Q.Sketch the output Y from NAND gate having input A and B given below–
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The NAND Gate: The "Not-AND" That Builds Everything
Imagine you have two switches in series, controlling a bulb. The bulb lights up only when both switches are on. That's an AND gate — output 1 only when all inputs are 1.
Now imagine you take that bulb and invert its behaviour: the bulb is on except when both switches are on. That's the NAND gate. The name itself tells you: Not-AND.
NAND is the most fundamental gate in digital electronics. With enough NAND gates, you can build any other gate — AND, OR, NOT, XOR — and therefore any digital circuit. It's called a universal gate.
The Precise Definition
A NAND gate has two or more inputs and one output. The output is:
- 0 (LOW) only when all inputs are 1 (HIGH)
- 1 (HIGH) for every other combination of inputs
In other words: it's the exact opposite of an AND gate.
Truth Table (2-input NAND)
| Input A | Input B | Output (A NAND B) |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Notice the pattern: three rows give output 1, only one row gives output 0. That single 0 happens when both inputs are 1.
The Boolean Expression
If AND is written as , then NAND is its negation:
You read this as "Y equals NOT (A AND B)". The bar over the whole expression means the negation applies to the AND result, not to individual inputs.
A common mistake is to write for NAND. That's wrong — that expression is actually a NOR gate. NAND is , not . The bar covers the entire AND operation.
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