Question

A NAND circuit with positive logic will operate as :

• A. NOR with negative logic
• B. AND with negative logic
• C. OR with negative logic input
• D. NOT with negative logic output

Hint:

In digital electronics, remember these important equivalences: \[ \text{NAND in positive logic} \equiv \text{AND in negative logic} \] \[ \text{NOR in positive logic} \equiv \text{OR in negative logic} \] These relationships are based on De Morgan’s theorem and logic duality principles.

Answer 1

The Correct Option is B

Digital circuits can operate under different logic conventions:

• Positive Logic: Higher voltage = logic 1, lower voltage = logic 0
• Negative Logic: Higher voltage = logic 0, lower voltage = logic 1

De Morgan’s theorem:

• ̅A·B = ̅A + ̅B
• ̅(A + B) = ̅A · ̅B

Because of duality, gates under positive logic can behave differently under negative logic.

Step	Explanation
1. NAND gate (Positive Logic)	Y = ̅(A·B); output LOW only if both inputs HIGH. Truth table: 00→1, 01→1, 10→1, 11→0
2. Negative Logic Interpretation	HIGH voltage → logic 0, LOW voltage → logic 1; NAND behaves like AND
3. Verification (Duality)	NAND under positive logic ≡ AND under negative logic
4. Analyzing Options	Correct equivalence: AND with negative logic
Final Answer	(2) AND with negative logic