩ and C = 1.6 nF, what is the theoretical
of the three signal integrity problems?
cutoff frequency (fc )?
A. Amplitude Mismatch
A. 16 Hz
B. Impedance Mismatch
B. 1.6 Hz
C. Noise & Frequency Mismatch
C. 1.0 Hz
D. Quantization Noise
D. 10.0 Hz
156. Referencing a ”Cumulative SNR Improvement”
chart, what is the total improvement in Signal-toNoise Ratio (SNR) when moving from a raw signal
state (40 dB) to a full conditioning chain (70 dB)?
A. 10 dB
B. 20 dB
C. 25 dB
D. 30 dB
161. Examining the ”Anti-Aliasing with a Low-Pass Filter” plot (described below), where is the 60Hz AC
line noise primarily located relative to the desired signal passband?
A. In the extreme low-frequency region (< 1 Hz)
B. Completely within the Signal Passband
C. Near the edge of the Passband, where the LPF
begins significant attenuation.
D. Far above the Passband, in the high-frequency
interference region.
157. Referencing the ”Effect of Impedance Mismatch”
plot (described below), what physical effect is represented by the vertical difference labeled ”Attenuation 162. In the case study for the Pt100 RTD conditioning
chain (Divider → Non-Inverting Amp (Gain=2) →
/ Droop”?
LPF (fc = 1Hz) → ADC), the temperature resolution
A. The limitation of the bandwidth.
improved from ∼ 1◦ C to approximately what value
B. The instantaneous voltage drop due to the resisafter conditioning?
tive voltage divider formed by Zout and Zin .
C. The virtual short created by the Op-Amp.
A. ∼ 0.5◦ C
D. The effect of environmental noise on the signal
B. < 0.1◦ C
magnitude.
C. 0.05◦ C
D. 0.01◦ C
158. For the worked problem involving the thermistor
circuit with Zout = 10 kΩ and Zin = 50 kΩ what is 163. What Op-Amp characteristic dictates Rule 1: ”No
the calculated Voltage Error, expressed as a percentcurrent flows into the input terminals”?
age of the source voltage?
A. Infinite Open-Loop Gain (AOL = ∞)
A. 10.0%
B. Zero Output Impedance (Zout = 0)
B. 16.7%
C. Infinite Input Impedance (Zin = ∞)
C. 20.0%
D. Infinite Bandwidth
D. 50.0%
159. When designing a signal conditioning chain for a 164. If a sensor signal needs large amplification (Gain =
-50) and requires impedance matching, which config10 kΩ NTC Thermistor, why is a buffer stage critical
uration chain is suggested?
early in the chain?
A. Non-Inverting Amplifier → Buffer
A. To prevent the high gain of the subsequent amB. Buffer → Inverting Amplifier
plifier from oscillating.
C.
Inverting Amplifier alone
B. To ensure the signal is inverted for proper proD. Active LPF → Non-Inverting Amplifier
cessing.
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ECOR 1032
165. The capacitor was charged to 6 V and then built
into the circuit while the switch was opened. The
the switch is suddenly closed. Immediately after the
switch closes what is the current in the 2kΩ resistor?
2 kΩ
+
−
10 µF
10 V
Figure 3
a) 0 A
b) 2 mA
c) 5 mA
d) 10 mA
166. In the Bode plot of a LPF depicted in Fig. 2, assuming the y-axis is in dB and the x-axis is in rad/s,
which point corresponds to the value of the cut-off
frequency fc ?
A.
v2 − v 1 v2 − v 3 v2
+
−
=0
R2
R3
i̇s
B.
v2 − v 1 v2 − v 3 v2
+
+
=0
R2
R3
is
C.
v2 − v 1 v2 − v 3
+
− is = 0
R2
R3
D.
v2 − v 1 v2 − v 3
+
+ is = 0
R2
R3
168. Given that is i = 1.25mA, what is the value of the
voltage Vab in the circuit of Fig. 4?
Figure 2
A. A
B. B
C. C
D. D
Figure 4
A. -13.75 V
B. -12.5 V
C. -11.25 V
D. -15 V
167. Assuming the currents entering the node are negative, what is the KCL equation at node 2 in the circuit 169. What is the value of the voltage v for the circuit of
of Fig. 3?
Fig. 5. Suggestion: Use mesh analysis.
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ECOR 1032
Figure 6
A. 4.5 V
B. 1.2 V
C. 2.25 V
D. 6.75 V
171. Using superposition theorem, find the voltage vo
due only to the current source in the circuit of Fig. 7.
Figure 5
A. -32.5 V
B. -7.5 V
C. -27.5 V
D. -37.5 V
Figure 7
170. Using superposition theorem, find the voltage vo
due only to the voltage source in the circuit of Fig. 6.
A. 4.5 V
B. 13.5 V
C. 9 V
D. 18 V
WISHING YOU ALL THE BEST IN YOUR FUTURE ENDEAVOURS!
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End of Exam.