Lecture 2 - Boolean Algebra and ADC

Question 1

What are the steps (in order) of the duality principle?

Answer 1

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

Question 2

What is important to remeber when it comes to the duality principle?

Answer 2

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.

Question 3

What is a common use of the duality principle?

Answer 3

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

Question 4

What are the steps (in order) to determine boolean formulas from truth tables?

Answer 4

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’

Question 5

XOR and X-NOR gates are a result of combination of which gates?

Answer 5

OR and AND gates

Question 6

What are XOR gates’ useful properties?

Answer 6

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

Question 7

What are some XOR applications?

Answer 7

1) Controlled inverter
2) Equality check
3) Odd parity

Question 8

In a sinusoid expression V(m) stands for:

Answer 8

Amplitude (measured in V or A)

Question 9

In a sinusoid expression, T stands for:

Answer 9

1/f (Signal period; length of time for one cycle)

Question 10

In a sinusoid expression, f stands for:

Answer 10

Signal frequency (measured in Hertz; Hz)

Question 11

In a sinusoid expression, omega (w) stands for:

Answer 11

2 x f x pi (Angualr frequency; in units of radians/seconds (rad/s))

Question 12

In a sinusoid expression, phi stands for:

Answer 12

Phase (degrees or radians)

Question 13

What system is used to convert analog signals into their digital equivalent?

Answer 13

‘Sample and Hold’ system

Question 14

What do ‘Analog to Digital Converters’ do?

Answer 14

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

Question 15

Describe the Analog to Digital Conversion in 3 steps

Answer 15

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

Question 16

Resolution/Quantization Step-Size (Q)

Answer 16

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

Question 17

Quantization step size (Q) can be calculated using the following formula:

Answer 17

Q = (V(max) - V(min)) / n(states)

Question 18

Sampling rate or frequency

Answer 18

This is the frequency at which the ADC evaluates a analog signal

Question 19

What is Aliasing

Answer 19

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

Question 20

What does the Nyquist Rule say

Answer 20

The nyquist rule says to use a sampling frequency at least twice as high as the maximum frequency in the signal to avoid aliasing

Question 21

Name two ways to improve accuracy of A to D conversions

Answer 21

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

Question 22

How can one convert a voltage value into its binary value?

Answer 22

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