It is possible to express every Boolean expression using:
2015
It is possible to express every Boolean expression using:
Answer: D. NAND alone — To express every Boolean expression, we need a set of logical gates that is functionally complete. A functionally complete set can represent all possible…
- A.
AND alone
- B.
OR alone
- C.
NOT alone
- D.
NAND alone
- E.
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Correct answer: D
To express every Boolean expression, we need a set of logical gates that is functionally complete. A functionally complete set can represent all possible Boolean functions. Let's evaluate each option: AND alone: Cannot produce NOT, so it is not functionally complete. OR alone: Cannot produce NOT, so it is not functionally complete. NOT alone: Cannot produce AND or OR, so it is not functionally complete. NAND alone: NAND is functionally complete because it can be used to construct NOT, AND, and OR operations. For example, NOT A = NAND(A, A), and A AND B = NOT(NAND(A, B)). Therefore, NAND alone is sufficient to express every Boolean expression.