Which of the below given statement(s) is/are false about NAND Gate?
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Which of the below given statement(s) is/are false about NAND Gate?
I) NAND gate is combination of AND gate and NOT gate
II) NAND gate is the inverse of basic AND gate
III) The output of the NAND gate is equal to the complement of the output of the AND gate.
IV) We can't design any basic logic gate by using NAND gate
Show answer & explanation
Statements I, II, and III are all true descriptions of a NAND gate—it is indeed a combination of AND and NOT gates, it is the inverse/complement of an AND gate, and its output equals the complement of the AND output. Statement IV is false because NAND is a universal gate; any basic logic gate (AND, OR, NOT) can be designed using only NAND gates. Therefore, only statement IV is false.
Step-by-step Derivation:
Analysis of each statement:
Statement I: TRUE - NAND gate = AND gate + NOT gate. The NAND operation is: Y = NOT(A AND B) = (A·B)'
Statement II: TRUE - NAND is the inverse/complement of AND. If AND(A,B) = X, then NAND(A,B) = X' (the complement).
Statement III: TRUE - This is equivalent to Statement II. NAND output = complement of AND output. Output of AND = A·B; Output of NAND = (A·B)'
Statement IV: FALSE - NAND is a universal gate. We can construct:
- NOT gate: Y = A' using NAND(A, A)
- AND gate: Y = A·B using NAND(NAND(A,B), NAND(A,B))
- OR gate: Y = A + B using NAND(NAND(A,A), NAND(B,B))
Since three statements are true and only one (IV) is false, the answer is C) Only (IV).