Lecture 4 - DeMorgan's Law Flashcards
What is DeMorgan’s Law?
Theorem relating ANDs and ORs
What is the first DeMorgan’s Law?
OR gate with inverted inputs = AND gate with inverted output
What is the second DeMorgan’s Law?
AND gate with inverted inputs is = OR gate with inverted output
What is the third DeMorgan’s Law?
Inverting inputs and outputs of an OR gate = AND gate
What the fourth DeMorgan’s Law?
Inverting inputs and outputs of and AND gate = OR gate
How can DeMorgan’s Law’s logic be implemented in real circuits?
They can be implemented through the use of Complementary-symmetry Metal-Oxide-Semiconductor (CMOS) transistors
How can DeMorgan’s be applied during design?
Typically, inversion gates are the ones used, but since they can be confusing to understand, instead, the more easily applicable AND/OR gates are used then DeMorgan’s is employed to convert them into implementable gates (NAND/NOR/NOT)
What should be noted when wanting to convert a circuit to exclude any inversion circles?
One output circle cancels all the input circles it feeds
How can a circuit be converted to only include AND and OR gates?
First start by converting the output-most to their DeMorgan equivalent and check for cancelling circles
What are the steps to applying DeMorgan’s Law (in the general form) to find the equivalent of an expression?
1) Take a boolean expression as your input
2) Bracket all groups of ANDs
3) Take the dual of the expression (clean up bracketed terms once done)
4) Invert all variables
What are some common mistakes to avoid in regards to solving DeMorgan’s Laws problems?
1) Not bracketing all AND terms before swapping the AND and OR signs
2) Not using the less error prone graph method, instead of the algebraic method (not always possible)
3) Equating the following three: F, F(dual), F(bar)
