Information and Systems Flashcards
What defines something as analogue in nature?
- The signal can take any value and there are infinite possibilities
- The value of the signal varies with time
What defines something as digital in nature?
- Anything that deals in the realm of the discrete
- There is a limited set of values they can take
Define a bit
A binary digit
Define a byte
A sequence of 8 bits
Define a word
A sequence of N bits
What base is decimal?
Base-10
What base is binary?
Base-2
What base is hexadecimal?
Base-16
What does ADC stand for?
Analogue-to-digital converter
What is the role of an ADC?
To sample an analogue signal in order to produce a digital representation of the data in such a way that no important information is lost
State the Nyquist-Shannon Theorem
The sampling frequency must be at least two times the maximum frequency
In practice, what is the range of the sampling frequency?
Between two times and ten times the maximum frequency
Why is the Nyquist-Shannon Theorem used?
- Most signals consist of a mix of frequencies
- So, twice the max frequency ensures it is captured
What happens when sampling below the Nyquist rate?
Signal information is lost meaning received signal will appear lower than original signal
Define ADC resolution
The smallest voltage that can be represented digitally
How do you calculate resolution?
Voltage range/N - 1
How finely will an 8-bit ADC digitise a signal that occupies a voltage range of 0V to 5V?
- 2⁸ = 256
- 5/256-1 = 0.02V or 20mV
What is combination logic?
- In a circuit, output depends only on combination of its inputs
- Output is not influenced by previous inputs
- Circuit has no memory
What are the typical applications of combination logic?
- Data transfer circuits: control logic flow around a system
- Data processing circuits: process/transform data
How can data circuits be described?
- Truth table
- Boolean expression
- Circuit diagram
- Timing diagram
What type of Boolean expressions can’t be obtained from a truth table?
Expressions in minimised form
When can Boolean expression not be obtained from a truth table?
Never, they always can be obtained
Define Shannon’s expansion theorem
If there is a simplified Boolean expression, it’s fundamental form can always be found
How does Shannon’s expansion theorem work?
By normalising each “AND” term with (X + X̄), where X is the missing variable
Use Shannon’s expansion theorem to find the fundamental form of Y = A + BC
- Y = A(¬B+B)(¬C+C) + BC(¬A+A)
- Y = A¬B¬C + A¬BC + AB¬C + ABC + ¬ABC + ABC
- Y = A¬B¬C + A¬BC + AB¬C + ABC + ¬ABC
Why are Boolean expressions minimised?
- Complex Boolean expressions lead to complex very circuits
- So, by minimising, complexity and ultimately cost are reduced
What are the minimisation techniques?
- Boolean algebra/Inspection of truth tables
- Karnaugh maps
- Quine McCluskey techniques
In a Boolean expression, what are product terms?
Expressions where Boolean variables are AND’d together
In a Boolean expression, what are sum terms?
Expressions where Boolean variables are OR’d together
What are octets, quads and duals?
Groups of 8,4 and 2 minterms in the K-map respectively
Define minterms
A 1 in a single cell of a K-map which represents a fundamental product term
Define prime implicants
A grouping of minterms
Define essential prime implicants
- A term which must be included in the minimised Boolean expression
- Otherwise, all minterms won’t be captured and an incorrect expression will result
What is a “don’t care” product term?
- A term which value isn’t defined by the problem
- Therefore, a 0 or 1 can be added to these terms to aid minimisation
What does the number of columns in a truth table represent?
The sum of the number of inputs and the number of outputs
What does the number of rows in a truth table represent?
The number of input combinations
What is a fundamental product term?
- A term containing all input variables which are AND’d together
- Relates to a unique combination of input variables and therefore represents a single unique truth table row
Determine the appropriate specification of an ADC for an analogue signal with max frequency 20kHz, min frequency 0Hz, voltage range 0V-2V and peak-to-peak noise voltage of 64µV
- Resolution(ΔV) = Vrange/N-1
- N = Vrange/Resolution(ΔV) + 1
- N = 2V/64µV + 1 = 31251 levels
- log₂(31251) = 14.93… = 15 bits
State De Morgan’s Theorem
- Complementing the result of OR’ing variables together is equivalent to AND’ing the complements of the individual variables
- Complementing the result of AND’ing variables together is equivalent to OR’ing the complements of the individual variables
Use De Morgan’s Theorem on “Y = ¬(A+B)”
Y = ¬A x ¬B
What can be constructed from an AND gate and 2 inverters?
A NOR gate
What can be constructed from an OR gate and 2 inverters?
A NAND gate
Simplify A.A
A.A = A
Simplify A + A
A + A = A
Simplify A.¬A
A.¬A = 0
Simplify A + ¬A
A + ¬A = 1
Simplify A.0
A.0 = 0
Simplify A.1
A.1 = A
Simplify A + 0
A + 0 = A
Simplify A + 1
A + 1 = 1
True or False, Y = A + B is the same as Y = B + A?
True
True or False, Y = A.B is the same as Y = B.A?
True
True or False, Y = (A.B).C is not the same as Y = A.(B.C)
False
True or False, Y = (A+B)+C is the same as Y = A+(B+C)
True
Expand A.(B+C)
A.(B+C) —-> (A.B)+(A.C)
Expand A+(B.C)
A+(B.C) —-> (A+B).(A+C)
Expand (A+B).(C+D)
- Let X = A+B
- X.(C+D) = (X.C)+(X.D)
- (A+B)C + (A+B)D
- AC + BC + AD + BD
