The Boolean expression for NOR gate is:

A. NOT (A AND B) = Y

B. A OR B = Y

C. A AND B = Y

D. NOT (A OR B) = Y

The Boolean expression for a NOR gate is best described by option D: NOT (A OR B) = Y. To understand why this is the correct choice, let’s break down what a NOR gate does and how it operates in terms of Boolean logic.

Understanding the NOR Gate

A NOR gate is a digital logic gate that outputs true or high (1) only when both of its inputs are false or low (0). In simpler terms, it produces a low output when at least one of its inputs is high. This behavior can be summarized with the following truth table:

A	B	Y (Output)
0	0	1
0	1	0
1	0	0
1	1	0

Breaking Down the Expression

The expression for the NOR gate can be derived from the basic operations of AND, OR, and NOT. The expression "A OR B" evaluates to true if either A or B is true. The NOR gate negates this result, which is represented as:

• First, evaluate A OR B.
• Then, apply the NOT operation to the result.

This leads us to the expression: NOT (A OR B) = Y. This means that Y will only be true (1) when both A and B are false (0).

Comparing with Other Options

Let’s briefly look at the other options to clarify why they do not represent a NOR gate:

• A. NOT (A AND B) = Y: This expression describes a NAND gate, which outputs true unless both inputs are true.
• B. A OR B = Y: This is simply the OR operation, which outputs true if at least one input is true.
• C. A AND B = Y: This represents an AND gate, which outputs true only when both inputs are true.

Each of these expressions corresponds to different types of gates, highlighting the unique functionality of the NOR gate.

Real-World Analogy

Think of the NOR gate like a light switch that only turns on when no one is in the room. If even one person enters (representing a high input), the light stays off. It’s only when the room is completely empty (both inputs are low) that the light turns on. This analogy helps visualize how the NOR gate operates in a practical sense.

In summary, the correct Boolean expression for a NOR gate is indeed NOT (A OR B) = Y, as it accurately reflects the gate's behavior in digital logic. Understanding these fundamental concepts is crucial for working with digital circuits and logic design.