NAND Gate

The NAND gate is an AND gate followed by a NOT gate — it outputs the inverse of AND. NAND is called a "universal gate" because any other logic gate can be built using only NAND gates. This makes it incredibly important in digital circuit design.

Objectives

• Understand NAND as inverted AND
• Build NOT, AND, and OR from NAND gates
• Understand why NAND is efficient in CMOS
• Recognize the NAND gate symbol and notation
• Build memory elements (SR latch) from NANDs

Key Takeaways

• NAND = NOT AND = inverted AND gate
• Output is LOW only when ALL inputs are HIGH
• UNIVERSAL GATE: Any logic function can be built using only NANDs
• Most efficient gate in CMOS technology (4 transistors)
• Common IC: 74HC00 (four 2-input NAND gates)
• Used for SR latches, and as universal building block
• NAND is NOT associative — be careful when cascading!

Applications

• SR Latch: Two cross-coupled NANDs form basic memory cell
• CMOS Logic: NAND is the most efficient gate in CMOS (4 transistors)
• Universal Building Block: Complex circuits designed entirely with NANDs
• Enable with Inversion: Gating with inverted output

Practice Problems

Problem 1: What is 1 NAND 1?

Problem 2: What is 1 NAND 0?

Problem 3: How do you make NOT using a NAND?

Problem 4: How many NANDs needed to build an AND?