Digital vs Analogue, Logic Devices, and Boolean Logic and Logic Gates

Question 1

What is the difference between analogue and digital signals?

Answer 1

• Analogue signals has a continuously varying voltage

- Digital signals represent things as distinct voltage values (HIGH and LOW) (1 or 0)

Question 2

What are the advantages of digital systems?

Answer 2

• Known level of accuracy
• Reliable (immune from interference, temperature/humidity and aging)
• Can introduce intelligence
• Can change the design easily

Question 3

What are the disadvantages of digital systems?

Answer 3

• Circuits are more complex (more wires0

- Increased cost of manufacture

Question 4

What are the three basic logical operations?

Answer 4

OR, AND & NOT

Question 5

What is a relay?

Answer 5

• Electromagnetic device

- Allows current through a coil to close one or more independent set of switch contacts

Question 6

What are the 2 states of a relay?

Answer 6

NO (normally open)

NC (normally closed)

Question 7

What are the disadvantages of a relay?

Answer 7

Bulky, slow, unreliable and power hungry

Question 8

What are the benefits of transistors?

Answer 8

Fast, very small, very reliable

Question 9

What are transistors?

Answer 9

• 3 terminal devices
• an input voltage is applied to the control terminal which causes a conducting path between the other 2 terminals to be opened or closed

Question 10

What is a CMOS FET?

Answer 10

Type of transistor where current flows between two electrodes (the source and the drain) via a channel. Above the channel, there is a gate (another electrode)
Acts as a switch

Question 11

What is the difference between a N channel FET or a P channel FET?

Answer 11

• N-channel FET uses the flow of electrons (output is HIGH when input is HIGH)
• P-channel FETs uses holes (OUTPUT is HIGH when INPUT is LOW)

Question 12

What are the values of Boolean logic?

Answer 12

• 1 or TRUE (meaning HIGH or ON)

- 0 or FALSE (meaning LOW or OFF)

Question 13

What are logic gates?

Answer 13

Logic gates are electronic circuits constructed from transistors with 1 or more input wire and 1 output wire

Question 14

How does an OR gate function?

Answer 14

• OUTPUT is HIGH if either or both INPUTs are HIGH

- OUT = A + B

Question 15

How does an AND gate function?

Answer 15

• OUTPUT is HIGH if both INPUTs are HIGH

- OUT = A.B

Question 16

How does a NOT gate function?

Answer 16

• OUTPUT is HIGH if INPUT is LOW

- OUT = A\

Question 17

How does XOR gate function?

Answer 17

• OUTPUT is HIGH if either INPUTs are HIGH but not both

- OUT = A+0B

Question 18

How does NAND, NOR and XNOR function?

Answer 18

• AND, OR and XOR gate respectively without inversions

Question 19

Which gates can be used to implement all other operations?

Answer 19

NAND and NOR

Question 20

How do you make a NOT get from a NAND gate?

Answer 20

Split the input of the NAND gate into 2

Question 21

How do you make an OR from a NAND?

Answer 21

Connect 2 NOT gates (made from NANDs) to a NAND gate

- Represented in De Morgan’s Theorem

Question 22

What is De Morgan’s theorem?

Answer 22

A\ . B\ = (A+B)\

Question 23

How many inputs can OR and AND gates have?

Answer 23

Any number of inputs

Question 24

How many inputs can XOR and XNOR gates have?

Answer 24

2 inputs

Question 25

How many inputs can NOT gates have?

Answer 25

1 input

Question 26

What is the commutative law?

Answer 26

• Order of the variables makes no difference

- AB = BA

Question 27

What is the associative law?

Answer 27

• Grouping of variables makes no difference
• A + (B + C) = ( A + B) + C = A + B + C
• A(BC) = (AB)C = ABC

Question 28

What is the distributive law?

Answer 28

• The operator outside the bracket operates on all variables inside the bracket
• A(B + C) = AB + AC
• A + (BC) = (A+B)(A+C)

Question 29

Solve A + 0

Answer 29

A

Question 30

Solve A + 1

Answer 30

1

Question 31

Solve A.0

Answer 31

0

Question 32

Solve A.1

Answer 32

A

Question 33

Solve A + A

Answer 33

A

Question 34

Solve A + A\

Answer 34

A

Question 35

Solve A.A

Answer 35

A

Question 36

Solve A.A\

Answer 36

0

Question 37

Solve A\

Answer 37

A

Question 38

Solve A + AB

Answer 38

A

Question 39

Solve A = A\B

Answer 39

A+B

Question 40

What is the SOP form?

Answer 40

• Sum of Products form
• When two or more product terms are summed by Boolean addition
• eg. ABC + CDE + B\CD\
• Can be directly translated into gates but may not be the most efficient design

Question 41

What is canonical form?

Answer 41

• Standard SOP Form
• All the variables in the domain appear in each product term in the expression
• eg. f(A,B,C,D) = ABC\D + AB\CD + AB\CD\
• each product term s known as a minterm
• not efficient but useful in analysis and design

Question 42

How do you convert SOP to Canonical SOP?

Answer 42

• Multiply by (X + X) where X is the missing variable

Question 43

What is an SOP equal to if any of the product terms is equal to 1?

Answer 43

1

Question 44

What does f = SIGMA(3,6,7) mean?

Answer 44

The sum of the row numbers having TRUE minterms

Question 45

Why would you want to simplify things?

Answer 45

• To minimize the cost of implementation (minimize the number of operations needed/number of gates)
• Increases the speed of operation

Question 46

How can you minimize by Boolean Algebra?

Answer 46

• Grouping (adsorption rules)
• Multiplication by redundant variables (eg. (A+A)
• De Morgan’s theorem