ECOR1044 Mechatronics Final Exam Prep | Questions & Verified Answers
Analog Most of the world that we experience is Analog:
• There are an infinite number of 'increments'
• There are an infinite number of colors to paint an object
• There are an infinite number of sounds levels
- The common theme among all analog signals is there are infinitepossibilities
Digital Digital signals and objects deal in the realm of the discrete or finite things.
• This means there is a limited set of values through which they can be
represented.
• This could mean 2 possible values, 255, or anything ridiculously large, provided
it's not infinity.
how do we represent digital signals the Binary system
a group of 4 bits is called a ______ a group of 4 bits is called a nibble
a group of 8 bits is called a ______ a group of 8 bits is called a byte
each of the 1s and 0s in binary is called a _______ each of the 1s and 0s is called a ________
Word 'Word' is another group of bits whose length is processor dependent. It could be
16 bits, 32 bit or 64 bits etc.
In an n-bit word, we can represent up to _____ states In an n-bit word we can represent up to 2^n states
-What's the range ( 0 to 2n - 1)
- equation to find the max. number max num = (2^n) - 1
- rearranged equation to find the minimum number
min num of bits required to represent = log2(NumToRepresent + 1)
- Always round the result of this equation UP
tow common methods of communicating digital signals in series and in parallel
Accuracy - For analog, 0.1% is very good accuracy
Digital vs. Analog - For digital, add more circuitry to get more accuracy. Subject to accuracy of
analog sensor input (might have external factors limiting)
Grade A+ | Updated
, ECOR1044 Mechatronics Final Exam Prep | Questions & Verified Answers
Long Term Storage - Analog circuits store data as a voltage on a capacitor. Max storage time is
~30 minutes.
Digital vs. Analog
- Digital circuits store data in memory. Max storage time is years.
speed - Fastest circuits are analog.
- The highest frequency circuits in your cell-phone etc. are analog
Digital vs. Analog
Design Cost/Time Analog designers have to worry about:
- noise, power-supply variation, cross-talk between-wires, inaccurate values,
Digital vs. Analog temperature variation of component values, ground bounce, clock feed-through, .
..
- To digital designers, these are 2nd order effects.
- Digital chips work on "first silicon" over 90% of the time. For analog chips this is
more like 60%
- Analog designers typically need several years experience. Digital designers can
be productive soon after graduation.
- There are many more people doing digital design than analog.
- Analog circuits are rapidly being redesigned in digital.
Digital Is Essentially Analog- Analog problems become especially important in
digital for:
• very fast circuits.
• very low supply voltages (1.0 V)
• very large circuits (5 million gates per chip).
which does 0 and 1 represent: 0:
- Low
high or low - False
true or false - Off
on or off
1:
- High
- True
- On
boolean AND gate A (dot) b
Grade A+ | Updated
, ECOR1044 Mechatronics Final Exam Prep | Questions & Verified Answers
boolean xor gate symbol is a plus inside a circle
how to take the dual of an expression Take any valid Boolean identity:
- REDUCE EXPRESSION
- is the dual equal to the original expression? - Place brackets around all AND terms
- Substitute ⋅ and +
- Substitute 0 and 1
These two expressions are duals, but they are NOT equals
The formulas for XOR and XNOR are combinations of The formulas for XOR and XNOR are combinations of AND as well as OR gates
_______ and ______ gates
how to change the XOR gate into an XNOR gate Inverting any of the leads (a, b, or X) changes the XOR gate into an XNOR gate
how to make an XOR gate into an inverter Making one input a static "1" makes the XOR gate an inverter
Applications of an XOR (3) - controlled inverter (by setting one input to a static '1')
- equality check (outputs low if both inputs are equal)
- odd parity (how many odd numbers are inputted - outputs high if there's an odd
amount of inputs set to high)
equation for an analog signal (sinusoidal) and what each v(t) = Vm • sin(ωt + Φ)
variable means
Vm = Amplitude (measure in V or A)
ω = 2𝜋f = Angular frequency, units of radians/second (rad/s)
Ф = Phase (degrees or radians)
T = 1/f = Signal period (length of time for 1 'cycle')
f = Signal frequency, measured in Hertz (Hz)
curves on a graph for analog vs. digital analog signals have an infinite number of increments, therefore when we plot a
voltage signal for example we get a smooth curve
As digital signals have a limited number of values we instead see something
similar to a staircase (choppy)
Grade A+ | Updated
Analog Most of the world that we experience is Analog:
• There are an infinite number of 'increments'
• There are an infinite number of colors to paint an object
• There are an infinite number of sounds levels
- The common theme among all analog signals is there are infinitepossibilities
Digital Digital signals and objects deal in the realm of the discrete or finite things.
• This means there is a limited set of values through which they can be
represented.
• This could mean 2 possible values, 255, or anything ridiculously large, provided
it's not infinity.
how do we represent digital signals the Binary system
a group of 4 bits is called a ______ a group of 4 bits is called a nibble
a group of 8 bits is called a ______ a group of 8 bits is called a byte
each of the 1s and 0s in binary is called a _______ each of the 1s and 0s is called a ________
Word 'Word' is another group of bits whose length is processor dependent. It could be
16 bits, 32 bit or 64 bits etc.
In an n-bit word, we can represent up to _____ states In an n-bit word we can represent up to 2^n states
-What's the range ( 0 to 2n - 1)
- equation to find the max. number max num = (2^n) - 1
- rearranged equation to find the minimum number
min num of bits required to represent = log2(NumToRepresent + 1)
- Always round the result of this equation UP
tow common methods of communicating digital signals in series and in parallel
Accuracy - For analog, 0.1% is very good accuracy
Digital vs. Analog - For digital, add more circuitry to get more accuracy. Subject to accuracy of
analog sensor input (might have external factors limiting)
Grade A+ | Updated
, ECOR1044 Mechatronics Final Exam Prep | Questions & Verified Answers
Long Term Storage - Analog circuits store data as a voltage on a capacitor. Max storage time is
~30 minutes.
Digital vs. Analog
- Digital circuits store data in memory. Max storage time is years.
speed - Fastest circuits are analog.
- The highest frequency circuits in your cell-phone etc. are analog
Digital vs. Analog
Design Cost/Time Analog designers have to worry about:
- noise, power-supply variation, cross-talk between-wires, inaccurate values,
Digital vs. Analog temperature variation of component values, ground bounce, clock feed-through, .
..
- To digital designers, these are 2nd order effects.
- Digital chips work on "first silicon" over 90% of the time. For analog chips this is
more like 60%
- Analog designers typically need several years experience. Digital designers can
be productive soon after graduation.
- There are many more people doing digital design than analog.
- Analog circuits are rapidly being redesigned in digital.
Digital Is Essentially Analog- Analog problems become especially important in
digital for:
• very fast circuits.
• very low supply voltages (1.0 V)
• very large circuits (5 million gates per chip).
which does 0 and 1 represent: 0:
- Low
high or low - False
true or false - Off
on or off
1:
- High
- True
- On
boolean AND gate A (dot) b
Grade A+ | Updated
, ECOR1044 Mechatronics Final Exam Prep | Questions & Verified Answers
boolean xor gate symbol is a plus inside a circle
how to take the dual of an expression Take any valid Boolean identity:
- REDUCE EXPRESSION
- is the dual equal to the original expression? - Place brackets around all AND terms
- Substitute ⋅ and +
- Substitute 0 and 1
These two expressions are duals, but they are NOT equals
The formulas for XOR and XNOR are combinations of The formulas for XOR and XNOR are combinations of AND as well as OR gates
_______ and ______ gates
how to change the XOR gate into an XNOR gate Inverting any of the leads (a, b, or X) changes the XOR gate into an XNOR gate
how to make an XOR gate into an inverter Making one input a static "1" makes the XOR gate an inverter
Applications of an XOR (3) - controlled inverter (by setting one input to a static '1')
- equality check (outputs low if both inputs are equal)
- odd parity (how many odd numbers are inputted - outputs high if there's an odd
amount of inputs set to high)
equation for an analog signal (sinusoidal) and what each v(t) = Vm • sin(ωt + Φ)
variable means
Vm = Amplitude (measure in V or A)
ω = 2𝜋f = Angular frequency, units of radians/second (rad/s)
Ф = Phase (degrees or radians)
T = 1/f = Signal period (length of time for 1 'cycle')
f = Signal frequency, measured in Hertz (Hz)
curves on a graph for analog vs. digital analog signals have an infinite number of increments, therefore when we plot a
voltage signal for example we get a smooth curve
As digital signals have a limited number of values we instead see something
similar to a staircase (choppy)
Grade A+ | Updated
