Chapter 41 - Simplifying Boolean expressions Flashcards
What is the purpose of De Morgan’s laws?
» Can manipulate and simplify Boolean expressions
» Why are De Morgan’s laws beneficial to manufacturing?
» Any Boolean function can be converted to which uses only NAND or only NOR functions
Why is it beneficial for any integrated circuit to be built just from one type of logic gate?
» Costs can be kept down by using only one type of gate
What is De Morgan’s First Law?
» States that ¬(A v B) = ¬A ∧ ¬B
What is De Morgan’s Second Law?
» ¬( A ∧ B ) = ¬A v ¬B
What are the three steps to implement each of de Morgan’s Law?
» Complement both terms in the expression
» Change AND to OR and OR to AND
» Complement the results
What does X and 0 equal to?
» 0
What does X and 1 equal to?
» X
What does X and X equal to?
» X
What does X and NOT X equal to?
» 0
What does X or 0 equal to?
» X
What does X or 1 equal to?
» 1
What does X or X equal to?
» X
What does X or NOT X equal to?
» 1
What are the 2 Commutative rules?
» x AND y = y AND x
x OR y = y OR x
What is the purpose of a Truth table?
» Shows every possible input and output combination
What does the commutative rule state?
» That any value in AND or OR expressions can be swapped without changing the results
What does the Associative law state?
» Confirms that the order of operators in an expression has no impact on the results
What are the associative rules?
» x and ( y and z ) = ( x and y) and z
» x or (y or z) = (x or y) or z
What does The distributive law state?
» A value outside of a set of brackets can be distributed between the values within the brackets
What are the Distributive Laws?
» X.(Y+Z)=(X.Y)+(X.Z)
» X+(Y.Z)=(X+Y).(X+Z)
What does the absorption rule state?
» A value outside the bracket can cancel out a value inside the bracket
What are the 2 rules in order for absorption to happen?
» The value outside the brackets must be present within the brackets
» The operators inside and outside the brackets must be different
