IA: 1P3: Digital Circuits and Information Processing Flashcards
1
Q
What is combinational logic?
A
Output is dependent only on a combindation of the inputs
2
Q
What is sequential logic?
A
Output is dependent on a combination of the inputs and previous outputs (memory)
3
Q
How are computers build from semiconductors?
A
- Semiconductors are used to build transistors
- Transistors are used to build logic gates
- Logic gates are used to build logic functions
- Logic is used to build Flip-flop bistables
- Flip-flops are used to build counters and sequencers
- Sequencers are used to build microprocessors
- Microprocessors are used to build computers
4
Q
What is a variable that can only take 2 values called?
A
- Logic variable
- Binary variable
- Boolean variable
All names for the same thing
5
Q
What are the 2 values a boolean variable can take?
A
- TRUE or FALSE
- ON or OFF
- high or low
- 1 or 0
etc etc
6
Q
What are the 2 states of a logic variable represented by in an electronic circuit?
A
Voltage levels, i.e. high voltage for 1 and low voltage for 0
7
Q
What can be used to denote NOT?
A
A bar above the symbol,
8
Q
What is a logic / digital circuit?
A
Electronic circuits that have logic signals as their inputs and outputs
9
Q
What are logic gates?
A
Basic logic / digital circutis with one or more inputs, and one output. They represent a single basic function.
10
Q
What is the graphical symbol for a NOT gate?
A
11
Q
What is the input-output map for a NOT gate
A
12
Q
What is the boolean representation of a NOT gate?
A
13
Q
What is an inverter?
A
A NOT gate
14
Q
What does a circle on the output of a gate mean?
A
It always means that it is an inverting output
15
Q
What is the graphical symbol for an AND gate?
A
This is a 2 input AND gate, more than 2 inputs is possible
16
Q
What is the input-output map for an AND gate?
A
17
Q
What is the boolean representation for an AND gate?
A
18
Q
What is the graphical symbol for an OR gate?
A
This is a 2-input OR gate, more than 2 inputs is possible
19
Q
What is the input-output map of an OR gate?
A
20
Q
What is the boolean representation of an OR gate?
A
21
Q
What does a NOT gate do?
A
The output is TRUE only if the input is FALSE - it “inverts” the input
22
Q
What does an AND gate do?
A
The output is TRUE if and only if both of the inputs are TRUE
23
Q
What does an OR gate do?
A
The output is TRUE if any (or all) of the inputs are TRUE
24
Q
What does a XOR gate do?
A
The output is TRUE if an odd number of inputs are TRUE
It is an EXCLUSIVE OR gate
25
What is the graphical symbol for a XOR gate?
They are usually 2-input
26
What is the input-output map for a XOR gate?
27
What is the boolean representation of a XOR gate?
28
What does a NAND gate do?
It is a NOT AND gate, it is like having a NOT gate after the output of an AND gate. The output is FALSE if and only if both of the inputs are TRUE
29
What is the graphical symbol for a NAND gate?
## Footnote
Note: the circle on the output of the gate denotes an inverter
30
What is the input-output map for a NAND gate?
31
What is the boolean representation of a NAND gate?
32
What is a NOR gate?
It is a NOT OR gate, it is like having a NOT gate on the output of the OR gate. The output is TRUE if and only if both of the inputs are FALSE
33
What is the graphical symbol for a NOR gate?
## Footnote
Note: the circle on the output of the gate denotes an inverter
34
What is the input-output map for a NOR gate?
35
What is the boolean representation of a NOR gate?
36
How would you solve this setup graphically?
1. For the resistor: Vᵣ = IR
2. For the "thing": Vₜ = 10 - Vᵣ
3. Plot the line for the resistor on an I-R graph
4. Plot the characteristic of the "thing" but flip it horizontally, with it touching the x-axis at 10V. By doing this you make it so "Vₜ = 10 - Vᵣ"
5. The operating point is where both lines intersect
## Footnote
Rule of thumb: Whatever is connected to ground you just plot normally, whatever is connected to the supply rail you flop horizontally
37
When does an enhancement mode NMOSFET start conducting?
When Vgs reaches a threshold voltage (Vₜ)
38
What is the circuit to implement an inverter using an NMOS FET?
39
If the input-output characteristics of the gate are far from the ideal we originally wanted, how can we still make the logic gate work?
You can define voltage levels for the logic variables.
For example:
* Voltage > 9V is logic 1
* Voltage < 2V is logic 0
The gate will work if:
* Vᵢₙ > 9V ⟹ Vₒᵤₜ < 2V
* Vᵢₙ < 2V ⟹ Vₒᵤₜ > 9V
40
What is a trace table?
A tool used in digital circuits to help track the values of logic variables step by step through the circuit.
41
What sort of gate is this?
NOR gate
42
What sort of gate is this?
NAND gate
43
What are the benefits of using gates?
When you have to implement a complicated logic function you don't have to design a special transistor circuit to provide the functionality. Instead you just but an integrated circuit (or chip) that provides the appropriate gates
44
What limits the speed of NMOS logic?
Stray capacitance:
The output of each gate is connected by a length of metal track to the input of the next. This has capacitance to ground. Therefore the circuit model is modified by connecting a capacitor between Vₒᵤₜ and ground. This means that each time the input switches, the output does not switch immediately - there is a time delay.
45
Why may a FET be used to replace the resistor?
Transistors are far smaller than resistors, therefore by using a FET you save a lot of space on the silicon chip. This allows the logic gate to be about 100x smaller (and cheaper!)
46
How can you make a MOSFET behave like a resistor?
You can make a MOSFET behave (almost) like a resistor by connecting the gate to the drain. Thus Vgs = Vds. This does not create a completely linear line when plotting Ids against Vds, so it will not behave exactly the same as a resistor, however it is fairly close.
47
What does the NMOS inverter look like when a FET has been used to reduce its size?
48
What is the problem with NMOS logic?
Power consumption. NMOS's use resistors/NMOS transistors which dissipate large amounts of energy even when idle. Therefore NMOS circuits consume a lot of energy even when not switching as there is always a current flowing. This leads to a high energy usage and heat generation in larger circuits.
49
What is CMOS logic?
Complementary MOS. CMOS logic uses both NMOSFETS and PMOSFETS. It tackles the issue of power dissipation in NMOS logic.
50
Functionally how does a PMOSFET differ from an NMOSFET?
A PMOSFET is essentially an NMOSFET with all the polarities reversed:
## Footnote
Note: The arrow direction on the PMOS (opposite to NMOS)
51
When is a PMOS on?
When Vgs is negative
52
What is a CMOS inverter?
53
Why does CMOS not struggle from the same power dissipation issues as NMOS?
In a CMOS circuit at a given state, only one of the PMOS and NMOS are ever on at a time - one of them is off at all times. The circuit only draws current momentarily during transitions from one state to another (when both transistors are momentarily on at the same time). Therefore there is no static power dissipation.
54
If Vᵢₙ was 6V, how would you choose suitable characteristic curves for the NMOS and PMOS to solve it graphically?
* Vgs for the NMOS would be 4V, so you must choose the Vgs = 4V characteristic curve and plot it.
* Vgs for the PMOS would be -6V, so you must choose the Vgs = -6V characteristic curve and then **flip it horizontally** (as it is connected to the supply rail) and then plot it
55
What does the diagram for power consumption look like for a CMOS inverter?
Neither high or low state dissipate power. Power is only dissipated when the states are switched.
56
What type of CMOS logic gate is this?
## Footnote
* Be careful whether they are PMOS or NMOS
* Use a trace table to determine what the gate does
NAND gate
57
What are the 4 types of logic families?
* NMOS (N-channel MOSFET)
* CMOS (Complementary MOSFET)
* TTL (Transistor-Transistor Logic)
* ECL (Emitter Coupled Logic)
58
What is important in combinational logic design?
* Try to minimise the number of gates being used. This can lead to smaller chips and lower costs.
* You must also be able to manipulate the expressions to use only gates of certain types if there is a limitation on the types of gates - some gates may be readily available and cheap.
59
What is commutation in boolean algebra?
60
What is association in boolean algebra?
61
What is distribution in boolean algebra?
## Footnote
Note the bottom one in particular (unique to boolean algebra)
62
What is absorption in boolean algebra?
63
What are the rules with OR in boolean algebra?
64
What are the rules with AND in boolean algebra?
65
Does AND or OR take precedence in boolean algebra?
AND
66
What is meant by "every boolean law has a dual"?
Any valid statement is also valid when:
## Footnote
ONLY valid when all 4 of these changes are made simultaneously
67
What is a useful technique for simplifying a boolean expression?
Expand each term until it includes one instance of each variable (or its compliment). This may then make it possible to simplify the expression by cancelling terms in the expanded form
68
What is De Morgan's theorem?
In a simple expression you can change all the operators from OR to AND (and vice versa) provided that you put a bar over each term individually and a further bar over the whole expression.
69
How can you turn a 2 input NAND gate into an inverter?
Connect the inputs
70
How can you turn a 2 input NOR gate into an inverter?
Connect the inputs
71
What are the 2 standard boolean forms?
* Sum of Products (SOP)
* Product of Sums (POS)
It can be difficult to convert between SOP and POS by algebraic manipulation
72
How can you obtain a Sum of Products (SOP)?
It is easiest to write down an expression for what you want directly
73
How can you obtain a Product of Sums (POS)?
It is easiest to write down an expression for the inverse of what you want and then use De Morgan's theorem and an inversion to obtain what you want.
74
What is VHDL?
A hardware description language used to describe systems.
75
What does VHDL stand for?
**V** = Very high speed integrated circuits
**H** = Hardware
**D** = Description
**L** = Language
76
What is the structure of VHDL?
* Interface
* Architecture Specification
77
How do you write "equal to" in VHDL?
<=
78
What is the VHDL definition of an inverter?
79
What is the VHDL definition of a 3 input NOR gate?
80
How can you use a logic gate in a larger design with VHDL?
81
How can you express this circuit in VHDL?
82
What is a karnaugh map?
A rectangular array of cells. Each possible state of the input variables corresponds uniquelt to one of the cells, and in the cell we write the corresponding output state. They are a powerful visual tool for carrying out simplification and manipulation of logic expressions with up to 5 input variables
83
What is important to remember when making the Karnaugh map?
**The pattern of high and low inputs.** i.e. 00, 01, 11, 10
84
Map the following expression on a Karnaugh map:
85
How can you use a Karnaugh map for circuit design using NAND gates?
* Write down the simplest sum-of-products expression for the output from the Karnaugh map
* Use De Morgans theorem to convert this to an expression using NAND gates
86
How can you use a Karnaugh map for circuit design using NOR gates?
* Use the Karnaugh map to write down the simplest sum-of-products expression for the inverse of the output. This involves finding terms to cover the blanks between the boxes filled with ones
* Use De Morgan's theorem to convert this to an expression using NOR gates.
87
Previously when using a Karnaugh map the rule has been to map the 1's to produce a simple NAND circuit or map the 0's to produce a simple NOR circuit. What is an alternative way of doing this?
Map the opposite way and then use a final inverter gate to change the output back again.
88
Are Karnaugh map's only available for 4 input variables?
No they can be used for up to 5 input variables
88
What is a "Don't care state" on a Karnaugh map?
For some output states, a certain combination of input variables may not matter. These are known as "Don't care states" and are marked with an **X** on the Karnaugh map. They can be chosedn to be 0 or 1, whichever helps to produce the simplest logic.
89
What is a static hazard?
A static hazard is when a signal undergoes a momentary transition when it is supposed to remain unchanged.
90
What is a dynamic hazard?
A dynamic hazard is when a signla changes more than once when it supposed to change just once.
91
Explain how a static hazard can occur (use static 1-hazard as an example)
92
How can you remove a static 1-hazard?
Fix a static 1-hazard by drawing the Karnaugh map of the output concerned. Make sure all the sum-of-products terms overlap.
93
How do you remove a static 0-hazard?
Fix a static 0-hazard by drawing the Karnaugh map of the inverse of the output concerned. Make sure all the sum-of-products terms representing the inverse overlap.
94
How do you remove a dynamic hazard?
Fix dynamic hazards by redesigning the circuit to simplify the logic
95
What is unit distance code?
A type of binary code in which only one bit changes between two successive values
96
How can you use Karnaugh map to produce a unit distance code?
As you move from a cell to its neighbour in a Karnaugh map only one variable changes. Because the map wraps round this is also true when moving from top to bottom and from far left to far right. This property can be used to produce a code in which only one bit changes at a time.5
97
What is Gray code?
A binary numbering system where two consecutive values differ by only one bit (a type of unit distance code).
98
Why can a unit distance code be important?
In regular binary counting (e.g. 0111 to 1000), multiple bits can change at once. If a signal is delayed or misread during a transition, it can cause a hazard (e.g. between 0111 and 1000 the output may momentarily be 1111). By using a unit distance code the chance of these hazards occuring is reduced.
99
What are 3 examples of number systems?
* Binary - base 2
* Octal - base 8
* Decimal - base 10
* Hexadecimal - base 16
100
Explain binary numbers.
Binary is base 2. Each digit is either 1 or 0.
101
What is a bit?
A binary digit
102
What is a byte?
a storage location for an 8 bit binary number
103
In computers how long are binary numbers?
8 bits (one byte)
104
What numbers can a byte store?
* **Unsigned byte** (positive numbers only): It can store numbers from **0 to 255** (2⁸ - 1)
* **Signed byte** (can store positive and negative numbers): It can store numbers from **-128 to +127**.
105
What is the most significant bit (MSB)?
It’s the leftmost bit in a binary number. It holds the highest place value.
106
What is the least significant bit (LSB)?
It's the rightmost bit in a binary number. It holds the lowest place value.
107
How do you convert from decimal to binary?
Use the remainders from successive division by 2. Read upwards from MSB to LSB.
108
Explain the octal number system:
Octal is base 8. Each digit can be one of 8 numbers, 0-7.
109
How can you convert from decimal to octal?
Use the remainders from successive division by 2. Read upwards from MSB to LSB.
110
How can you convert from binary to octal?
Divide the binary number into 3-bit groups and work out the octal digit to represent each group.
111
What is the hexadecimal number system?
Hexadecimal is base 16. Each digit can be one of 16 **symbols**, 0-9 and then special symbols for 10-15.
112
What symbols are used to represent the digits 10-15 in hexadecimal?
113
What is 42₁₀ in hexadecimal?
2A₁₆
114
How do you indicate a number is hexadecimal?
| Use 89₁₀ as an example
* 59**₁₆**
* 59**ₕ**
* **$**59
* **0x**59
115
How do you convert from decimal to hex?
Use successive division by 16, reading the remainders upwards from MSB to LSB
116
How do you convert from binary to hex (or the otherway round)?
Divide the binary number into **four-bit groups** and work out the hex digit to represent each group.
117
How can you represent positive and negative numbers (signed numbers) in binary?
We use a strategy called 2's complement. In this form:
* The MSB for all positive numbers is zero
* The MSB for all negative numbers is 1
118
How can you read a signed binary number?
Look at the first digit of the binary number:
* If this is zero, then it is a positive number. In this case you can read it off/convert it to decimal as you would an unsigned binary number.
* If this is one, then it is a negative number. In this case you must first reverse the 2's complement. To do this you must invert all the bits and then add 1. Read this off like a normal binary number - this is the magnitude of the number. The final number is the the negative of the magnitude.
119
How can you change the sign of a 2's complement number (i.e. change a negative to a positive or a positive to a negative)?
Invert all the bits and then add one.
120
How does addition (and subtraction) work with 2's complement?
When adding 2 signed 8 bit binary numbers (in 2's complement form), we can use normal binary addition. For subtraction we simply add the 2's complement negative version of the number.
* Perform the addition as usual
* Ignore the carry out of the 8th bit (carry bit) - we are only concerned with 8 bits.
* The result should be interpreted as a signed 8-bit number (-128 to 127)
121
How can you detect if there has been overflow in binary arithmetic?
* **For unsigned binary arithmetic**: If the carry bit is 1, then there was a carry out from the MSB. Therefore if the carry bit is 1 then there has been an overflow.
* **For signed binary arithmetic**: Overflow occurs if the carry into the MSB ≠ carry out of the MSB.
122
What does the plot of signed 2's complement 8 bit numbers against unsigned 8 bit numbers look like?
123
What is the sign and magnitude representation of a signed binary number and why is it rarely used?
The MSB indicates the sign (0 ⟹ +, 1 ⟹ -). The remaining 7 bits contain the magnitude. It is not commonly used as:
* We will have 2 0's (-0 and +0)
* Separate circuits are required to add and subtract numbers
124
What is binary coded decimal (BCD)?
**BCD is when each decimal bit is coded into a 4-bit group.** It is not an efficient way of storing numbers, but is easy to code and decode.
125
What are Alphanumeric Character Codes?
Alphanumeric character codes are numeric representations of letters (A-Z, a-z), digits (0-9), and sometimes symbols that are used by computers to store and process text. Examples include ASCII and Unicode.
126
What is ASCII?
It is the "American Standard Code for Information Interchange". It is a very commonly used Alphanumeric Character Code system. The standard version is a 7 bit code with the remaining but set to zero or used for parity. It includes 32 "control codes". The rest of the numbers are for lower case letters, upper case letters, numbers, and punctuation. The extended version of ASCII uses all 8 bits to provide 128 additional graphics characters.
127
What is unicode?
It is a 16 bit alphanumeric character code system. It includes all the same features as extended ASCII but also Covers ALL characters in every language, emojis, and mathematical symbols.
128
What is parity and how does it work?
Parity is the simplest method for error detection coding when transferring binary data through an imperfect data channel.
A parity bit is added as to ensure there is always an even number of 1's in the byte. If the byte has an odd number of 1s the parity bit is set to 1 to make it even, and if the byte has an even number of 1s the parity bit is set to 0 so that there are still an even number of 1s.
Once the byte has been transferred through the channel, we count the number of bits that are on in each number, accepting any that have an even number and rejecting any that have an odd number. This allows you to detect 1-bit errors.
129
What is the limitation of parity?
It can only detect 1-bit errors, more serious errors may go undetected
130
What is a flip flop?
A bistable
131
What is a bistable?
A circuit which has 2 stable internal states and can remain in either state indefinitely until an external input causes it to switch to the other state.
132
How is are D-type latches and JK bistables built?
* We start with the set-reset (SR) bistable
* A gated-SR bistable is built using an SR bistable
* A master-slave bistable is built using two gated-SR bistables
* A D-type latch is built from a master-slave bistable
* A JK bistable is built from a master-slave bistable
133
What is the structure of a Set-Reset (SR) bistable?
134
How does a Set-Reset (SR) bistable work?
**Inputs:** S (Set), R (Reset)
**Outputs:** Q1 and Q2
**Behaviour:**
* S = 1, R = 0: Sets Q1 = 1, Q2 = 0
* S = 0, R = 1: Resets Q1 = 0, Q2 = 1
* S = R = 0: Retains previous state (memory)
* S = R = 1: Invalid condition
**Operation:**
* S will turn Q₁ on and Q₂ off. They will stay at this state even if S is turned off.
* Until R turns on (RESET event, Q₁ = 0 Q₂ = 1)
* R turns Q₂ on and Q₁ off. They will stay at this state even if R turns off.
* Until S turns on (SET event, Q₁ = 1 Q₂ = 0)
We therefore have memory. The circuit state depends not onlt on the current values of S and R but also on their values in the past.
135
What is the state diagram of the SR bistable?
Note: S = R = 1is not allowed, it is invalid
136
