Unit 4 - Propositional Logic, Boolean Algabra and circuit design

Question 1

What is a statement in logic?

Answer 1

A phrase that says something is or is not. It is always true or false and can be objectively evaluated.

“It is more than 26 degrees celcius”

Question 2

What is a proposition in logic?

Answer 2

A proposition is the idea behind a statement.

If the statement is ‘It is more than 27 degrees celcius’ then the proposition is that the temperature is currently hotter than 26 degrees outside.

Question 3

What is the Not operator?

Answer 3

Indicates negation.

“It is Not more than 27 degrees celcius”

Question 4

What is the And operator?

Answer 4

It is a combined proposition connecting two ideas. The statement contains two propositions and both must be true.

“It is colder than yesterday and it is raining”

Question 5

What is the Or operator?

Answer 5

Similar to And, except only one proposition has to be true.

Question 6

What is propositional logic?

Answer 6

Using propositions that can be true or false, and combining them via logical connectives. These sentences are translated into symbols.

Also known as sentential logic.

Question 7

What is a negation and what is its symbol?

Answer 7

Saying something is not true. You use the negation symbol (Alt 170):

¬

Question 8

What is a conjunction and what is its symbol?

Answer 8

And is a conjunction in propositional logic. Symbol is an upwards arrow (Alt 24). (though really more of a ^)

↑

Question 9

What is a disjunction in propositional logic and what is its symbol?

Answer 9

The ‘Or’ operator. It is a downwards arrow (alt 25) (though really more of a V)

↓

Question 10

What is an implication?

Answer 10

It means if one proposition is true, then the other is also true. Written as: if…then. “If it is raining outside, then I should bring my umbrella).

Written as a right arrow (Alt 26)

→

Question 11

What is the difference between imply and infer?

Answer 11

Imply is something that information does. It’s the sender.

Infer is receiving that information and understanding it.

“He inferred the implication”

Question 12

What is a truth table in propositional logic?

Answer 12

A structured way to display false and true values of propositions.

T = true, F = false.

Question 13

What does a conjunctive truth table look like?

Answer 13

T, F, F, F

Question 14

What is an exclusive disjunction?

Answer 14

If both propositions are true, the outcome becomes false.

Question 15

What does the disjunctive truth table look like?

Answer 15

T, T, T, F

Question 16

What does an implication truth table look like?

Answer 16

T, F, T, T

Question 17

What is a literal?

Answer 17

Any element that can be evaluated as true or false. Also called a boolean system.

Question 18

What is the conjunctive normal form?

Answer 18

A single conjunction (just one AND) but both parts are made up of multiple propositions (disjunctions). The example below has four literals.

( P v ¬q) ^ (r v s)

Question 19

What is the disjunctive normal form?

Answer 19

A single disjunction (one OR) but both parts are made up of multiple propositions (e.g. conjunctives)

In this example the conjunctives are evaluated first, the disjunction later.

(p ^q) v (¬r ^ ¬s)

Question 20

What is the satisfiability?

Answer 20

That at least one outcome is true in your logic formula.

An example of an unsatisfiable formula that can never be true:

p ^ ¬p

Question 21

What is a logic circuit?

Answer 21

It accepts different inputs (1 and 0) and returns a value at the end.

Question 22

What are the operators in a digital circuit known as?

Answer 22

Logic gates.

Question 23

What is NAND?

Answer 23

The opposite of AND

Question 24

What is NOR?

Answer 24

The opposite of OR (a.k.a Neither). If neither input is 1, then the output is 1

Question 25

What is XNOR?

Answer 25

Exclusive NOR, it is only true if both values are the same. (If both values are 0 or both are 1, then the output will be 1)

Question 26

What is XOR?

Answer 26

Exclusive OR. If either value is true then true, but if both values are true then it is false.

Question 27

Show me logic gates binary truth tables

Answer 27

Here!

Question 28

Which logic gates symbols are used?

Answer 28

The U.S. version seems to be used most, even though there is also an international version (and a German one)