Question

Which of the following statements are not true?

• A. When a Boolean variable is multiplied by its complement, the result is the variable.
• B. A VHDL program consists of an entity and an architecture.
• C. Multiplication in Boolean algebra is equivalent to the NAND function.
• D. The complement of a product of variables is equal to the sum of the complements of each variable.

Hint:

Recall fundamental Boolean operations and their correspondence to logic gates to evaluate such statements.

Answer 1

The Correct Option is A

Statement (A) is false, as \(A \cdot A = 0\), not \(A\). Statement (B) is true; VHDL programs comprise an entity and an architecture. Statement (C) is false because Boolean multiplication corresponds to the AND operation, not NAND. Statement (D) is true, since De Morgan’s theorem indicates the complement of a product is the sum of complements. Therefore, statements (A), (C), and (D) are incorrect.