Chapter 41 - Simplifying Boolean expressions

Question 1

What is the purpose of De Morgan’s laws?

Answer 1

» Can manipulate and simplify Boolean expressions

Question 2

» Why are De Morgan’s laws beneficial to manufacturing?

Answer 2

» Any Boolean function can be converted to which uses only NAND or only NOR functions

Question 3

Why is it beneficial for any integrated circuit to be built just from one type of logic gate?

Answer 3

» Costs can be kept down by using only one type of gate

Question 4

What is De Morgan’s First Law?

Answer 4

» States that ¬(A v B) = ¬A ∧ ¬B

Question 5

What is De Morgan’s Second Law?

Answer 5

» ¬( A ∧ B ) = ¬A v ¬B

Question 6

What are the three steps to implement each of de Morgan’s Law?

Answer 6

» Complement both terms in the expression
» Change AND to OR and OR to AND
» Complement the results

Question 7

What does X and 0 equal to?

Answer 7

» 0

Question 8

What does X and 1 equal to?

Answer 8

» X

Question 9

What does X and X equal to?

Answer 9

» X

Question 10

What does X and NOT X equal to?

Answer 10

» 0

Question 11

What does X or 0 equal to?

Answer 11

» X

Question 12

What does X or 1 equal to?

Answer 12

» 1

Question 13

What does X or X equal to?

Answer 13

» X

Question 14

What does X or NOT X equal to?

Answer 14

» 1

Question 15

What are the 2 Commutative rules?

Answer 15

» x AND y = y AND x
x OR y = y OR x

Question 16

What is the purpose of a Truth table?

Answer 16

» Shows every possible input and output combination

Question 17

What does the commutative rule state?

Answer 17

» That any value in AND or OR expressions can be swapped without changing the results

Question 18

What does the Associative law state?

Answer 18

» Confirms that the order of operators in an expression has no impact on the results

Question 19

What are the associative rules?

Answer 19

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

Question 20

What does The distributive law state?

Answer 20

» A value outside of a set of brackets can be distributed between the values within the brackets

Question 21

What are the Distributive Laws?

Answer 21

» X.(Y+Z)=(X.Y)+(X.Z)
» X+(Y.Z)=(X+Y).(X+Z)

Question 22

What does the absorption rule state?

Answer 22

» A value outside the bracket can cancel out a value inside the bracket

Question 23

What are the 2 rules in order for absorption to happen?

Answer 23

» The value outside the brackets must be present within the brackets
» The operators inside and outside the brackets must be different