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Chapter 41 - Simplifying Boolean expressions

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Total cards: 23•Content version: v4•Public deck•Updated: 8/1/2026

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#1
Front (Question)

What is the purpose of De Morgan’s laws?

Back (Answer)

» Can manipulate and simplify Boolean expressions

#2
Front (Question)

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

Back (Answer)

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

#3
Front (Question)

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

Back (Answer)

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

#4
Front (Question)

What is De Morgan’s First Law?

Back (Answer)

» States that ¬(A v B) = ¬A ∧ ¬B

#5
Front (Question)

What is De Morgan’s Second Law?

Back (Answer)

» ¬( A ∧ B ) = ¬A v ¬B

#6
Front (Question)

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

Back (Answer)

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

#7
Front (Question)

What does X and 0 equal to?

Back (Answer)

» 0

#8
Front (Question)

What does X and 1 equal to?

Back (Answer)

» X

#9
Front (Question)

What does X and X equal to?

Back (Answer)

» X

#10
Front (Question)

What does X and NOT X equal to?

Back (Answer)

» 0

#11
Front (Question)

What does X or 0 equal to?

Back (Answer)

» X

#12
Front (Question)

What does X or 1 equal to?

Back (Answer)

» 1

#13
Front (Question)

What does X or X equal to?

Back (Answer)

» X

#14
Front (Question)

What does X or NOT X equal to?

Back (Answer)

» 1

#15
Front (Question)

What are the 2 Commutative rules?

Back (Answer)

» x AND y = y AND x x OR y = y OR x

#16
Front (Question)

What is the purpose of a Truth table?

Back (Answer)

» Shows every possible input and output combination

#17
Front (Question)

What does the commutative rule state?

Back (Answer)

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

#18
Front (Question)

What does the Associative law state?

Back (Answer)

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

#19
Front (Question)

What are the associative rules?

Back (Answer)

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

#20
Front (Question)

What does The distributive law state?

Back (Answer)

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

#21
Front (Question)

What are the Distributive Laws?

Back (Answer)

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

#22
Front (Question)

What does the absorption rule state?

Back (Answer)

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

#23
Front (Question)

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

Back (Answer)

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