These two expressions are duals, but they are NOT equals
The formulas for XOR and XNOR are combinations of _______ and ______ gates -
ANSWER The formulas for XOR and XNOR are combinations of AND as well as
OR gates
how to change the XOR gate into an XNOR gate - ANSWER Inverting any of the leads...
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:
high or low
true or false
on or off - ANSWER 0:
- Low
- False
- Off
1:
- High
- True
- On
boolean AND gate - ANSWER A (dot) b
boolean xor gate - ANSWER symbol is a plus inside a circle
how to take the dual of an expression
, - is the dual equal to the original expression? - ANSWER Take any valid Boolean
identity:
- REDUCE 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 _______ and ______ gates -
ANSWER The formulas for XOR and XNOR are combinations of AND as well as
OR gates
how to change the XOR gate into an XNOR gate - ANSWER 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 - ANSWER Making one input a static
"1" makes the XOR gate an inverter
Applications of an XOR (3) - ANSWER - 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 variable means - ANSWER
v(t) = Vm • sin(ωt + Φ)
Vm = Amplitude (measure in V or A)
ω = 2 f = 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 - ANSWER 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)
How do you convert an analog signal to it's 'equivalent' digital? - ANSWER Use
'sample and hold' system
input analog signal, clock it (sample and hold), then take this analog signal segment
and convert to digital, then output the equally spaced digital signal
What does an 'Analog to Digital Converter' do?
The more bits the binary number has, the higher _________ - ANSWER • Converts
analog signals into binary words
• These binary words can be in different length 2, 4, 8, 10-bit.
• The more bits the binary number has, the higher the resolution of the analog to digital
converter (ADC , A/D, or A to D).
Analog to Digital Conversion - 3 Steps - ANSWER - Sampling - Conversion of a
continuous signal to a discrete-time signal
- take the signals value after every T seconds
- We measure the amplitude of the signal at that time
, - Now we have a signal which is discrete in time but continuous in amplitude as it can
still have any value
- Quantizing - Conversion of a discrete-time signal to discrete amplitude signal
- take your number of bits, and assign each value sampled to a state. Depending
on how many bits, you can only round to a certain amount
- Encoding - Conversion of a discrete signal to binary word
Resolution/Quantization Step-Size (Q) - ANSWER - The smallest voltage that can be
encoded digitally, in other words the voltage represented by the least significant bit.
- It describes the general performance of an ADC, how finely it can convert signals.
- The quantization step size (Q) can be calculated as follows:
Q = (Vmax - Vmin)/Nstates
Limitation: Aliasing
Nyquist Rule - ANSWER • An effect that causes different signals to
become indistinguishable when sampled.
• Occurs when the input signal is changing much faster than the sample rate.
Nyquist Rule:
• Use a sampling frequency at least twice as high as the maximum frequency in
the signal to avoid aliasing.
If I want to convert a 100 kHz analog signal into a digital signal, what is the
minimum sampling frequency to avoid aliasing? - ANSWER 200 kHz
two ways to best improve accuracy of A/D conversion - ANSWER There are two
ways to best improve accuracy of A/D conversion:
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