Digital Electronics Flashcards
Analogue signals take…
Continuous values
Digital signals take…
Restricted rages of amplitude
Binary signals are ____ signals that take only _ ____
Binary signlas are digital signlas that take only 2 ranges
What does an anolog and digital signal graph look like?
Why digital?
Reliability
- Anologue circuits are more vulnerable to noise
- Digital circuits can tolerate some levels of noise
Base 2 means?
We can only use 0 and 1
How would you write 11010.1 in binary?
How do you convet decimal to binary?
The hexadecimal number system represents…
A larger range of values with one digit
Basic Boolean operations are…
AND, OR and NOT
If the variable doesn’t have the value 0, it must have…
The value 1 and vice versa
Symbols like ____ to represent Boolean ____
Symbols like A, B etc to represent Boolean variables
What do truth tables do?
Describe how a logic circuit (gate) outputs depend on it’s inputs
What sign is commenly used to represent an Or gate?
The plus sign (+)
What does an Or gate look like?
What gate produces an output of 1 whenever when all of the inputs are 1?
An Or gate
What does an And gate look like?
What is the Boolean expression for an Or gate?
z = x + y
What is the Boolean expression for an And gate?
z = x . y
What sign is used to commonly represent the And gate?
The period (dot) sign .
What gate produces an output of 1 only when all of the inputs are 1
An And gate
What is the symbol for a Not gate?
What is the Boolean expression for a Not gate?
z = ¬x
What sign is commonly used to represent a Not gate?
The ¬ sign is commonly used to represent not. Sometimes a bar over the variable is used also
A Not gate is a…?
Circuite that inversts - or negates - the input signal
What gate produces an output of 1 whenever the input is 0, and an ouput of 0 when the input is 1
A Not gate
What is the symbol for a Nand gate?
What is the Boolean expression for a Nand gate?
z = ¬ ( x . y )
Sometimes you will see this written in the notation that has a bar over the top
What gate produces an output of 1 only when any one of the inputs are 0?
A Nand gate
A Nand gate is…
the logical not of the output of an And gate
What is the symbol of a Nor gate?
What is the Boolean expression of a Nor gate?
z = ¬ ( x + y )
What gate has an output of 0 whenever any of the inputs are 1?
A Nor gate
A Nor gate is…
The logical not of the output of an Or gate
What is the symbol for an Xor gate?
What is the Boolean expression for an Xor gate?
Xor (____) gate
(Exclusive Or) gate
Define Commutative laws
Talk about variabls interchanging
Define Associative laws
Talk about bracketing variable groups
Define Absorption laws
talk about variables absorbing others
Define Distributive laws
talk about multiplying through groups
Boolean products are ____ functions e.g….
AND functions e.g. A. ~B.C
Boolean sums are ____ functions e.g….
OR functions e.g. A+~B+C
Why are Minterms products?
Becuase they are the logical AND of a set of variables
Why are Maxterms sums?
Becuase they are the logical OR of a set of variables
What is a Karnaugh Map?
A diagram consisting of a rectangular array of squares each representing a different combination of the variables of a Boolean function
What is looping?
Grouping squares in the map that contain 1
You loop pairs that are…?
Above or beside each other
K-maps reduce the…?
…cost of logic synthesis
What cannot be define by a Boolean expression?
Incomplete specified functions
What are “Don’t care” terms and what are they represented by?
Terms of functions that we don’t care about, corresponds to lines in the truth table where we don’t specify the output, represented by x
Define propagation delay
A small time it takes to change state when the inputs change
What are the two types of hazards in gate propagation delays?
Static Hazard and Dynamic Hazard
Define static hazard
When the output undergoes a momentary transition when it is supposed to remain unchanged
Define dynamic hazard
When the output changes more than once when it is supposed to change only once
What do static and dynamic hazards look like?
When are hazards a problem?
Hazards are always a problem if they occur in logic providing the input to a system with memory
Nand and Nor are common because…?
- They are simpler to build
- They are “logically complete”
When is a set of circuit gates logically complete?
A set of circuit gates is said to be logically complete if any boolean function representable by a truth table can be implemented using gates from only that set
Logically complete sets include…
- Sets containing AND, OR, INVERTER gates
- Sets containing only NAND gates
- Sets containing only NOR gates
How do you implement circuits in NAND?
- First obtain the function in simplest sums of products form
- Invert the function twice (this leaves it unchanged)
- Use de Morgans theorem on the lower inversion
- The function can now be implemented using only NAND gates
NAND is negation of…?
AND
What is the condition for static hazard?
If two groups of 1’s on the K-map are adjacent and non-overlapping (horizontally or vertically) then changing a single input variable can move out of one group into another
How do you elimate a static hazard?
By including extra groups that overlap the offending transitions
- This adds in circuitry to protect the hazard
What are combinational circuits?
Combinational circuits cannot remember a previous output value when an input value changes
What are sequential circuits?
Sequential ciruits take into account (or remember) their previous state
How is a sequential circuit synchronized?
By a clock signal that consists of periodic 1 pulses
What does SoP stand for
Sums of products
What does SR Flip-flop stand for?
Set/Reset Flip-slop
What does a SR Flip-flop consist of?
Two NOR gates
What happens when the S and the R are low?
The NOR gates act as inverters for the other input signal
What happens when S becomes high and R is low?
¬Q is forced low and Q is high (set)
When S returns low after being high in an SR Flip-flop, Q…?
Remins high (it is in the set state)
What happens when R becomes high and S is low?
Q is forced low
When R returns low after being high, what happens to Q?
Q remains low (the reset state)
Are R and S normally allowd to be high at the same time?
No, so with R and S low, the flip-flop remembers whihch input was high most recently
What can we achieve with a D type flip-flop?
Setsome data and stores it
What is the cost of the function directly related too when it is synthesised using AND and OR?
The
- Number of gates
- Gate inputes
A minimum SoP expression is one which has…?
- A minimum number of gates
- A minimum number of gate inputs
Why is it helpful to represent K-maps in text form?
- Helpful if we consider larger and larger maps, of more than 4 terms
- And the underlying princioples that we are representing graphically
How do you represent a K-map?
By simply recording the decimal equivalent of the high outputs
When is a product an implicant?
When any 1, or group of 1’s that may be combined represent a product term
When is an implicant prime?
An implicant is prime if it cannot be combined with another term to eliminate a variable
- A single 1 is prime if it is not adjacent to any other 1
- Two adjacent 1’s are prime if they are not contained in a group of 4
- Four adjacent 1’s are prime if they are not contained in a group of 8
- …etc…
When can a SoP term not be minimal and why?
When it is containing a term which is not prime because if a non prime term is present the expression maybe further simplified
In order to minimise…
we must find the minimal number of prime implicants needed to cover all 1s on a map
A minimal solution…
Must include all essential prime implicants
How do you find the minimal SoP expression?
- First loop all essential prime implicants
- For simple maps, this can be done by inspection
- For maps of 5 variables or more, it needs a systematic approach – this is where our ∑ notation is useful
Define a static hazard
A circuit contains a static hazard where, when one input variable changes, the output may change more than once
How is it possible to overcome static hazards?
By linking the adjacent groups to an additional group
