Lecture 2 - Boolean Algebra and ADC Flashcards
What are the steps (in order) of the duality principle?
1) Take any boolean identity
2) Place brackets around all it’s AND terms
3) Substitute all AND for OR; and all 0’s for 1’s
What is important to remeber when it comes to the duality principle?
The result after applying the duality principle will be that of another valid identity. Although, one musn’t forget that these two expressions are duals therefore they are not equal to one another.
What is a common use of the duality principle?
1) The duality principle can be used to convert complexe problems into more familiar formats
2) If one set of laws is memorized, duality can be used to determine their 2nd form
What are the steps (in order) to determine boolean formulas from truth tables?
1) Write out the truth table
2) Look for wherever the result may be ‘1’
3) Write down the letters corresponding to the inputs
4) AND the letters
5) The equation is the OR of all the terms where the output is equal to ‘1’
XOR and X-NOR gates are a result of combination of which gates?
OR and AND gates
What are XOR gates’ useful properties?
1) When inverting any of the gate’s inputs (a, b , X) transforms the XOR gate into a X-NOR gate
2) Making one input a permanent ‘1’ makes the XOR gate into a inverter
What are some XOR applications?
1) Controlled inverter
2) Equality check
3) Odd parity
In a sinusoid expression V(m) stands for:
Amplitude (measured in V or A)
In a sinusoid expression, T stands for:
1/f (Signal period; length of time for one cycle)
In a sinusoid expression, f stands for:
Signal frequency (measured in Hertz; Hz)
In a sinusoid expression, omega (w) stands for:
2 x f x pi (Angualr frequency; in units of radians/seconds (rad/s))
In a sinusoid expression, phi stands for:
Phase (degrees or radians)
What system is used to convert analog signals into their digital equivalent?
‘Sample and Hold’ system
What do ‘Analog to Digital Converters’ do?
Converts analog signals into binary words, the resolution of the analog to digital signal is directly proportional to the number of bits in the binary word
Describe the Analog to Digital Conversion in 3 steps
1) Sampling: Conversion of a continuous signal to a discrete-time signal
2) Quantizing: Conversion of a discrete-time signal to a discrete-amplitude signal
3) Encoding: Converion from a discrete signal to a binary word
Resolution/Quantization Step-Size (Q)
The smallest voltage that can be encoded digitally, in other words, the voltage represented by the LSB (difference in voltage that one can basially change by changing that 1 or 0); describes the general performance of an ADC and how finely it can convert a signal
Quantization step size (Q) can be calculated using the following formula:
Q = (V(max) - V(min)) / n(states)
Sampling rate or frequency
This is the frequency at which the ADC evaluates a analog signal
What is Aliasing
An effet that causes different signals to be unable to be differentiated from one another when sampled, this happens when the input signal is changing must faster than the sampling rate
What does the Nyquist Rule say
The nyquist rule says to use a sampling frequency at least twice as high as the maximum frequency in the signal to avoid aliasing
Name two ways to improve accuracy of A to D conversions
1) Increasing the resolution which improves the accuracy in measuring the amplitude of the analog signal
2) Increasing the sampling rate which increases the maximum frequency that can be measured
How can one convert a voltage value into its binary value?
Must be given the number of bits and the voltage range
ADC reading = (number of states / voltage range) x analog voltage
Round down if the answer is not an integer for this calculation, before converting it into it’s binary equivalent
