Lectures 8 & 9

Question 1

What is another name for the And gate?

Answer 1

Conjunction

Question 2

What is another name for the Or gate?

Answer 2

Disjunction

Question 3

What is another name for the Not gate?

Answer 3

Negation

Question 4

What is a representation of an And gate in Boolean algebra?

Answer 4

A semicircle with ends on the bottom (Like a smooth n)

Question 5

What is a representation of an Or gate in Boolean algebra?

Answer 5

A semicircle with ends at the top (Like a smooth u)

Question 6

What is the definition for Equivalence?

Answer 6

If both arguments passed are the same, then the result is true

Question 7

What is the definition for Implication?

Answer 7

If the value for the second variable is possible given the value of the first variable then the result is true

Question 8

What is the Boolean logic commutativity law?

Answer 8

x or y = y or x

All operators

Question 9

What is the Boolean logic associativity law?

Answer 9

(x and y) and z = x and (y and z)

All operators

Question 10

What is the Boolean logic distributivity law?

Answer 10

x or ( y and z) = (x or y) and (x or z)
x and ( y or z) = (x and y) or (x and z)

Question 11

What is De Morgan’s law?

Answer 11

Split and switch

Question 12

What is the Boolean logic elimination of implication law?

Answer 12

x → y = (Not x) or y

Question 13

What is the Boolean logic elimination of equivalence law?

Answer 13

x ↔ y = ( x → y) and ( y → x)

Question 14

How can we simplify how we represent functions

Answer 14

If we agree on the row order, then a value vector can be used

Question 15

What is a minterm?

Answer 15

A conjunction of all n variables (either negated or not) is called the minterm for these n variables. It will only ever return true with a specific combination

Question 16

What are the steps to generate a function from a truth table?

Answer 16

1. We need to see which combinations of the variables gives a true result.
2. For these, we need to find the minterm that gives a true result. For example, if 1 0 1 gives true, the minterm would be x(Not y)z
3. Combine these minterms using Boolean Or.

Question 17

What are the steps to generate a truth table from a function?

Answer 17

1. Write out all combinations of the variables.
2. Work out the values of computing the first sub expression with the relevant variables.
3. Repeat step 2 for all sub expressions
4. Compute the result of any combinations of sub expressions and others/ variables.
5. The final column is the value vector for the function.