Question

How does a NAND gate work?

Answer 1

A NAND gate (NOT-AND gate) is a fundamental digital logic gate with two or more inputs and one output. It performs the logical NAND operation, which is the negation of the AND operation. In simple terms, a NAND gate produces a LOW (logic 0) output only when all of its inputs are HIGH (logic 1). Otherwise, it produces a HIGH (logic 1) output.

Here's the truth table for a two-input NAND gate:

Input A    Input B    Output
0    0    1
0    1    1
1    0    1
1    1    0

The symbol for a NAND gate looks like this:

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Copy code
      __
A ----|  |
      NAND
B ----|__|
      Y


The logical expression for a two-input NAND gate is:

Output Y = NOT (A AND B)

To understand how it works, let's break it down based on the truth table:

When both inputs A and B are 0, the AND operation (A AND B) yields 0. Then, the NOT operation negates this result, producing a 1 at the output.

When either input A or B is 0 (but not both), the AND operation (A AND B) still yields 0. The NOT operation negates this result, producing a 1 at the output.

When both inputs A and B are 1, the AND operation (A AND B) yields 1. Then, the NOT operation negates this result, producing a 0 at the output.

So, a NAND gate behaves like an AND gate followed by a NOT gate, effectively inverting the AND gate's output. It is an essential building block in digital circuits and is used to construct various complex logical functions and arithmetic operations. In fact, all other logic gates can be constructed using just NAND gates, which is why they are considered universal gates.