Questions: Boolean Algebra and Fundamental Laws

Question 1

Applying De Morgan's law to NOT(A AND B) gives which of the following?

• A. NOT A AND NOT B
• B. NOT A OR NOT B
• C. A OR B
• D. NOT A AND B

Answer: (B)

De Morgan's law states: NOT(A AND B) = NOT A OR NOT B. The negation distributes over each operand AND the operator flips from AND to OR. A common error is to distribute the NOT without flipping the operator, yielding the wrong answer NOT A AND NOT B.

Question 2

NOT(A OR B) simplifies to NOT A OR NOT B by applying De Morgan's law.

• T. True
• F. False

Answer: False

De Morgan's second law states NOT(A OR B) = NOT A AND NOT B — the operator flips from OR to AND when the negation is distributed. NOT A OR NOT B is actually equivalent to NOT(A AND B), the other form of De Morgan's law. Confusing which operator flips is the most common De Morgan's error.

Question 3

Why is Boolean algebra's distributive law important for circuit minimization?

Model answer: The distributive law lets you factor common terms (AB + AC = A(B+C)), reducing the number of distinct gate inputs and often eliminating gates entirely. Without it, you could only apply simpler laws like identity and complement, which don't reduce gate counts as effectively.

Circuit minimization aims to implement a logic function with the fewest gates (and hence fewest transistors, less power, less area). Algebraic laws let designers transform an expression into an equivalent but simpler form. The distributive law is especially powerful because it can collapse two product terms sharing a factor into one, directly reducing a gate.